1. PharmAm Pharmaceuticals (PAP)
introduces a new, patented antiviral pill to the market. The new pill is
the result of five years of research and development that cost the company
a total of $100,000,000 most of which was raised through selling bonds.
As a result the annual fixed capital cost of the pill (at 10% interest
rate) is $10,000,000 plus $10,000,000 for the amortization of the principal.
The company has estimated the total
production cost function of
its new drug as follows.
TC = 20,000,000 + .01 Q
The worldwide demand for this antiviral firm has also been estimated:
Q = 500, 000,000 – 100, 000, 000 P
Given its patent right, as the
sole producer of this pill, PAP has a very secure monopolistic position
in the market for this pill.
a. Determine the MC, AVC, and
ATC of the pill.
b. Try to draw these three cost
measures. (Your scales do not have to be precise. Just demonstrate the
general shapes of these measures relative to each other.)
c. Plot the demand function
in the same space as well.
d. Determine the price PAP could
charge for its pill as a monopoly.
e. Determine the quantity of
pills it could sell at the monopolistic price.
f. Determine the monopolistic
profit of the company.
Now suppose the company’s patent on this drug has expired. As a result a generic version of the pill is produced and introduces to the market. PAP loses some of its customers to the competing generic drug company. The demand PAP is facing now is:
Q = 400,000,000 – 133,333,333.33 P
The generic drug company’s demand is:
Q’ = 100, 000,000 – 50,000,000 P’
Because the generic drug company has not had any research costs, its fixed cost is much lower than that of PAP, but its marginal cost is the same. The cost function of the generic company for this drug is:
TC’ = 1,000,000 + .01Q’
g. Determine the output of PAP
after the patent expiration.
h. Determine the price PAP could
charge for its (brand-name) pill after the patent expiration.
i. Determine the profit of PAP
after the expiration of the patent.
j. Determine the price the generic
drug company charges for its generic pill.
k. How many pills would the
generic drug company sell?
2. Snow White Corporation (SWC) is a producer of detergents and other cleaning agents. SWC introduces a new liquid detergent that contains both a softening agent and a whitening agent. As the sole producer of this kind of detergent SWC has monopolistic power in the market for this product and it faces a market demand as follows:
Q = 100 – 10 P
where Q is the weekly quantity
(in 1000 of gallons) sold and P is the unit price. The company's cost function
has been estimated as follows:
TC = 20 + 2Q + .05 Q ^{2}
a. Determine the profit-maximizing
price of the product for SWC.
b. Show your work on a carefully
drawn diagram.
c. Determine the profit of the
company.
d. If the company were to produce
as perfectly competitive firm, how much would it produce?
e. What price should it charge
as a competitive firm?
f. Would it still make a profit
if it behaved like a competitive firm?
g. As a result of the success
of this product other firms start producing similar detergents and selling
them at lower prices. As SWC’s customers gradually switch to other brands,
SWC’s demand curve gradually shifts to the left, while it slope remains
the same. (Parallel shits to the left) Eventually SWC’s (economic) profit
on this product disappears; its profit becomes zero. Determine the revenue
of the SWC from this product at this zero profit level of output.
h. Show your work on a diagram.
i. (Bonus points) Write the
equation for this new (zero profit) demand curve.
3. The new Ford's compact car, Focus, has been relatively successful. Other car makers have come up similar models. Ford's marketing department has concluded that the demand the company faces for this car is a kinked demand curve represented by the following two equations:
Q = 4000 -.2
P
Q’ = 8000 -.5 P
a. Carefully plot this kinked
demand curve.
b. Determine the price and the
number of cars Ford sells.
c. Assuming the cost function
TC = 2000,000 + 8000 Q, determine Ford's profit on this product.
d. Suppose as a result of a
combination of higher energy prices and a new labor contract the marginal
cost of production for this model has increased by $2000. Should Ford increase
its price? Explain.
e. Show your answer to (d) on
your diagram.
f. Will Ford still be making
a profit on this car after the cost increase? Explain.
Practice Problems
1. Auto Maintenance Services (AMS)
is a small auto service outlet in a suburban area of Syracuse. In reaction
to a small increase in wages that has caused the marginal cost of this
auto service establishment to increase from $25 to $30, the owner is considering
raising the prices of the services AMS offers. The owner's daughter, who
is studying economics and, at the time, takes care of her father's books
and finances advises him against that. She has estimated that if AMS raises
its prices it will face
the weekly demand curve Q = 140
- 2.5 P, whereas if it lowers its price it will face the demand curve Q'=
55-.625P. (10 points)
a. Determine the (average) price
AMS is charging for its services, presently.
b. Determine the number of cars
it services each week.
c. Assuming that the owner's daughter
is correct, what is the MC range within which AMS should not change its
price?
d. AMS's weekly total fixed cost
is $250. Assuming that the firm's marginal cost and average variable cost
are equal (AVC =MC), determine its weekly profit after the wage increase.
e. What should AMS do if its MC
goes up to $40? Explain.
2. The market for color copy machine
is dominated by a large firm with significant production capacity. The
market demand for color copy machines is
QM = 2000 - 4 P.
The dominant firm has projected
the supply by the small firms in the market to be:
Qs = -700 + 2 P
I. Write the demand curve faced
by the dominant firm.
II. What price should the leader
charge to drive all the small firms out of the market?
III. Write the marginal revenue
function of the dominant firm.
IV. Assuming the leader's cost
function is TC = 2000 + 300 Q + 1/84 Q^2, determine the following:
a. The price
b. The total quantity demanded
(purchased)
c. The leader's share of the market
d. The small firms' share of the
market
e. The leader's profit
---------------------------------------
1. With two full-time mechanics,
Jack's service station repairs/services 20 cars per week. Each worker is
paid $400 per week. By hiring another mechanic, at the same salary, he
can increase his weekly output to 24 cars. A fourth mechanic would increase
his output to 26. Calculate Jack's total variable cost (TVC), marginal
cost (MC), and average variable cost (AVC) at these three levels of output.
If, on average, Jack receives $100 for each repair job, how many mechanics
should he hire? Explain. Suppose the weekly "fixed" of Jack's auto repair
operation is $1000. Is he making any profits from his auto repair business?
2. What is the significance of the crossing point of the short-run ATC and MC? How does this point relate to the average product of the variable input?
3.Your friend plans to open up a small bagel shop. She has her eyes on a shop in a shopping strip near the college. The shop can be rented for $800 per month. She has estimated that the fixed part of her monthly utility bill would be $200. In addition, she expects to pay another $200 each month for insurance and maintenance costs. Each dozen of bagels takes $1.75 worth of ingredients and $.10 worth of electricity to produce. Each dozen of bagels also needs $.15 worth of bags or other packaging materials.
She can lease all the equipment that she needs for $400 per month. She also needs $10,000 for up-fitting the shop and a small amount of inventory. Her bank has agreed to give her a loan in that amount and let her pay only the interest, $100 per month, for five years. At the end of the five years she would have the option of renewing the loan or paying it off.
Your friend plans to quit her present job and, with the help of a full-time employee, run her bagel shop herself. Her monthly salary form her present job is $1,500. She expects to pay her full-time employee $1000 per month.
a. Identify all the fixed and variable costs of the operation.
b. Write the total cost function
of your friend’s bagel shop.
(Hint: It is a linear function.)
c. Assuming the market price of bagel is $5 per dozen, how many dozens of bagels would she have to sell (per month) to break even?
d. How many dozens would she have to sell to have $1,000 profit each month?
e. Suppose in the second year of
her operation, the monthly lease for the shop is expected to go up to $1,200.
Assuming no other changes, how will that affect her break-even quantity
and the profitability of her business?
4. The following is the estimated
short-run cost functions of a firm.
TC = 750 + 50 Q + .5 Q ^2
MC = 50 + Q
The firm is faced with the following demand:
Qd = 600 - 5 P
a. Determine the profit maximizing
level of the output for this firm.
b. What price should the firm charge
to maximize its profit?
c. What is the firm's profit at
the profit-maximizing output?
d. What is its average variable
cost at this level of output?
e. What price should it charge
if it were to maximize it revenue?
f. At what level of output is the
firm's average total cost minimized?
------------------------------------------
Production/Cost Exercises
Do the following two problems.
1. The following is a short-run production table for a firm with labor
as its only variable input.
Wage = $125
Capital Quantity = 50
Capital Price= $20
Product Price= $12.50
Labor
Output
0
0
1
45
2
100
3
150
4
190
5
220
6
240
7
250
8
255
9
255
10
250
a. Determine the following measures at all levels of output:
MPL, APL, TFC, TVC, TC, TR, MR, MC, PROFIT
b. At what level of output is the profit maximized?
c. What kind of observations can you make about MC, the product price,
MRPL , and wage?
Note: The following problem is a little more challenging. Do the best you can. We'll go over it in class.
2. Medfin Accounting Company (MAC) specializes in providing accounting and tax services for medical firms and professionals. Presently, the company's production method is highly labor-intensive because many of the bookkeeping tasks are done manually. MAC employs 25 workers (L) paying them each, on average, $25,000 per year. MAC also has 20 computers (K). The company has leased these computers along with their accompanying software packages at $2,400 per year each. Presently the firm provides accounting and tax services to 100 clients.
a. Write the equation for the company's isocost.
b. At this given mix of inputs ( K = 20, L= 25) the firm's marginal rate of technical substitution (MPL/MPK) is -5. Is this mix of capital and labor that MAC is using efficient (optimal)? Explain as specifically as you can.
c. If your answer to (b) is no, what changes should the firm make in its production style?
d. Assuming that the firm wants to serve the same number of clients, how would the changes that you might be suggesting would affect the company's profit?
e. Now starting back from the original mix of computers (capital) and labor -- that is 25 workers and 20 computers -- suppose the company wants to increase the size of its clientele. How do you suggest the company should pursue its expansion plan? What is the most efficient approach to this expansion? Should the company hire more labor and acquire more computers right away?
----------------------------------------------------------
Do the following two problems.
1. ABC Shoes, Inc. faces the
following (daily)demand function:
Qd = .1 Income + .5 Ad + .4 Weather - .2 P
where: Income = 100, Ad(vertisement) = 40, Weather = 60
a.
Carefully draw (plot) the daily demand curve for this firm.
b.
How many pairs of shoes can the company sell at the price of $120 ?
c.
What is the price elasticity of demand at this price level? (Hint: If you
want to calculate the
arc elasticity assume a price increase of $5, but the point elasticity
is preferred)
d.
Write the firm's total revenue function, and show it on a diagram. Hint:
TR = P.Q
e.
Can you determine the quantity of shoes (sold) at which the company’s daily
total
revenue is maximized?
f.
Determine the income elasticity of demand at income = 100, while keeping
the values
for "Ad" and weather the same.
g.
Now suppose income has increased to $200 (per day). Keeping the other variables
the same, recalculate the price elasticity of demand.
2. Three Peaks Ski resort has estimated the following demand curve for their lift tickets.
Q
= 7000 - 160 P + 40 A
where
Q = weekly number of lift tickets; P = price of lift tickets; A = number
of
newspaper
ads per week.
a.
The Three Peaks charges $25 per ticket and has five advertisement notices
in
the local papers. How many lift tickets do they expect to sell?
b.
Keeping the advertisement level the same (at five), calculate the point
(price) elasticity of
demand at the above price.
c. Determine the elasticity of demand with respect to advertisement.
d.
Now suppose that the manager of the Three Peaks increases the number the
newspaper ads
to 10 per week. Examine the effect of this change on the price elasticity
of demand for lift
tickets. Should the Three Peaks lower its price while increasing its advertisement?
Explain.
In recent months the pharmaceutical industry has been subject to a lot of criticism by various consumer groups (as well as some politicians) for its pricing and marketing practices. Drug companies are criticized not only for their rapidly rising prices but also for charging their US consumers much higher prices than consumers in other countries. For example, the prices of some prescription drugs are 75 percent lower in Canada than in the US. What is you opinion on this issue? Do you think American consumers should be allowed to buy their prescription drugs from Canada, Europe or Japan?
Note: Try to use as much as what you learned about supply and demand and the consumer theory in your arguments.
Hint: In observing the consumer’s behavior you might want to consider a (hypothetical) consumer with a certain amount of income buying drugs (as one good) and other things (as another good). Working with the budget line and indifference curves of this consumer, explain how a possible change in the price of drugs might (or might not) affect the behavior of the consumer. Assign your own price to each of the two categories of goods.
Here are some references:
Price Discrimination against Seniors
A firm faces the following demand curve:
Qd = 100 –5 P or P = 20 -0.2 Qd
a. Plot the demand curve.
b. What is the slope of this demand curve?
c. Given that the total revenue of the firm is price
(P) times the quantity sold (Q), write the firrm's TR function.
d. Plot the TR function.
e. At what level of Q is the total revenue maximized?
f. What is the MR at this level of output?
g. What is MR when Q = 80
h. What is MR when Q = 120
Now suppose the firms cost function is:
TC = 4 + 5 Q + .002 Q^{2}
i. Write the marginal cost function.
j. Write the firm’s profit function.
k. At what level of output would the firm break even?
l. At what level of output is the firm’s profit maximized?
Assignment
As we discussed in class, it is generally accepted that the primary
objective of the manager of a business firm is (or should be) to maximize
the value of the firm. Consider a decision making situation that the manager
of a hypothetical firm might face. In a one-page essay, explain how his
or her decision would relate to the value maximization goal of the firm.
Try to use or borrow from one of the cases or issues addressed in your
other business courses. For example, suppose the firm needs to raise capital
for its expansion plans. What are its options? How might its decision affect
its "value?" This is just an example. Come up with your own problem!
The Supplementary Assignment to the Final Exam
Answer the following three questions:
===========================
1. PharmAm Pharmaceuticals (PAP) introduces a new, patented antiviral
pill to the market. The new pill is the result of five years of research
and development that cost the company a total of $100,000,000 most of which
was raised through selling bonds. As a result the annual fixed capital
cost of the pill (at 10% interest rate) is $10,000,000 plus $10,000,000
for the amortization of the principal. The company has estimated the total
production cost function of its new drug as follows.
TC = 20,000,000 + .01 Q
The worldwide demand for this antiviral firm has also been estimated:
Q = 500, 000,000 – 100, 000, 000 P
Given its patent right, as the sole producer of this pill, PAP has
a very secure monopolistic position in the market for this pill.
a. Determine the MC, AVC, and ATC of the pill.
b. Try to draw these three cost measures. (Your scales do not have
to be precise. Just demonstrate the general shapes of these measures relative
to each other.)
c. Plot the demand function in the same space as well.
d. Determine the price PAP could charge for its pill as a monopoly.
e. Determine the quantity of pills it could sell at the monopolistic
price.
f. Determine the monopolistic profit of the company.
Now suppose the company’s patent on this drug has expired.
As a result a generic version of the pill is produced and introduces to
the market. PAP loses some of its customers to the competing generic drug
company. The demand PAP is facing now is:
Q = 400,000,000 – 133,333,333.33 P
The generic drug company’s demand is:
Q’ = 100, 000,000 – 50,000,000 P’
Because the generic drug company has not had any research costs,
its fixed cost is much lower than that of PAP, but its marginal cost is
the same. The cost function of the generic company for this drug is:
TC’ = 1,000,000 + .01Q’
g. Determine the output of PAP after the patent expiration.
h. Determine the price PAP could charge for its (brand-name) pill
after the patent expiration.
i. Determine the profit of PAP after the expiration of the patent.
j. Determine the price the generic drug company charges for its
generic pill.
k. How many pills would the generic drug company sell?
2. The Blue Dragon is a new Chinese Restaurant in town. As the only Chinese restaurant in the area, it faces the following daily demand curve:
Q = 400 – 20 P
Where Q is the number of meals it serves per day and P is the average
price of its meals.
The estimated cost function of the restaurant has been estimated
as follows:
TC = 200 + 6 Q + .02 Q ^{2}
a. Determine the profit-maximizing price of the each meal assuming
The Blue Dragon is acting as monopoly.
b. Show your work on a carefully drawn diagram.
c. Determine the profit of the Restaurant.
d. If the company were to produce as perfectly competitive firm,
how much would it produce?
e. What price should it charge as a competitive firm?
f. Would it still make a profit if it behaved like a competitive
firm?
As a result of the success of its success, other Chinese restaurants
start appearing in the area. As The Blue Dragon’s customers gradually start
trying other (new) Chinese restaurants, its demand curve gets flatter (more
elastic) and shifts to the left. In reaction, The Blue Dragon lowers its
price and adjust its output to the point that, eventually, its (economic)
profit disappears; its profit becomes zero. At that point the slope of
its demand curve becomes -.02.
g. Determine the new (equilibrium) average price The Blue Dragon
charges for its meals.
h. Write the equation for this new (zero profit) demand curve.
i. Show this equilibrium in a diagram.
Hint:The equation for the slope of the ATC is: Slope of ATC= -200/Q^{2} + .02
3. Use a diagram to demonstrate the “kinked demand curve” oligopoly model and explain how this model explains the relative price stability observed in oligopoly markets.
A Kinked demand curve exercise.
Auto Maintenance Services (AMS) is a small
auto service outlet in a suburban area of Syracuse. In reaction to a small
increase in wages that has caused the marginal cost of this auto service
establishment to increase from $25 to $30, the owner is considering raising
the prices of the services AMS offers. The owner's daughter, who is studying
economics and, at the time, takes care of her father's books and finances
advises him against that. She has estimated that if AMS raises its prices
it will face the weekly demand curve Q = 140 - 2.5 P, whereas if
it lowers its price it will face the demand curve Q'= 55-.625P.
a. Determine the (average) price AMS is charging
for its services, presently.
b. Determine the number of cars it services
each week.
c. Assuming that the owner's daughter is correct,
what is the MC range within which AMS should not change its price?
d. AMS's weekly total fixed cost is $250.
Assuming that the firm's marginal cost and average variable cost are equal
(AVC =MC), determine its weekly profit after the wage increase.
e. What should AMS do if its MC goes up to
$40? Explain.
Answers:
a. P = 45.33
b. Q = 26.67
c. Upper bound: MC = 34.66
Lower bound: MC = 2.656
d. Profit= TR- TC = 1208.95 - 1050.10 = 158.85
e. P = 48 , Q = 20
In this case the upper part
of the demand curve is used to set the price because MC is above the upper
bound. Chances are though that as a result of competitors' reactions another
(higher) "stable" price would get established.
Note: Be sure to review the related chapter in the textbook as well.
Imperfect Competition
In the previous section we looked at the two extreme cases of the
spectrum of market structures, namely, perfect competition and (pure) monopoly.
In this module we are going to examine
the interior parts of this spectrum.
Although the two polar market models provide us with useful points
of reference, they do not represent the real-world market situations. The
economists have categorized the broad range of
intermediate market structures into two types: monopolistic competition
and oligopoly.
Monopolistic Competition
This is a case where many firms produce similar but differentiated
products. While the similarity of the products makes them close substitutes
and allows for some degree of competition
among the firms, the fact that the product of each firm is (or is
perceived to be) different from those of the competitors gives each firm
some say over its price. This allows a monopolistically
competitive firm to assume a market share for itself and estimate
the demand for its product accordingly. In other words, given the market
demand, the firm would assume a separate (but
related) downward-sloping demand curve for its own product whose
shape would reflect the relationship between the price and the quantity
demanded for its share of the market.
The characteristics of a monopolistic market:
· Many firms producing similar but differentiated products
· More or less free entry and exit
· Each firm perceives a demand curve reflecting the relationship
between its price the quantity demanded of its own product.
· The firm can influence the price by change the quantity
it supplies or differentiating its product.
· The firm's output and price are in equilibrium when the
price the firm charges is consistent with its market share
To demonstrate how a monopolistically competitive firm achieves equilibrium we need to first understand the relationship between its market share curve and its demand curve.
The firm's market share curve is a curve that shows its market share
at different prices assuming that all the firms in the market change their
prices together. (Their prices do not have to be
the same.)
In the above diagram MS represents the firm's market share curve.
At price P1 the firm's market share is Q1. If all firms lower their prices
(proportionally) to P2 the quantity of this firm's
market share will go up to Q2. This increase in the market share
would be proportional to the increase in the total market demand; all other
firms' market shares would increase as well. Now
if the firm advertises that its product has been "improved", assuming
other firms are not making the same claim, the firm's market share could
shift to MS`. By differentiating its product
further the firm has increased its market share at all price levels.
Other things remaining unchanged the monopolistically competitive
firm can change its price to affect the quantity that it sells. In other
words in addition to the market share curve the firm
can assume a downward sloping demand curve for itself along which
the quantity demanded of its product increases as the firm lowers its price.
The "True" Demand Curve Faced by a Monopolistically Competitive Firm
The "true" demand curve of a monopolistically competitive firm cannot
be easily estimated. The shape of this demand curve depends not only on
the reaction of customers to changes in its
price, but also on the reaction of the competitors. It is however
useful to understand how such a demand curve would emerge.
As demonstrated in the diagram below, suppose a firm's initial market
share curve is represented by MS1. At the price P1, the firm's market share,
given the prices of all competitors, is q1.
Now suppose the firm lowers its price to p2. If all other firms
in the industry also raise their prices, our monopolistically competitive
firm will move along it's market share curve to point b
and the quantity of its market share will increase to Qo. But, if
other firms keep their prices unchanged and only our firm lowers its price,
then its market share will increase to q2, making its
market share curve shift to the right. This new combination of price
and market share corresponds to the point c in the diagram.
Further reductions in the price by our firm (keeping other firms'
prices unchanged) will cause additional shifts in the market share curve,
moving our firm to points d, e, f. The locus of these
points would form the "true" demand curve faced by our monopolistically
competitive firm, line d in the diagram.
Profit Maximization by a Monopolistically Competitive firm in the Short Run
As mentioned earlier the "true" demand curve a firm faces is not
known to it. The best the firm can do, initially, is work with an estimated
demand curve. Using its estimated
downward-sloping demand curve the firm would behave like a monopoly
maximizing its profit by setting its MR equal to its MC. In order for the
firm to be successful with this strategy, its
output level and the price it charges must be consistent with its
market share. If the estimated demand curve were the "true" this objective
would be automatically achieved. But if the
estimated demand curve does not reflect the "true" demand curve,
the firm will have to make further adjustments to reach equilibrium.
In the following diagram the monopolistically competitive firm's
estimated demand is represented by line "d " based on which its marginal
revenue curve, MR has been drawn. Following the
profit -maximizing rule, the firm sets its MC equal to its MR, and
produces the quantity Q2, expecting to charge the price P. But if the firm's
market share is the MS line, at that price the
firm can only sell Q1. This excess output will force the firm to
either adjust its estimated demand (resulting in a lower price) or increase
its market share through differentiating its product
further (say, by advertising), or both.
These changes would bring the firm to equilibrium. The diagram below
shows the short-run equilibrium for a monopolistically competitive firm.
Note that in this diagram the intersection
point between MS curve and the demand curve correspond to the profit
-maximizing price. Note that the demand curve d' could now be regarded
as the "true" demand curve. In this diagram
the SATC curve has been added so that we can show the firm's profit:
the area "abcPe."
Adjustments in the Long Run
As you recall in a monopolistically competitive market there are
no major barriers to entry. As new firms come into the industry to take
advantage of the profit making potential of the
industry, existing firms try to preserve their profits by lowering
their costs through economies of scale while striving to keep their products
differentiated. Besides, in addition to some price
competition, the firms in this kind of market tend to emulate each
other. In other words, by offering closer and closer substitutes for a
successful product which was initially introduced by
one firm, the competing firms gradually cut into its market and
over time make its market share shrink to the point where it would no longer
be able to realize an economic profit. Thus, the
long run equilibrium in this market, like in perfectly competitive
markets, is characterized by zero economic profit. Nonetheless, in this
case because the demand faced by each firm remains
downward-sloping (n0n-horizontal) the price stays above the marginal
revenue and the marginal cost and, generally, the production level stops
short of the minimum long-run average total
cost. The long-run equilibrium for a monopolistically competitive
market is depicted in the diagram below.
Because monopolistically competitive firms tend to produce at levels
below their capacities, these markets are often characterized by excess
capacity. Many retail markets exhibit this
characteristic. Another distinct feature of this market is variety,
which is the result of firms' efforts to differentiate their products from
those of their competitors.
Review the numerical example on Page 391.
Oligopoly
An oligopoly market is a market with a few firms, each large enough
to have some influence on the price. Oligopoly firms may produce homogenous
or differentiated goods. The key feature
in an oligopoly market is the existence of some degree of interdependence
among the firms in the industry. The effect of this interdependence on
the behavior of the firm varies depending on
the particular characteristics of each market. For instance, in
an oligopoly market where a firm, because of its size or superior efficiency,
is dominant other firms tend to follow its lead. In
certain cases oligopolies may attempt to openly or tacitly collude.
In many cases because of their uncertainty about the reactions of their
rivals to their actions oligopolies try to strategize their
behavior based on their guesses (which in some cases are calculated)
about their rivals' behavior.
Because of the variations among oligopolies, over years, economists
have developed several models to explain different types of oligopoly markets.
Some of the more modern
models have been developed with antitrust laws in mind. In this
course we are going to examine only some of these models.
The Cournot Model: A Model for an Oligopoly with Two Firms
This model was developed by a Frenchman by the name of Augustin Cournot
based on a set of rather simplistic assumptions. He initially assumed a
market with only two firms (a duopoly)
with zero production cost. By setting its MR equal to zero (MC),
each firm would maximize its profit, assuming the other firm would keep
its output constant.
Let us start with the first firm assuming it is facing the (linear)
market demand Dm. With zero marginal cost this firm would produce at the
point its marginal revenue line intercepts with the
horizontal axis. In the diagram in your book (Page 393), that is
Q1. In diagram below it is quantity 50. Based on the market demand curve
the price that corresponds to this quantity would
be P1.
Now the second firm takes output of the first firm as given and constant
and assumes it is facing the lower half of the demand curve (from point
a down). Based on the lower segment of the
demand curve the second firm's marginal revenue line will be MR2;
it intercepts the Q axis at 75, the midpoint between 50 and 100. That means
the second firm would produce 25 units of
output selling them at price P2.
When the second firm starts selling the good at P2, which is much
lower that P1, the first firm would have to make some adjustments. Otherwise,
it would lose its customers to the second
firm. The way firm 1 could solve its problem, according to Cournot,
is to take the second firm's output as given and this time assumes it is
facing the residual of the market demand. Setting
its new marginal revenue equal to zero, now firm 1 would produce
½ (100-25) = 37.5. Note that Firm 1 did the same thing the firm
2 did in the first round of adjustment. Now the price Firm
1 is charging is P3 which is lower than P1 but still higher that
P2.
Now it is the second firm's turn to react to this new situation.
Now that the first firm is producing less that before the second firm's
adjustment would be upward. The second firm now
assumes that the first is producing 37.5 and adjust its production
to ½(100-37.5)=31.25. This process would continue until the two
firms reach equilibrium. The equilibrium is achieved when
the output level of each firm reaches 1/3(100)=33.33.
Cournot generalized this duopoly analysis for an n-firm oligopoly market. For the an n-firm monopoly the equilibrium output could be determined by the following formula.
Q e = {n/(n+1)] Qo , where n is the number of firms in the market and Qo is the market demand at zero price. In our duopoly example, for each firm, Q e = [1/(2+1)]x100 = 33.33
The Kinked Demand Curve Model
One of the characteristics of some oligopoly markets is price stability.
It is not unreasonable to assume that due uncertainty about the reaction
of their competitors managers of monopolies
might hesitate a little before reacting to changing market conditions.
One of the oligopoly models that explains this phenomenon is the kinked
demand curve model. This model is based on
the assumption that in a monopoly market when a firm lowers its
price its competitors tend to follow its lead and also lower their prices,
whereas when it raises its price they may not. This
scenario is depicted in the diagram below. Suppose an oligopoly
is at point "a" that corresponds to the price Pe and the quantity Qe in
the diagram. Because the oligopoly's competitors'
reaction to a price reduction is stronger than it is to a price
increase, the oligopoly is in fact facing two differently sloped demand
curves that intersect at point "a". These two demand curves
are represented by lines d and d` in the diagram. Line d which is
more elastic at point "a" is the demand curve the oligopoly faces when
it raises its price; an increase in the firm's price is not
likely to be matched by similar increases in the competitors' prices
because the firms who do not raise their prices would gain the business
that that the firm that raises its price would lose.
On the other hand, when an oligopoly lowers its price it faces the
demand curve d` which is less elastic than d at point "a"; a price reduction
by an oligopoly is not as effective in increasing
the firm's quantity demanded as other firms are likely to match
this price reduction to keep their customers from switching. These two
demand curves make the kinked demand curve D the
oligopoly faces. The kinked demand curve gives the oligopoly a segmented
marginal revenue line. This line is depicted by the broken line MR in the
diagram. (Note how each segment of the
TR line has been drawn relative to its corresponding demand curve.)
A profit maximizing oligopoly that sets its MC to its MR would produce
Qe at all four marginal cost levels represented by lines MC1, MC2, MC3,
and MC4, and charges the price Pe. This
implies that increases in production costs might not result in quick
adjustments in the equilibrium price and quantity of an oligopoly. And,
this is the reason for relative price rigidity that we
some times observe in oligopoly markets.
Be sure to review the numerical example on pages 403-406 of the textbook.
The Price Leadership Case
Firms in oligopoly markets do not always have the same level of
market power. Some times, due to either its size or its technological superiority,
a firm may acquire a leadership role in an
oligopolistic market. In such cases the price is often set by the
dominant firm and the other firms eventually end up accepting that price.
The Case of a Technologically Superior Firm
When a firm is relatively more efficient than its rivals in the
industry it can set the price lower than its competitors, forcing them
to either leave the market or accept the lower price.
A simple duopoly example of this case is demonstrated in the diagram
below. In this diagram it is assumed that the market demand is equally
divided between the dominant low-cost firm and
the rest of the less efficient . D` is the demand curve each firm
faces; it is drawn by splitting the market demand (D) at each price level
into two equal parts. MCa is the marginal cost of the
efficient firm whereas the higher MCb representsthe marginal cost
of the less efficient firm. MR` is the marginal revenue drawn based on
the D`. To maximize its profit, by setting its
marginal revenue, MR`, equal to its marginal cost, MCa, the dominant
firm would produce Qa and charge Pa. Using the same marginal revenue curve,
the less efficient firm (higher-cost)
firm would want to produce less, Qb and charge a higher price, Pb.
This situation cannot last very long because as the customers of the less
efficient firms learn that they can buy the product
at a lower price from the efficient firm, the market share of the
inefficient firm would shrink, forcing it to either accept the dominant
firm's price, Pa, or leave the market. The industry
equilibrium output would be at QT which is equal to the sum of the
two firm's output. The profit of each firm would be the difference between
Pe and its average total cost (not drawn).
The Case of A Large Firm
The leadership position of the dominant firm in an oligopoly market
could be due to its size. In this case the dominant firm makes its decisions
with the small firms in mind. In other words, it
takes the collective supply of the small firms as given and assumes
that the demanded curve it faces is the (horizontal) difference between
the market demand and the collective supply of the
small firms. The dominant firm's demand curve is represented by
line DL in the diagram below. The marginal revenue of the leader is drawn
based on this demand curve, MRL. To
maximize its profit, the leader sets its marginal revenue equal
to its marginal cost, MCL, and produces QeL. It would determine the price
according to its demand, DL, at Pe. This price
would be taken as given by the small firms, giving them the market
share of Qes. Note that the distance OQeL ( the leader's output) in the
diagram is equal to the distance Qes Qem.
Graphical derivation of the leader's demand curve: At price Pb that
corresponds to the intersection between the market demand and the small
firms aggregated marginal cost (or supply
curve) the market demand is fully satisfied by the small firms'
supply and, thus, there is no demand for the leader's output. That gives
us the intercept of the leader's demand curve with the
price axis. At price Pf the small firms' supply is zero --that is
where the small firms' supply intercepts with the price axis. At this price
the leader's demand is the market's quantity demanded.
That is the quantity Pf h which is equal to the distance Pf g. By
connecting points g and Pb on the vertical axis we will get the demand
curve faced by the dominant firm.
Note that if the price falls below Pf the small firms will leave the industry and the leader will face the market demand.
Algebraic derivation of the leader's demand:
If the market demand is Qdm = 1000 - 20 P and the small firms' supply
is Qss = -100 + 10 P, the demand faced by the leader is:
QdL = Qdm -Qss = 1000 - 20 P - ( -100 + 10 P ) = 1100 - 30 P
A graphical exercise:
a. Change the leader's marginal cost and examine the effect on the
small firms' market share.
b. Chance the small firms' marginal cost and examine the effect
on the leader.
See the steel industry example on pages 409-412.
Cartels
When the number of firms in the industry is small enough to allow
efficient coordination among them, provided that it is not against the
law, the most desirable way for them to maximize the
collective profit is to collude. This kind of arrangement is called
a "cartel". Such collusions are against the law in the United States and
most other industrial countries.
To maximize their profit a cartel estimates its marginal revenue
based on the market demand and sets the aggregated (collective) marginal
cost of the members equal to it determine the total
output of the cartel. The cartel price would be determined based
on this quantity along the market demand. To determine the output share
of each cartel member the collective marginal
revenue is set equal to each firm's marginal cost. Because the price
is above each member's marginal cost, there is tendency on the part of
cartel members to cheat and overproduce.
Cheating by cartel members often results in the collapse of the
cartel's price fixing arrangement.
See the example on page 415 in the textbook.
Answer: Neither production efficiency nor allocative
efficiency achieved in perfectly competitive markets would be achieved
in a monopolistic market.
Monopoly: P>MR, P>MC , MC # ATC Perfect
competition: MR = P = MC = ATC
2. Do problem 4, page 378, from the textbook
Set MC = Price; 80 -12 Q + .6 Q^2 = 260
Or, -180 - 12 Q + .6 Q^2 = 0
Using the quadratic equation and solving for Q, Q = 30
Profit = 4400
3. Use a diagram to explain how under perfect competition a long-run
equilibrium is achieved. Outline the sequence of the adjustments. What
are the efficiency properties of such an equilibrium?
See the lecture and/or page 363 in the book.
4. Part 3: A monopolistic firm faces the following demand curve.
Q = 4000 -10 P
This monopoly's cost function has been estimated
as follows:
TC = 110,000 + 20 Q
a. What price should this monopoly charge to maximize its profit?
MR = 400 -.2 Q
MC = 20
MR = MC ; 400 -.2 Q = 20
Q = 1900
P = 210
b. What would be its equilibrium profit?
Profit = TR - TC = 251,000
c. If this monopoly were to behave like a competitive firm, what price
should it charge and what quantity
should it produce?
Set P = MC ; 400 -.10 Q = 20
Q = 3800
d. Would the monopolist still make an economic profit if it were to behave like a competitive firm?
Profit = TR - TC = - 110,000
e. Show your work on a diagram.
Assignment of the week:
We know that the real-world markets are neither perfectly competitive
nor purely monopolistic. Changes in market conditions occur as a result
of technological changes on the production
(supply) side, on the one hand, and changes in consumers' preference
and incomes on the demand side, on the other hand. As a result, over time,
some industries become more competitive
and some become more monopolistic. Here are links to some
sites you might find useful. We will try to discuss the evolution of different
industries in out next class.
Concentration, Mergers, and Antitrust Policy
Do the following two problems to the best of
your ability. This assignment will supplement your grade on the in-class
test. The in-class test will include questions on supply and demand and
elasticity as well as on production and cost analysis. The questions given
in the in-class exam will be mostly short and conceptual.
1.Your friend plans to open up a small bagel shop. She has her eyes on a shop in a shopping strip near the college. The shop can be rented for $800 per month. She has estimated that the fixed part of her monthly utility bill would be $200. In addition, she expects to pay another $200 each month for insurance and maintenance costs. Each dozen of bagels takes $1.75 worth of ingredients and $.10 worth of electricity to produce. Each dozen of bagels also needs $.15 worth of bags or other packaging materials.
She can lease all the equipment that she needs for $400 per month. She also needs $10,000 for up-fitting the shop and a small amount of inventory. Her bank has agreed to give her a loan in that amount and let her pay only the interest, $100 per month, for five years. At the end of the five years she would have the option of renewing the loan or paying it off.
Your friend plans to quit her present job and, with the help of a full-time employee, run her bagel shop herself. Her monthly salary form her present job is $1,500. She expects to pay her full-time employee $1000 per month.
a. Identify all the fixed and variable costs
of the operation.
b. Write the total cost function of your friend’s
bagel shop.
(Hint: It is a linear function.)
c. Assuming the market price of bagel is $5
per dozen, how many dozens of bagels would she have to sell (per month)
to break even?
d. How many dozens would she have to sell
to have $1,000 profit each month?
e. Suppose in the second year of her operation,
the monthly lease for the shop is expected to go up to $1,200. Assuming
no other changes, how will that affect her break-even quantity and the
profitability of her business?
2. The following is the estimated short-run cost functions of a firm.
TC = 750 + 50 Q + .5 Q ^{2}
MC = 50 + Q
The firm is faced with the following demand:
Qd = 600 – 5 P
a. Determine the profit maximizing level of
the output for this firm.
b. What price should the firm charge to maximize
its profit?
c. What is the firm’s profit at the profit-maximizing
output?
d. What is its average variable cost at this
level of output?
e. What price should it charge if it were
to maximize it revenue?
f. At what level of output is the firm’s average
total cost minimized?
g. Show your work in a diagram.
Production/Cost Exercises
Do the following two problems. You do not have to turn in the first
one, but the second one I would for you to turn in.
1. The following is a short-run production table for a firm
with labor as its only variable input.
Wage = $100
Capital = 45
Capital Price= $15
Product Price= $10
<<Those of you who are familiar with a spreadsheet package (Excel,
etc. ) should try to use it.>>
Labor Output
0
0
1 40
2 90
3 140
4 180
5 210
6 230
7 240
8 245
9 240
10 235
a. Determine the following measures at all levels of output:
MPL, APL, TFC, TVC, TC, TR, AVC,
ATC, AFC, MC, PROFIT
b. At what level of output is the profit maximized?
c. What kind of observations can you make about MC, MPL?
d. What is the marginal product of the 7th unit of labor?
e. What is the marginal cost at the output level 210?
f. At what level of output is the firm's average total cost minimized?
g. At what level of output is the firm's total revenue maximized?
2. Medicount Accounting Company (MAC) specializes in accounting and tax services for medical establishments. Presently, MAC employs 20 accountants paying them each, on average, $40,000 per year. The company has leased 8 computer units. Each unit comes with a complete accounting software and service package. MAC pays $500 per year for each computer unit.
a. Write the equation for the company's isocost.
b. Carefully draw the isocost on a diagram. (Be sure to scale your
diagram carefully.)
c. Identify the point on the diagram at which the company is producing.
d. The company's operation manager has estimated that the company can
increase its output, measured in terms of the number of clients served,
by 2 if it hires one additional accountant, whereas leasing another computer
will increase the company's output by only .04 clients. Based on this information,
is the mix of capital (computers) and labor (accountants) the company is
presently using efficient (optimal)? Explain. If your answer is no,
what kind of changes would you recommend?
e. Draw an isoquant consistent with the situation described in (d).
Explain your answer to question (d) by referring to your diagram.
(Note: The exact shape of the isoquant each student draws does not
have to be the same as those drawn by others.)
f. What would be the effect of your recommended changes on the company's
cost, assuming the company wants to maintain the level of its output the
same?
g. Now suppose that after the company has followed your recommendation,
the lease price of computers has gone up to $1000 per unit per year. Show
the effect of this change on your diagram.
h. Using your graph demonstrate the level of cost (isocost) at which
the firm can efficiently produce the same quantity of output
that it produced before the increase in the lease price of computers.
i.What is the MRS at this new mix of capital and labor?
Q = 8000 - 160 P + 50 A
where Q = weekly number of lift tickets; P = price of lift tickets; A = number of
newspaper ads per week.
a. The Three Peaks charges $25 per ticket and has five advertisement notices in
the local papers. How many lift tickets do they expect to sell?
b. Keeping the advertisement level the same (at five), calculate the point (price) elasticity of demand at the above price.
c. Determine the elasticity of demand with respect to advertisement.
d. Now suppose that the manager of the Three Peaks increases the number the newspaper ads to 10 per week. Examine the effect of this change on the price elasticity of demand for lift tickets. Should the Three Peaks lower its price while increasing its advertisement? Explain.
e. Suppose each newspaper ad costs $800, would you recommend spending more money on advertisement? Explain.
=============================================
1. Plot the following supply and demand equations in a diagram measuring
price on the vertical axis and quantity on the horizontal
axis.
Qs = - 600 + 40 P
Qd = 1200 -50 P
a. Identify the price and quantity intercepts
for each equation.
b. Determine the slope of each line.
c. Write each equations for price (P) in terms
of quantity (Q).
d. Determine the equilibrium price and quantity.
e. Explain the market conditions when the
price is set at $18
f. Explain the market conditions when the
price is set at $ 25
2. The demand for seats on flights to Orlando, Florida, has been estimated as follows:
Qd = 900 -2 Price + .05 Income - 5 Weather +
1.25 Pc ( where Pc is the price offered by the competition)
Assuming: Income( I ) = 1000, Weather = 60 Pc = $160,
a. Write the equation for the demand curve.
d. Determine and show on your diagram the effect of an increase in
the weather temperature (W)
from 60 to 90 on the demand.
e. Keeping the weather temperature (W) at 90, determine and show
the effect of an increase in
the price of the competition from $160 to $200 on
the demand.
f. Now keeping the weather temperature at 90, Pc at 200, and income
at 1000, use your demand
function to write the total revenue ( TR ) equation.
g. Using the same demand function, also write and plot the marginal
revenue (MR) function.
h. Using the same demand function, determine at what price level the
total revenue from this shuttle
flight is maximized. Try to show your work on a
diagram.
Here are a few references for you:
Guidelines for the Course Project
1. What distinguishes oligopolistic
markets from other market structures?
2. Describe the Cournot
model. Why was it criticized?
3. What is the distinguishing
feature of the kinked demand curve model?
4. The color copy machine
market is dominated by a large firm with significant production capacity.
the market
demand
for color copy machines is Q = 2000 - 4 P.
The dominant
firm has projected the supply by the small firms in the market to be:
Qs = -700 + 2 P
a. Plot
the demand curve faced by the dominant firm.
b. Write
the marginal revenue function of the dominant firm.
c. Assuming
the leader's cost function is TC = 2000 + 300 Q + 1/84 Q^{2},
determine the following:
Also give these problems a try.
6. An income property has been put in the market for $160,000. The property is presently occupied by a law firm that has a five year lease on it. The annual rent on the property is $12,000. Based on the information the present owner has provided you, on average, in the past five years the property has had $2,000 maintenance cost per year. In addition there is $3,500 property tax which is expected to remain the same in the foreseeable future. Your research indicates that in the past five years the property values in the area where this property is located have appreciated at an average annual rate of 4%. The market interest rate on (risk-free) investment instruments such as government bonds and certain bank deposits is 4.5%. Considering the five-year lease and the area's real estate market, you consider investment in this property relatively safe but, of course, not as safe as investment in government bonds or certain (insured) bank deposits? Would you buy this property at the asking price? Explain. If the asking price is not acceptable to you, how much would you offer for this property?
Now suppose that you do not have enough cash
but your bank is willing to finance up to $100,000 of the value of this
property. The interest rate the bank will be charging you on a 30-year
mortgage is 8%. Would this new circumstance affect your assessment of the
value of the property? If you answer is yes, how? Explain. You may use
the financial tables at the end of the book for your calculations.
Jeffrey has been told that on average each dozen of bagels needs the
following ingredients:
Price per pound
One pound of flour
$.80
Two ounces of sugar
$.50
One ounce of raisins
$.80
One ounce of onions
$.64
One ounce of sesame
$2.40
One ounce of poppy seeds
$3.20
One ounce of other flavoring additives
$1.20
One ounce of shortening
$1.60
(Note: On average there is an 8 percent waste and spillage of the ingredients.)
Jeffrey thinks he is going to need two full-time employees, each working six days a week, eight hours per day. He estimates that he will have to pay $9 per hour to his two employees. Jeffrey has estimated that his utility cost will be, on average, $200 per month plus an additional $100 for each 1,000 dozens of bagels that he produces.
a. Identify Jeffrey's implicit and explicit costs.
b. Identify the fixed and the variable costs of Jeffrey's Bagel Shop.
c. Can you write the cost function of the bagel shop?
d. Plot your cost function in a diagram.
e. Assume that the going market price of a dozen of bagel is $6.00.
Jeffrey however plans to sell his bagel at $5.00 per dozen, at least initially
to attract customers. Determine Jeffrey's break-even (monthly) level of
production based on his explicit costs.
f. Determine Jeffrey's break-even (monthly) level of production based
on his economic costs.
g. What would be Jeffrey's normal profit?
h. Calculate Jeffrey's TC, TVC, AVC, ATC for the normal-profit level
of output.
i. At what level of sales would Jeffrey's annual (economic) profit
reach $12,000?
Now try this L-R production function exercise.
2. The daily cost functions of Rapid Oil Change (ROC) have been estimated
as follows:
TC = 10 +2 Q +.2Q ^{2}
MC = 2 + .4 Q
a. Determine the average total cost and the marginal cost for the quantity
levels 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 25, 35
b. Carefully plot the average total cost and the marginal cost on a
diagram.
c. Now suppose that the market price for an oil change $12.
Determine the firm's output level and its profit.
Article
I
Article
II
Article
III
Explain the problem faced by the industry in
the context of a supply and demand analysis.
(Hint: Note that the short-run market supply
of air travel is expected to get quite steep as the industry gets closer
to its production capacity. Think about that!)
Explain the effect of the changes in the market
conditions on the price elasticity of demand for air travel services.
1. How do you think the changes in the air
travel market could have affected the crude oil market?
2. How does the state of the economy affect
the industry's recovery?
3. How does the government's "bailout package"
for the industry change the market conditions?
4. Will the "bailout package" change the demand?
5. Would the bailout package affect the price?
Explain.
6. Will the "bailout package" change the price
elasticity of demand for air travel?
7. Should the industry lower the airfare?
8. What industries are benefiting from the
situation in the airline industry?
9. What industries are likely to be affected
negatively by the decline in air travel?
10. Would mergers among the ailing airline
companies help the industry? What are the implications of such mergers
for (future) air travelers.
Reading Assignment for the Week of September 2, 2001
After reviewing Chapters 1 and 2 read the following articles from the South-Western EconNews Online (by John Kane):
Higher Health-Care Costs: Who Pays?
Review the question at the end of each article.
Also have a look at the following two articles from The Dismal Scientist:
Legalized
Price Gouging at the Pump
Q = 100 – 10 P
where Q is the weekly quantity (in 1000 of gallons) sold and P is
the unit price. The company's cost function has been estimated as follows:
TC = 20 + 2Q + .05 Q ^{2}
a. Determine the profit-maximizing price of the product for SWC.
b. Show your work on a carefully drawn diagram.
c. Determine the profit of the company.
d. If the company were to produce as perfectly competitive firm,
how much would it produce?
e. What price should it charge as a competitive firm?
f. Would it still make a profit if it behaved like a competitive
firm?
g. As a result of the success of this product other firms start
producing similar detergents and selling them at lower prices. As SWC’s
customers gradually switch to other brands, SWC’s demand curve gradually
shifts to the left, while it slope remains the same. (Parallel shits to
the left) Eventually SWC’s (economic) profit on this product disappears;
its profit becomes zero. Determine the revenue of the SWC from this product
at this zero profit level of output.
h. Show your work on a diagram.
i. (Bonus points) Write the equation for this new (zero profit)
demand curve.
2. OL
2. The new Ford's compact car, Focus, has been relatively successful.
Other car makers have come up similar models. Ford's marketing department
has concluded that the demand the company faces for this car is a kinked
demand curve represented by the following two equations:
Q = 4000 -.2 P
Q’ = 8000 -.5 P
a. Carefully plot this kinked demand curve.
b. Determine the price and the number of cars Ford sells.
c. Assuming the cost function TC = 2000,000 + 8000 Q, determine
Ford's profit on this product.
d. Suppose as a result of a combination of higher energy prices
and a new labor contract the marginal cost of production for this model
has increased by $2000. Should Ford increase its price? Explain.
e. Show your answer to (d) on your diagram.
f. Will Ford still be making a profit on this car after the cost
increase? Explain.
3. OL
AAA Computers is one of a few computer stores in town. Because
of recent decreases in chip prices the management is considering lowering
the prices of their computers. Their marketing advisor, however, has advised
the management that they need to be careful about their pricing and promotion
strategies (at their present price) because the reactions of their competitors
may be different to their different pricing strategies. She has estimated
that if AAA Computers raises its price it will face the annual demand curve
Q = 5000 -5 P, but if it lowers its price it will face Q' = 3000 -2.5 P.
a. Determine the price AAA Computers is charging presently.
b. Determine the number of computers they sell each year.
c. Calculate the price elasticity at this level of output (sales).
d. The cost function of the company is : TC = 600 +340 Q +
.1 Q^{2} . Determine the company's profit.
e. Determine the company's marginal cost at this level of production.
f. Assuming that the marketing consultant is correct, what is the
range of marginal cost within which AAA should not change its price?
a. Write the equation for the company's isocost.
b. Carefully draw the isocost on a diagram. (Be sure to scale your
diagram carefully.)
c. Identify the point on the diagram at which the company is producing.
d. At this mix of inputs the firm's marginal rate of technical substitution
(MPL/MPK) is -3. Is the mix of capital and labor MSC is using efficient
(optimal)? Explain. If your answer is no, what changes should the
firm make in its production process.
e. Draw an isoquant consistent with the situation described in (d).
Explain you answer to question (d) by referring to this diagram.
f. Now suppose the price of labor has increased to $40,000. Assuming
the same level of total cost show the effect of this change on your diagram.
g. Using your graph demonstrate the level of cost (isocost) at which
the firm can efficiently produce the same quantity of output that it produced
before the increase in the price of labor.
The following date show weekly consumption expenditures and incomes of ten individuals.
Consumption Income
120
180
150
200
80
90
160
210
200
300
75
80
180
200
80
100
120
160
140
180
Calculate the following:
a. The mean of each variable
b. The variance of each variable
c. The standard deviation of each variable
e. The covariance of the two variables
f. Assuming consumption is a linear function
of income, using the regression method estimate the intercept and the coefficient
of income.
g. Based on your estimated parameters, calculate
the elasticity of consumption with respect to income.
Note: You could use Excel, another
spreadsheet package, or a simple calculator to do your your calculations.
Also, if you would like to use another set of data to do the same type
of exercise, feel free to do so.
Elasticity(Answers)
Try the following two problems.
Answers
to Elasticity problem 1
a. Price intercept = 270 ;
Quantity intercept = 54
b. Q = 30
c. Ep = -.8
d. TR = 270 Q -5 Q^{2}
e. Q = 27
f. E _{I }= +.33
e. E p = -.60
Answers to Elasticity problem 2
a. Q = 3200
b. Ep = - 1.25
c. Ea = +.0625
d. Ep = - 1.17 ; Yes; at this price the
demand is still elastic.
The demand and supply functions for seats on flights to Orlando, Florida, have been estimated as follows:
Qd = 900 -2 Price + .05 Income - 5 Weather + 1.25 Pc ( where Pc is the price offered by the competition)
Qs = -100 + 4 Price
Assuming: Income( I ) = 1000, Weather (W) = 70, Pc = $160,
1. Write the equation for the demand curve.
2. Carefully plot both supply and demand curves.
3. Determine the equilibrium price and quantity.
4. Determine and show on your diagram the effect
of an increase in the weather temperature (W)
from 70 to 80 on the equilibrium
price and quantity.
5. Keeping the weather temperature (W) at 80,
determine and show the effect of an increase in
the price of the competition
from $160 to $200 on the equilibrium price and quantity.
6. Now keeping the weather temperature at 80,
Pc at 200, and income at 1000, use your demand
function to write the total
revenue ( TR ) equation.
7. Using the same demand function, also write
and plot the marginal revenue (MR) function.
8. Using the same demand function, determine
at what price level the total revenue from this shuttle
flight is maximized.
Try to show your work
on a diagram.
Qs = - 600 + 40 P
Qd = 1200 -50 P
1.What are some of the schemes used to encourage managers to make their decisions in accordance with the interest of share holders?
2. In the news: "Federal Reserve Chairman
Alan Greenspan gave his broadest endorsement of tax cuts to date Thursday,
while also indicating that the U.S. economy has slowed dramatically, raising
investors' hopes that further interest rate reductions
are on the horizon." What are the implications
of a tax cut for the business environment?
3. In the news: "Intel Corp., the world's biggest maker of semiconductors, is preparing to cut prices on some microprocessor chips by more than 40 percent," the Wall Street Journal reported on Thursday. What could be the possible considerations behind this managerial decision?
4. Give an example of a managerial decision that could result in a need for additional managerial decisions? What should a manager do under such circumstance?
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PROBLEM SETS
The PROBLEM SETS page contains sample questions and problems some of
which we will try to review in class. Additional questions may be added
during the semester.
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A TIME-SERIES EXERCISE
A time-series exercise: Here is a link to some income/consumption
data: Data
If you click on it, it takes you to a page with links to a number of
data sets. On the to of the list you'll see "1924-1994 consumption function
data" in three different formats, EXCEL, SAS and LIMDEP. Just click on
the format you like and save the data set on your disk. You can now go
to that file and open it. You'll see two columns of numbers. One is income
and the other is consumption.
Your assignment is to regress either consumption (C) or income (Y)on time using the three following specifications:
Y_{t }= a + b t
Y_{t }= a(1+g)^{t}
Y_{t } = a e ^{gt}
Here Y is your dependent variable--you could use income or consumption
for that-- g is the growth rate and t is time.
You can use EXCEL or LIMDEP.
Q. 1
a. Write the equation for the company's isocost.
Cost = 25000 L + 5000 K
b. Carefully draw the isocost on a diagram. (Be sure to scale your diagram carefully.)
In a two-dimensional space, with K measured vertically and L measured horizontally, draw a straight negatively sloped line intercepting K axis at 1050 and L axis at 210.
c. Identify the point on the diagram at which the company is producing.
A point on the isocost that corresponds to K = 50 and L = 200, call
it point B.
d. At this mix of inputs the firm's marginal rate of technical substitution
(MPL/MPK) is -3. Is the mix of capital and labor MSC
is using efficient (optimal)? Explain. If your answer is no,
what changes should the firm make in its production process.
No. At this point MRTS = -3 which is not equal to - w/r ; w/r
= 5; more capital and less labor should be used.
e. Draw an isoquant consistent with the situation described in (d). Explain you answer to question (d) by referring to this diagram.
Draw an isoquant that would cross the isocost at point B, having a slope
flatter than the isocost at that point.
f. Now suppose the price of labor has increased to $40,000. Assuming
the same level of total cost show the effect of this change on your diagram.
The new isocost would cross the L axis at 131.25 but the K axis at
the same point (1050)
g. Using your graph demonstrate the level of cost (isocost) at which the firm can efficiently produce the same quantity of output that it produced before the increase in the price of labor.
Move the new isocost ( in a parallel fashion ) to touch the desired isocost.
Q. 2
a. Determine the average total cost and the marginal cost for the quantity
levels 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
ATC : 7.20, 4.90, 4.27, 4.05, 4.00, 4.03, 4.11, 4.23, 4.36, 4.50
MC: 2.40, 2.80, 3.20, 3.60, 4.00, 4.40, 4.80,
5.20, 5.60, 6.00
b. Carefully plot the average total cost and the marginal cost on a
diagram.
Graph
c. Now suppose the demand curve faced by ROC is:
Q = 22 -.5 P
Determine the price ROC should charge to maximize
its profit.
P = 24
d. What is this firm’s profit at the profit-maximizing level of output?
Profit = 200
e. If the ROC wishes to maximize its total revenue, what price should
it charge?
P = 22
f. Show your work on a diagram.
Graph
g. To drive out the competition and increase its market share ROC decides
to lower its price to the
level of its average total cost. What price should
ROC charge for each oil change and how many
cars per day should it expect to service? What is
the marginal cost at this level of output?
Set ATC = P
Q = 19.76 , P
= 4.48 ,
Profit = 0
h. Will ROC still be making a profit if it produces at the cost minimizing level? Explain.
Set MC = AC , Q = 10
i. At what level of output does the average total cost of ROC reach
its minimum? Show it on your
diagram as well.
Yes, MC = ATC = MR
Note: This is not always the case. In this case MR line happens
to intersect the MC at the point where MC intersects ATC.
Read the Instruction carefully and, using the sample data given in the Instruction, go through the whole process. First try to run the model on line, and then through a batch file. Print the results.
Examine the results carefully. Look for the d-stat table first. In this table you'll find statistics such as the mean, standard deviation, maximum and minimum on each of the variables.
Then look for the correlation matrix. This is a table that contains the simple correlation ratios between variables. The correlation ratio tells you how closely two variables move (change) together. It could be positive or negative.
Next study the regression results. The regression results are printed in the form of a table. For each variable you'll see the estimated coefficient, the standard error, the t-value. You'll also see the coefficient for ONE which is the constant.
Next look at the regression statistics, printed above the regression results. In this table you'll find statistics such as the standard error of the regression, R-squared, F-test, Durbin-Watson statistics, etc. There are a couple of statistics that you do not have to worry about. I'll talk about those in class.
In this sample run there are four sets of results. Be sure to examine each carefully and match it to the relevant command statement in the batch file. There are one linear run and one log-linear run on the regression model. There are one linear run and one log run on the time series model.
Now you are ready to start your own project. The first thing is to think of a model. Think of some thing you are interested in. For example, you may be interested in finding out (measuring) the effects education, gender, age, experience, etc. on income. Here your dependent variable will be income, and your determinants will be the other variables. This is only one possible example. You should come up with your own idea. If you need help, let me know.
Write up your model in a general form: Y = f ( x, w , z. ......). Define all your variables and decide how you want to measure them. For example, income is the annual income measured in terms of, say, thousand of dollars; age is the age at the time the income was reported measured in years; education is the number of years of schooling, measured in years.
Construct a time series model: Y = f (Time). Your dependent variable could be the same dependent variable, if you can obtain time series data on it. If the dependent variable in your regression model is not suitable for a time series model, think of another dependent variable on which you can obtain time series data. Examples: GDP, industry sales, population, different industry expenditures, etc.
Next you need to obtain data on your variables. It is advisable to include a few substitutes in list of your variables just in case you are not able to find data on some of your variables. Many variables can easily be substituted with other variables that are highly correlated with them. You can start your search on the Web or at the library. Again, I'll be able to help you find the data you need when I know more about your project. Be sure to have enough data points to have at least about 20 degrees of freedom.
You are now ready to decide on the form of your model. You can try different forms of equations: linear or log-linear. Try differnt mixes of variables and see if your results change. Simply follow the instructions outlined in the hand out and run your model. Trying different forms of functions would be as easy as writing one or two extra commands in your batch file.
After you have completed your run, review your results, as you did those of the sample run, and write a one page report analyzing them.
This is just a start. We deal with any problems that may arise as we go on. Stay in touch.
HAVE FUN!