STUDY QUESTIONS
1. What is the main objective of a business firm?
2. Explain and compare “economic profit” and “accounting profit”.
3. What is a “sunk” cost? Why is it wrong to consider sunk costs in making business decisions?
4. Why is it sometimes difficult to assess implicit costs?
5. True or false? Explain. If in valuating (assessing)
a business firm we ignore its implicit costs, we are likely to overestimate
the value of the firm.
6. Why are the problems arising from the separation
of management from ownership in business firms
considered “principle-agents”
problems?
7. Why is it difficult for most share holders to influence the firm’s management?
8. Mike’s grandparents gave him a municipal (zero
ccoupon) bond with a face value of $10,000 as a graduation gift. The bond
matures in five years (in 2007).
When Mike tried to cash his bond his broker offered him only $7,425. Explain
to
Mike why and how the bank is offering
him $2,575 less that what he thought his bond would be worth.
9. For the past ten years ABA corporation has paid
an average of $2.50 dividend on each share of its common stock
with little variations. In addition,
over the past ten years the market value of a share of ABA common
stock (which was
$25 ten years ago)
has increased by about 62 percent. Assuming a risk-adjusted discount
rate of 12 percent, how much
would you pay for a share of ABA
common stock today, if you were to keep it for five years?
10. What are some of the options share holders have when they are not satisfied with the firm’s management?
11. What is a linear function?
12. Use an example to explain different components of a linear function and the information contained in the function.
13. Give some examples of the forms non-linear functions can take.
14. Take a simple two-variable linear function (e.g., Y
= a + bX) and plot it in a two-dimensional space. Assign different
values to your coefficients
and show how they affect the shape and position of your function on your
diagram.
15. What is meant by “fitting a regression line”?
16. What does a t-ratio measure? How do we use in the evaluation of our estimators?
17. What does the p-value measure?
18. What does the coefficient of determination, or R 2 , measure?
19. What does the F-statistic measure?
20. Use an example to demonstrate a log-linear regression function.
21. How is a log-linear function estimated?
22. What does the standard error of regression measure?
23. Carefully do problems 7, 8, 9, and 10 (pages 185-186).
24. Explain why an indifference curve is convex.
25. A consumer with a disposable income of $360 per week
spends all of her income on food and clothes. The average price
of clothing is $40 per unit
while the price of one unit (basket) of food is $30.
Write this consumer’s budget
line (constraint) equation and plot it on a diagram.
What is the slope of this
consumer's budget line?
Draw a set of indifference
curves (for your hypothetical consumer) against the budget line.
Determine and show
the utility maximizing combination of food and clothes for this consumer.
Suppose the price
of clothing drops to $25 per unit. Show the effect of this price change
on your diagram.
Can you derive the
demand curve for clothing from your analysis.
26. When a consumer’s marginal rate of substitution
(between X and Y) at a point along his/her budget line is greater than
Px/Py, the consumer
could increase his/her utility by increasing his/her consumption of .....................
and decreasing
his/her consumption
of ......................
Demonstrate your answers
on a diagram.
27. The income effect of a price increase in the case
of an inferior good is ........................... but it is ...........................
than
its substitution effect.
Demonstrate your answers on a diagram.
28. The income effect of a price reduction in the
case of a Giffen good is .............................and
..............................
than its substitution effect. Demonstrate your answers on a diagram.
29. What is the common identification problem in estimating market demand? How do we deal with this problem?
30. Between 1990 and 1998 BBC’s sales have increased
from $1,200,000 to $2,400,000. (a)Calculate the average linear
annual rate
of increase ( assuming St = So +bT ) in the company’s sale. (b)Calculate
the constant annual growth rate
of the company’s
sales ( assuming St = So(1+g)T ).
Qd = 100 - 10 P
Qs = -10 + 12 P
A. What are the equilibrium price and quantity in this market?
B. Show your work on a diagram.
C. What will happen if a price ceiling of $4 is imposed on the
market?
D. What if that price ceiling is $6?
E. What will happen to the equilibrium price and quantity if
the demand function is changed to:
Qd = 166 - 10 P
Show you work on a diagram.
2. ABC Shoes faces the following demand function:
P = 100 - 2.5 Q
It has estimated its daily cost
function to be:
TC = 50 + 10 Q
a. Write the firm's total revenue function, and show it on a diagram. Hint: TR = P.Q
b. Write the firm's total profit function.
c. Write the average and marginal profit functions.
d. At what level of output do the average and marginal profits become equal?
e. Determine the profit maximizing level of output. Show your work.
f. Determine the revenue maximizing level of output.
3. 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?
4. 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?
d. Keeping the advertisement
level the same (at five), calculate the point (price) elasticity of demand
at the above
price.
5. Comfort Shoes faces the following demand
function:
P = 158 - 3 Q
It has estimated its daily cost
function to be:
TC = 40 + 8 Q
a. Write the firm's total revenue function, and show it on a diagram. Hint: TR = P.Q
b. Write the marginal revenue equation.
c. Determine the profit maximizing level of output. Show your work.
d. Determine the revenue maximizing level
of output.
6. You have just inherited $1000,000 and are considering a number of investment possibilities. Among the investment projects offered you is a service/gas station whose present owner is asking exactly $1000,000 for it. The information he has provided you indicates that the sales and the expenses of the station have been relatively stable for the past 10 years. In fact, the present owner claims that he is so confident about the performance of the station that he is willing to provide the buyer with a money-back guarantee after three years. That is, after three years, if the buyer is not satisfied, he would buy the station back from him/her at exactly the same price. Based on the information given to you, you have estimated the annual costs and revenues of the station for the next three years as follows:
Revenue
Cost
Year 1 $500,000
$460,000
Year 2 550,000
480,000
Year 3 600,000
520,000
Assuming a 10 percent discount (interest) rate, what price would you put on this station? Would you buy it?
1.
Jack's Auto Shop is evaluating its operation to find out if it should invest
in a new diagnostic computer or in a new tool set
to increase its production capacity. The new
computer would cost $5000. The new power tool set would cost $1500.
Jack's accountant has calculated the financing
and depreciation cost of the computer to be $150 per week. The weekly
financing and depreciation cost of the tool
set has been calculated to be $50. Jack estimates that, with no other
change in
its operation, a new computer would increase
his production capacity from
the present average of 20 cars per week to
35. Whereas, the new tool set would increase it to 25.
Should Jack buy
the computer or the tool set?
Now suppose
that if along with the new computer Jack would hire a diagnostics specialist,
at a salary of 300 per
week, his capacity
would increase to 60 cars per week. An additional worker hired along with
the new power tool
set, at a weekly
salary of $200, would increase Jack's production capacity to 30. What is
your recommendation
now?
2. Consider
the following production function:
Q = 1000 K L - 20 K L 2
Assuming K =
200, calculate the output, Q, marginal product of labor, and average product
of labor for the
following levels
of labor:
L =10, L =15, L = 20, L =25, L=30, L=35
a. At what level of labor is the marginal product of labor equals zero?
b. What is the
average product of labor when the marginal product of labor reaches zero?
3. Based on the production table below answer the questions that follow.
Capital 1 2 3 4 5 6
Labor
1 ................. 30 ...... 32 ...... 36 ..... 38 ...... 39 ......
39
2 ................. 34 ...... 37 ...... 40 ..... 42 ...... 43 ...... 43
3 ................. 38 ...... 44 ...... 48 ..... 50 ...... 51 ...... 51
4 ................. 40 ...... 48 ...... 54 ..... 57 ...... 59 ...... 60
5 ................. 41 ...... 51 ...... 56 ..... 60 ...... 62 ...... 63
6 ................. 41 ...... 53 ...... 57 ..... 62 ...... 64 ......
65
Given the capital level 3, calculate the average and marginal
product of labor.
Given the labor level 4, calculate the average and marginal
product of capital.
If the price of labor is $10 per unit, and the price of capital
is $15 per unit, what combination of capital and labor would you
use to produce 60 unites of output?
What kind of returns to scale does this table show?
4. Ellen and Kevin work for the college's tutoring center as economics tutors. Ellen's hourly wage is $4 and Kevin's is $3. The total weekly budget for economics tutoring is $24. The tutoring center has estimated the (weekly) marginal products of these two tutors in terms of the number of students tutored per hour. These estimated marginal products are listed in the table below.
HOUR:
1st 2nd 3rd 4th 5th
6th
MPe (Ellen):
10 9 8
6 4 2
MPk (Kevin):
12 10 8
5 2 0
a. What is the general rule to determine the optimal mix of inputs.
b. Determine for how many hours each of the two tutors should be hired
each week, to maximize your output (the number of students tutored). Note
that you have only $24 to spend.
c. Now suppose both Ellen and Kevin are paid $4 per hour. How many
students can the center serve in this case?
5. The consultants of a medical clinic have determined that,
in that clinic, the hourly marginal product of a doctor is 4(patients),
while the marginal product of a practical nurse is 2. The clinic’s hiring
policy has always been to hire two nurses for each doctor on its staff.
Presently the clinic is staffed with 4 doctors and 8 nurses. The hourly
wage of a doctor is $200, whereas a nurse is paid $50 an hour.
a. Is the clinic hiring policy economically efficient? Explain.
b. Under what conditions would the clinic’s hiring policy be efficient.
c. What do you recommend that the clinic do?
6. Consider the following production function:
Q = f ( K , L) ; Q = output
K = capital
L = labor
a. Assuming a given level of output, explain how the firm decides
what mix of labor and capital to use to minimize its cost.
b. Demonstrate why a change (say an increase)in the price of one of the inputs, ceteris paribus, will cause the firm to alter the combination of its inputs.
7. AAA Airline runs a shuttle program between Washington, D. C. and New York City. At the round-trip ticket price of $250 the airline flies 1800 passengers a day. The full capacity of the shuttle flights is 2000. The elasticity of demand for this service has been estimated to be -.90 . What price should the airline charge to increase the number of its daily shuttle passengers to the full capacity?
8. A firm faces the following demand function:
Q = 24 - .2 P
and its total cost function is:
TC = Q3 - 16 Q2 + 80 Q + 50
d. At what level of output is the firm’s total revenue maximized?
e. At what level of output is the firm’s profit maximized?
f. Calculate the firm’s profits at both levels of output.
******************************
Solution:
(a)
P = 120 - 5Q ; TR = P.Q = 120 Q - 5 Q2 ; MR = 120 - 10 Q = 0 ; Q = 12
(b)
MC = 3 Q 2 - 32 Q + 80 ; Set MR = MC
120 - 10 Q = 3 Q 2 - 32Q + 80
===> 3 Q 2 - 22 Q - 40 = 0
===> ( Q - 8.7 )( 3 Q + 4.6 ) = 0 ( or use the quadratic equation)
===> Q = 8.7
or Q = -1.5
(We ignore the negative quantity. )
(c)
When Q = 12 , TR = 720 , TC
434 , Profit = 286
When Q = 8.7 TR = 665.5 ,
TC = 193.5 , Profit = 472
***********************
9. Armstrong Corporation makes a special type of (patented) exercise
machine. Presently, at the price of $1600 per set, they sell 200 machines
per week. The company’s marketing strategists have estimated the price
elasticity of the demand for Armstrong machines to be -1.20. In order to
boost sales the company lowers its price to $1500. How many units does
the company expect to sell at this new price? Is this a good marketing
strategy? Briefly explain.
10. Payless Tax Services (PTS)hires temporaries during the tax
season to meet the higher demand of the season. The average hourly wage
of a temporary tax preparer is $20. The following table shows the (daily)
levels of output of temporary workers for different levels of input (temporary
staffing).
Temporary Hours Hired Total
Number of Clients Served
4
12
8
22
12
30
16
36
20
40
24
42
a. Assuming that PTS charges $15 for each tax return, as a profit maximizing firm, how many hours of temporary worker should the firm hire?
b. What if they (PTS) raise their price to $20?
11. Nutribase Cosmetics, a producer of cosmetic products, introduces a new facial cream to the market, claiming that it reduces wrinkles. The product was developed by the company's research and development division and has been patented. The Marketing Department has estimated the following demand for the product:
Q = 12 - .5 P
The cost of production and sale (total cost) has also been estimated:
TC = 5 + 3 Q + .1 Q2
a. Write the product's marginal revenue.
b. Carefully plot both MR and the demand curve.
c. Assuming that the firm initially behaves like a monopoly,
determine the quantity and the price at which the company's profit (on
this product) is maximized.
d. Calculate the profit at this output level.
e. How much would the company produce and what price would it
charge if it behaved like a competitive firm?
Now suppose that, as a result of the success of this product, other companies in the industry introduce similar products to the market and advertise them as having the same effect as the Nutribase anti-wrinkle cream while being less expensive. Faced with competition and rapidly declining sales, the company's marketing department estimates a new demand function for the product:
P = 11 - 1.5 Q
It also suggests that since most of the product's R&D expenses have
already been depreciated the production of the cream does not have any
fixed cost and, therefore, they adjust the cost function as follows:
TC = 3 Q + .1 Q2
f. Assuming that the company no longer pursues a profit maximization
goal but, instead, it wants to keep as much of its market share as it can,
without incurring a loss, determine what price it should charge and the
quantity it should produce.
12. The (short-run)weekly production function of ABC Accounting
Company is as follows:
Q = 20L -.5L2
where Q is the number of clients, and L represents the number of accountants.
The average weekly charge (price) for each client is $200. The going weekly wage for an accountant is $800.
a. What is the marginal revenue product of this firm?
b. Assuming that the firm is a profit maximizer,
how many accountants should it hire.
c. Assuming that ABC’s weekly fixed cost is $4000,
determine its weekly profit.
13. The following a simple production function for a manufacturing firm:
Q = 4 K .6 L .5
a. Assigning values to K and L, make a production table for
K = 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10,
and L = 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.
(Round your numbers to closest one)
b. Determine marginal and average product of labor for K = 7
c. Is this function exhibiting increasing, decreasing, or constant returns to scale?
d. Plot a set of isoquant map approximating your production table.
e. Can you demonstrate the marginal rate of (technical ) substitution along one of your isoquants?
14. With the aid of a diagram demonstrate and explain the properties
of a frm's long-run equilibrium in a perfectly competitive
market.
Explain why economists consider such
an equilibrium “efficient”?
15. Explain and compare the profit maximizing behaviors of a
perfectly competitive firm and a monopoly. What makes them
different, and why do economists
argue that monopolists are not economically efficient?
16. A small landscaping operation uses 40 units of labor and
10 units of capital. At this combination of labor and capital the
marginal product of labor is 4 units of output.The
price of labor is $5 (per hour), whereas the price of capital is $8.
a. Assuming labor is the variable input, determine the
marginal cost (of the output) at this level of operation.
b. If the mix of capital and labor at this level of operation
is optimal, what is the marginal product of capital?
c. Now suppose the price of labor is increased to $7. Assuming
that the firm wants to maintain its level of output at the present
level, while maximizing profit, what kind of change
should the firm make in its use of resources? Be specific in your reasoning.
1. The results of our estimation of the nonlinear function Y = aXbZc is as follows:
a= 30; b = 1.2 ; c = -.6
a. Determine the value of Y for X = 100 and Z = 40.
b. By what percentage will Y increased if X increased by 5 percent?
c. What is the elasticity of Y with respect to Z?
2. The following linear demand specification is estimated for Conlan Enterprises, a price-setting firm:
Q = a + bP + cM + dPR
where Q is the quantity demanded of the product Conlan Enterprises sells, P is the price of that product, M is income, and PR is the price of a related product. The results of the estimation are presented below:
DEPENDENT VARIABLE: Q
R-SQUARE
F-RATIO
P-VALUE ON F
OBSERVATIONS: 32
0.7984
36.14
0.0001
VARIABLE
PARAMETER STANDARD
ESTIMATE ERROR
T-RATIO
P-VALUE
INTERCEPT
846.30
76.70
11.03
0.0001
P
-8.60
2.60
-3.31
0.0026
M
0.0184
0.0048
3.83
0.0007
PR
-4.3075
1.230
-3.50
0.0016
a. How many degrees of freedom do we have in this regression analysis?
b. Evaluate all estimated coefficients based on their t-statistics.
Be specific.
c. What is the critical value of F-statistic at the 1% level of significance?
Based on this
statistics, what can you conclude about the
results of this regression?
d. Assuming that the income is $10,000, the price of the related good
is $40, and Conlan chooses to set the price of this product at $30, detremine
the following:
Qt = a + bt + cD
The equation is estimated using quarterly data from 1990I-1999III ( t = 1,..., 43). The variable D is a dummy variable for the second quarter where:
D = 1 in the second quarter, and 0 otherwise.
The results of the estimation are:
DEPENDENT VARIABLE: QT
R-SQUARE
F-RATIO
P-VALUE ON F
OBSERVATIONS: 43
0.8644
127.5
0.0001
VARIABLE
PARAMETER STANDARD
ESTIMATE
ERROR
T-RATIO
P-VALUE
INTERCEPT
22.5
9.32
2.41
0.0204
T
1.86
0.55
3.38
0.0016
D
2.0
0.71
2.82
0.0075
a. Evaluate the overall regression results based on the estimated R-square
and the F-statistics. Be specific.
b. At the 1 percent level of significance, is there a statistically
significant (time) trend in
sales? Explain.
c. What are the estimated intercepts of the trend line in the second
and third quarter?
c. Using the estimated trend line, what are the predicted levels of
sales in 1999IV and
2000I ?
4. Along an indifference curve a consumer’s combinations of good X and good Y are as follows:
Y X
10
120
20
60
30
30
40
10
a. What is the marginal rate of substitution of the 30th unit
of X?
b. If the price of X is $3 and the price of Y is $12, and the consumer
is consuming 30 units of each, what is the consumer’s income?
c. Can this consumer do better (increase her utility) by changing her
consumption mix? How? Explain.
5. Consider a consumer with a weekly income of $60. Suppose there only two goods in this consumer's consumption basket: A and B. The price of A is $4, while the price of B is $6.
a. Carefully draw the consumer’s budget line (income constraint) on
a diagram.
b. By adding a set of indifference curves (assumed to reflect this
consumer's utility function) to your diagram determine the quantities of
A and B this consumer purchases each week.
c. Now suppose that the price of good B increases to $12. Show the
effect of this price change on the consumer’s mix of consumption.
d. Is good B a normal or an inferior good? Demonstrate your answer
on the diagram by referring to the income and substitution effects of the
price change.
6. Consider the following production function:
Q = 1000 K L - 20 K L 2
Assuming K = 200, calculate the output, Q, marginal product of labor, and average product of labor for the following levels of labor:
L =10, L =15, L = 20, L =25, L=30, L=35
a. At what level of labor is the marginal product of labor equals zero?
b. What is the average product of labor when the marginal product of labor reaches zero?
c. If the price of one unit of labor (wage) is $60 and the price of one unit of capital is $10, what are the total cost, the average total cost, and the marginal cost at the labor level of 25?
7. The production function of a law firm has been estimated as follows:
Q = a Kb Lc
Where a = 5 , b = 1 , c = 1.5
a. Assuming the capital level (K) is 25 and the firm wishes to produce1000
(one thousand) units of output, how many units of labor should the firm
hire?
b. What is the marginal product of labor at this level of output?
c. What is the marginal product of capital at this level of output?
d. Suppose the price of labor is $60 and the price of capital is $10.
Are the levels of labor and capital optimal? In other words can the firm
increase its output without increasing its cost? Explain.
e. If you double both inputs, how much will the output increase?
f. Does the production function demonstrate increasing, decreasing,
or constant return to scale?
g. Calculate the firm's long-run average (total) cost at the following
combinations of capital and labor:
K
L
12
3
16
4
20
5
24
6
What kind of observation can you make about the long-run cost function of this production function?
1. Beaver Head Beer Inc. (BHB) is one of the few beer producers in
the market. Anticipating the reaction of its competitors, BHB speculates
that if it raises its price, Q = 90 - 2 P will be the demand curve it would
face. On the other hand, when lowering its price, it expects its
demand curve to be Q = 63 - .5555 P .
BHB's total cost function is:
TC = 26 + 20 Q + .2 Q2
a. Plot the two demand curves and explain the type of market
BHB is operating in.
b. Determine BHB's level of production.
c. Determine its price and profit at this level of output.
d. Write the firm's marginal cost function.
e. Determine the range of marginal costs within which the
firm is not likely to change its price.
2. Almost Like Spring Water (ALSW) bottling company has one plant, centrally located, which supplies all of its market. ALSW has estimated the cost function of this plant as follows:
TC = 14400 + 24 Q + .04 Q2
The company has also estimated the demand for its bottled water:
P = 600 - .01 Q
a. Assuming that ALSW supplies all of its market by expanding production at its existing plant, what is the profit maximizing level of output? Determine the company's profit.
b. The company's financial manager suggests that, given the size of its market, ALSW should expand into a multiple-plant production system. Do you agree? If yes, how many plants (of the same size) should the company open?
c. What will be its total profit under a multiple-plant system?
3. (More challenging) Icework Inc. is the single producer of small
refrigerators in a small country that does not allow refrigerator imports.
The monthly demand for small refrigerators in this country is depicted
by the following equation:
Q = 2 400 -16 P
The firm’s cost function is:
TC = 1200 + 30 Q + .05 Q2
i. Determine the price and the profit of this monopoly.
ii. Suppose that the company realizes that it can export
its product at the world (market) price while maintaining its monopolistic
position at home. What is the minimum world price that would make export
feasible for this monopolist?
iii. Now suppose the world price is $100. Is this price high
enough to allow the company to export? If your answer is yes, determine
the following :
• The quantity of export
• The quantity sold at home
• The domestic price
• the firm’s profit
• The welfare effect of the export on the country in
terms of the change in the producer surplus (profit) and consumer surplus.
4. The production function of a firm is : Q = L1/2. The firm operates in competitive market in which the price of its product is $100. That is
P = 100
Assuming the market wage is $5, how many units of labor will
this firm employ?
5. Kevin has a small landscaping operation with the following cost function:
TC = 200 + 10 Q +.02 Q2
He has two customers, A and B, with different demand function.
Customer A’s demand: Q = 40 - P
Customer B’s demand Q = 60 -2 P
a. If Kevin can price-discriminate, determine the price he should
charge each customer.
b. Determine and compare the price elasticities of the two customers
at these prices.
c. Determine Kevin's profit.
d. Try to show your work on a diagram.
6. A small fruit juice company has two plants. One plant (Plant 1) is an older plant and the other ( Plant 2) is a somewhat more modern plant. Their cost functions are as follows:
Plant 1 : TC = 50 + 100 Q + .5 Q 2
Plant 2 : TC = 100 + 150Q + .25 Q 2
The firm faces the following demand:
Q = 4000 - 5 P
a. Assuming that the firm is maximizing its profit, determine the
amount of fruit juice the firm should produce in each plant.
b. Determine the firm’s profit.
c. Try to show your work on a diagram.
SW
Answers
a) Q=26.66 P= 7.33
b)Graph c) 86.6 d) Q= 40
e) P = 6 f ) Profit = 60 g) Set
the lope pf ATC function
(curve) equal
to the slope of the demand curve (-.10). ==> Q = 11.54, P =
4.31 i) P = 5.46 -.10 Q
Answers
a) P = $13,333.33 b) Q = 1,333.33
c) Profit = $5,111,104 d) The marginal revenue at the
kink:
Upper = 10,666.66
Lower = 6,666.66
Old MC = 8000 , New MC = 10000
No, MC still within the range.
e) This will reduce Ford's profit by 2000x1333.33
= 2,666,660; The new profit level = $2,444,444
Answers
a) P = 800
b) Q = 1000 c)* (Point
) E'p - 2 , (Point) Ep = -4
d) Profit = 359,400 e) MC = 340 + .2 Q =
540
f) 400 and 600
* You may get slightly different figures if you
use the arc elasticity formula.