Insert figure 4.1 here
We will derive the demand curve for food.
Price of food = $1
Price of clothing = $2
Income = $20
Given the above information, the consumer will maximize utility subject to their budget constraint at point B in 4.1. The consumer will be on U2. At the initial equilibrium level the consumer will have 4 units of clothing and 12 units of food. We will derive the demand curve for food. When the price of food is $1 the consumer purchases 12 units of food. This can be seen on the diagram 4.1b. Notice the horizontal axis in 4.1b is also food but the vertical axis is the price of food, which is different than the vertical axis in 4.1a.
Suppose the price of food increases to $2.
Draw the new budget line. Notice that the slope became bigger.
Remember the slope is the price ratio. The original budget line in
4.1 slope is 1/2, (Pf/Pc) now the slope gets bigger
and is equal to 1 (2/2). The consumer maximizes utility at point
A on indifference curve U1.
Why is the consumer on a lower indifference curve?
Notice the amount of food the consumer now buys when the price is $2 at equilibrium is 4 units. This is shown in the 4.1b at point E.
Trace out what happens if the price of food goes from the original $1
per unit to 50 cents per unit.
What is the slope?
Equilibrium now occurs at point D and the consumer buys 20 units of food when the price falls to 50 cents.
Notice how utility has increased when the price fell, why utility
increase?
We just derived an individual’s demand curve for food. It shows the inverse relationship between quantity demanded for food and the price of food holding all things constant. Notice income stayed the same at $20 and the price of clothing was the same at $2.
The line that connects all the equilibrium points for each price in 4.1a is called a price consumption curve. The price consumption curve shows all the equilibrium amounts of food and clothing. While the price consumption curve shows the inverse relationship between quantity demand of food and the price of food, the relationship between quantity of clothing and the price of food is not so consistent. Clothing may go up or down.
The demand curve shows two important properties of consumer demand.
First, the lower the price of a good the higher the utility. The diagram shows how the consumer goes to a higher indifference curve when price falls because at lower prices the consumer’s purchasing power increased thus making the consumer happier.
The second property shows that at every point on the demand curve the consumer is maximizing utility because she is satisfying the condition that the MRS (marginal rate of substitution) of food for clothing equals the ratio of price of food and clothing.
Explain why this occurs and why the MRS declines as we move down
the demand curve
You just explained why the MRS declines as you move down the demand
curve. But keep in mind what that is telling us. As you buy
more food you are willing to substitute smaller amounts of clothing to
get an additional unit of food. We know that diminishing marginal
utility tells us that as we buy more food we get less utility from each
additional unit of food. Since getting less additional utility we are willing
to substitute less clothing for the unit of food that gives us less utility.
Changes in Income
When income changes the entire demand curve changes. The direction
of the change depends on if the good is a normal or inferior good.
Insert Figure 4.2 here.
If Price of food is $1 and price of clothing is $2 and income is $10
then the first budget line shows the equilibrium amount of food and clothing
associated with U1. D1 is the demand curve that would
be associated with every price change in food. (Exactly what we did above.)
Point E just shows the amount of food at $1 with income of $10.
Suppose income increased to $20 while prices remained the same.
Notice how the budget line shifts out and the new equilibrium occurs on
U2 point B. D2 shows the demand curve for every
price level of food associated with a fixed income of $20. At the
same $1 price of food point G on the demand curve shows that 10 units of
food will be bought. The demand curve shifted out also. The
same thing will happen if income goes up to $30. Notice when income
goes up the entire demand curve will shift thus there is a change in demand.
The income consumption curve is the equilibrium level of food and clothing for every level of income holding the price of the good constant.
Insert Figure 4.3 here.
Using the income consumption curve explain how we can tell if the
goods are normal or inferior.
Note in figure 4.3, at lower income levels hamburgers are a normal good.
But as income increased hamburgers became an inferior good.
Why do you suppose this happens?
From the income consumption curve we can derive Engel curves, which shows the amount of the good purchased for different levels of income.
Insert figure 4.4 here.
Figure 4.4a shows a positively sloped Engel curve, which comes from the income consumption curve of 4.2a. Notice that this good is a normal good. That is, as income goes up the consumer will always buy more of the good. Figure 4.4b shows that the good is normal until income is $20, then it becomes an inferior good above income of $20.
What are some types of goods that might have an Engles curve that
looks like figure 4.4b.
Engels curves are used as a measure of poverty. The curves lead to what is called Engels law. Ernst Engel (1821-1896) a Prussian economist first noted that the proportion of total income (of a nation) that is devoted to food declines as income rises. Income spent on food is often used as an indicator of poverty. In the 19th century people spent over 50% of their income on food. Today Americans earning between $40,000 and $50,000 spend 14.7% of income on food. People earning over $70,000 spend 11.4% while people earnings between $15,000-$20,000 spend 15.4%.
How can we tell if goods are substitute goods?
How can we tell if goods are complements?
Goods are independent if the price of one changes and there is no effect and the quantity demanded of the other.
The price consumption curve also tells us if the goods are substitutes or complements. In figure 4.1a when the price consumption curve has a negative slope it shows that when the price of food went up from $1 to $2 (equilibrium point B to A) the consumer bought less food but more clothing. Thus the two goods are substitutes. When the price consumption curve has a positive slope the goods are complements. That is, when the price of food declined from $1 to 50 cents the consumer bought more food and more clothing.
Remember when the price of one good changes, the demand curve for the other good changes. The direction of that change depends on if the goods are substitutes or complements. The equilibrium quantity of the other good changes when that goods entire demand curve changes.
We will examine in more detail how a change in the price of a good can affect consumer demand. In essence we want to explain the law of demand in a more theoretical manner. We do this by examining the substitution and income effects.
Substitution and Income Effects
When the price of a good falls there are two effects that both occur at the same time.
What is the substitution effect?
What is the income effect?
It is important to remember that when price falls both the income and substitution effects occur together. But it is easier to see how it all works if we discuss effect separately then combine them. First let’s examine exactly what happens when the price of a good falls and how our analysis shows the total effect on quantity demanded. That is, price goes down quantity goes up. We will then break down the two effects one at a time.
Insert figure 4.6 here.
Notice the consumer starts out at equilibrium at point A on indifference
curve U1 which is tangent to the budget line RS. The amount of food
the consumer purchases is F1.
If the price of food falls we see the budget line pivots out to RT.
Note the amount of clothing does not change on the vertical axis but if
we spent all income (that didn’t change either) on the cheaper food we
would be able to purchase more food (F2). The new equilibrium
occurs at point B on indifference curve U2.
Why is the consumer on a higher indifference curve when the price
of food declined?
Thus we see in figure 4.6 the price reduction of food caused the consumer to purchase more food which is equal to the line segment F1 F2. This is called the total effect because it is showing the total increase in quantity demanded of food when the price of food falls.
This line segment can be broken down into two effects, the substitution and income effects.
Substitution effect
Keep in mind that when we talk about the substitution effect resulting
from a decline in price, the level of utility is staying the same. That
is, we stay on the same indifference curve. The reason we stay on
the same indifference is to show that when the price of food declines food
is relatively cheaper than clothing and the consumer substitutes the relatively
cheaper good food for clothing. Thus the consumer is just moving
along the original indifference curve.
Remember the end result was that the consumer was on a higher indifference curve due to real income going up. The increase in real income was shown by the budget line pivoting to line RT.
Suppose we can take away just enough of the consumers income (money
or nominal) so that their utility did not change, that is take away enough
income to just offset the increase in real income so that the consumers
utility does not change. Thus the consumer will stay on the original
indifference curve. This is accomplished by creating the imaginary
budget line in figure 4.6.
Here is how we create the imaginary budget line. The final budget
line is RT. We also know that if income were taken away from the
consumer a new budget line that is parallel to RT would shift it to the
left. It is parallel because income declined (prices did not change
the price ratios are the same for parallel lines). The amount of income
that must be reduced is just enough so that we end up back on the original
indifference curve. So the imaginary budget line keeps declining
just until it is tangent to the original indifference curve U1.
Notice this occurs at point D. The amount of food that the consumer
buys at point D is E. The distance F1 (original food purchase)
to point E is due to the substitution effect.
Note since the consumer is on the same indifference curve they are neither better nor worse off. Going from point A to D at equilibrium show the consumer will purchase more food (and less clothing) and goes from F1 consumption of food to E. There is always an inverse relationship between price of food and consumption of food due to the substitution effect.
This negative relationship due to the substitution effect occurs because indifference curves are convex. Note that when the price of food declined the slope of the new budget line was flatter (smaller). Because the indifference curve is convex (slope getting smaller as you move down the curve) then the new flatter (smaller sloped) budget line has to be tangent to the original indifference curve somewhere to the right of the old equilibrium. Thus there is always an inverse relationship between price and quantity due to the substitution effect.
Income Effect
The income effect tells us the change in food consumption due to a reduction of price. This reduction is caused strictly by the change in purchasing power from the lower price of food. While we know that the substitution effect will always show the inverse relationship between quantity and price we don’t always know how the income effect will effect quantity when price changes. When we constructed the imaginary budget line we took money income away from the consumer. We did this to offset the gains in real income, which moved the consumer to the higher indifference curve. This would put the consumer back to the original indifference curve.
Now suppose we gave the consumer that income back! That is the income effect.
In figure 4.6 the income effect is going from E to F2. That is from where the consumer’s consumption of food due to the substitution effect, to the final amount the consumer buys.
In 4.6 how do we know that the good is a normal good?
Insert figure 4.7 here.
This figure shows the income and substitution effect for an inferior good. Remember we know a good is inferior if income goes up the consumer buys less of the good.
The total effect is going from F1 to F2. The substitution effect works the exact same way thus going from F11to E. But since this is an inferior good when real income went up the consumer buys less of the good. So consumption goes down from E to F2. Thus the income effect offsets some of the increases in consumption due to the substitution effect. Nevertheless, we see the substitution effect will always dominate the income effect so that the law of demand holds.
Giffen Good.
It is possible (though extremely rare) that the demand curve doesn’t have a negative slope. When this occurs that means that the income effect is stronger than the substitution effect.
Insert figure 4.8 here.
Notice the total effect shows that food consumption went down when the
price of food went down.
Sometimes in very poor countries we might see a Giffen good. In fact Giffen who was an Irish economist, noticed in the 19th century during the Irish potato famine that potatoes were an inferior good and that the income effect dominated. Potatoes were a staple of the Irish diet. The Irish potato famine caused prices of potatoes to rise (reduced supply). Real income declined. In Ireland at that time people started buying more potatoes. The reason was that prior to the famine people might have had potatoes 6 times a week for diner and on Sundays they would have meat and no potatoes. Because of the famine prices went up. But since they were having potatoes 6 times a week already (the major food staple) they had to spend more of their income on potatoes and didn’t have enough money left over to buy meat on Sunday. So instead they had potatoes on Sunday. Thus the price of potatoes went up they bought more. We can see how this might happen in very poor countries.
Market Demand
Insert table 4.2 and figure 4.10 here.
The market demand curve is found by horizontally summing all the individual demand curves. An application would be if a Corona beer manufacturer wants information about the demand for their beer. They can look at the demand for beer by college age students (high), then look at demand for corona for single individuals not in college, then look at demand for males, and demand for females. They would simply add all these demands together.
Elasticity of Demand (again)
We just discussed, in great detail, how to derive the demand curve. It is therefore useful to review elasticity again.
What does the elasticity of demand tell us?
The price elasticity of demand is
Ep = (DQ/Q)/( DP/P) = (P/Q)( DQ/DP) 4.1
If this is less than 1 then it is called inelastic, which means quantity demanded is not very responsive to changes in price. The percent change in Q is less than the percent change in P. (numerator is less than denominator)
If it is greater than 1 then it is called elastic, which means quantity demanded is responsive to changes in price. The percent change in Q is greater than the percent change in P.
Firms can also look at the amount of total revenue they receive when price falls (and quantity increases) to determine if the good is elastic or inelastic. This is useful because it saves the firm the trouble of actually calculating the exact elasticity it can just examine total revenue and see if elasticity is greater than or less than one.
Remember total revenue (TR) = P*Q. Note the same price and quantity that we use in calculating elasticity.
Thus if price is lowered, the firm will sell each unit for less thus a portion of their revenue will decline due to the lower price received for each good. But at the same time when they lower price they will sell more quantity (Q). Thus the loss of TR due to charging less per unit is offset by the gain in TR due to selling more Q.
How big of an offset tells us if the good is elastic or inelastic.
Inelastic. When price falls the percent change in Q is smaller than the percent change in P. So the thing that is causing TR to fall (lower price) is greater than the thing that is causing TR to rise (Q). TR falls as a result of the lower price. Thus if a firm simply multiplies P*Q if price falls and TR also falls then we know the firm is facing an inelastic portion of the demand curve.
Elastic. On the other hand if elasticity of demand is greater than one that means the percent change in Q is greater than the percent change in price. So if price falls some TR will be lost due to a lower price received for each unit sold. But the firm sells more goods (Q ) and TR is increased due to selling more Q. If this increase in TR due to selling more Q is more than the decrease in TR due to the lower price then TR increased when price fell and the good is elastic. Thus TR rises when price falls for an elastic demand curve. If price increases and firms receive more revenue for each unit sold. But they sell fewer units and the reduction of TR (due to less Q being sold) is greater than any gains in TR due to higher prices. If this happens, that is TR and price move in the opposite direction then demand is elastic. If TR and price move in the same direction then demand is inelastic.
If total revenue doesn’t change at all that means the percent change in Q is exactly the same as the percent change in price and elasticity is equal to one, which we call unitary elastic. Table 4.3 summarizes this.
Insert Table 4.3 here.
All this is very important because ultimately the decision of the firm to change prices is to increase profits. Thus if the firm is faced with an elastic demand curve raising prices will lower TR. Since profit = TR-TC then raising prices, which lowers TR, which lowers profit doesn’t accomplish anything and should not be done. However, if lowering price causes TR to rise then profit can be increased. Thus a firm facing an elastic demand curve should not increase the price of their product because TR will fall. Instead it should lower price.
On the other hand, if demand is inelastic (perhaps there are very few substitutes for your product or there is not too much time to shop around for another good like the day before Christmas) then the firm should raise prices. Because in doing so TR goes up since inelastic demand. If TR goes up (assuming costs stay the same) then profit will increase.
We did the followering material in chapter two. I will leave it on the web if you want to review it.
We will now explain why when calculating price elasticity arc elasticity should be used rather than point elasticity.
In equation 4.1 DQ/DP
is 1/slope thus
Ep = (P/Q)(1/slope) slope equal DP/DQ
Suppose a demand curve is graphed from the following schedule.
Q
P
1 6
10 4
20 2
30 0
The absolute change would be the following. The change in quantity from
1 to 10 is 9 while the change in price from 6 to 4 is
2. The absolute change is 9/2. However the percent change is very different.
To calculate the percentage change we use the following formula where Q1 is the first quantity and Q2 is the second quantity and P1 is the first price and P2 is the second price. Thus if we want to find the elasticity between the price of $6 and $4 we would use the following.
q2 -
q1
q1 - q2
--------
--------
E=
q2
Or q1
--- -----------
-----------------
p2 -
p1
p1 - p2
-----------
-------------
p2
p1
now q2 is 10 and q1 is 1 while p2 is 4 and p1 is 6.
Plug in the numbers in both formulas to see what you get.
Before you do this notice that the elasticity has to always be a negative number. Mathematically this is so because either the numerator or the denominator will be a negative number. After you plug in the numbers make sure you see that this number has to be negative from a mathematical point of view.
From an economic point of view it has to be negative because the demand curve has a negative relationship.
We will ignore the negative sign and simply present the absolute value of the elasticity that is the elasticity will always be a positive number.
Just ignore the sign of the fraction and make it a positive number or you can just multiple the negative fraction by -1 so that the elasticity is a positive number.
If you plug the numbers in the first formula you get:
10
-1
9
--------
--------
9
E=
10
=
10
= -----
-----------
-----------
5
4-6
2
--------
------
4
4
If you plug the numbers in for the second formula see what you get.
1
-10
9
------
-----
1
1
E = ----------- =
------------- =
27
6 -
4
2
-----
-----
6
6
Thus we see the price elasticity between $6 and $4 can be either 9/5 or 27 depending on which formula you use.
The question is which one is correct? Both are correct so to get around that problem we use the average of the two quantities and prices. That is the midpoint of the relevant price range. The formula we will always used and is called the arc elasticity of demand while the other is called the point elasticity of demand.
q2 - q1
------
q2 + q1
--------
2
E
=
---------------
p2 - p1
--------
p2+p1
-------
2
Or Ep = (DQ/DP)(AVG(P)/AVG(Q)
Since we are talking about the price elasticity between $6 and $4, calculate it now.
Simply plug in the numbers.
Notice the elasticity is 41/11 or 4.09
Now calculate the elasticity between $4 and $2
Calculate the elasticity between $2 and 0
It is important to note that the elasticity varies between different price ranges.
Consumer Surplus.
What is consumer surplus?
Demand curves are important because they provide information about how willing consumers are to make transactions. That is, they tell us how much a consumer is willing to spend on goods. If prices are to change we can see how that effects consumer’s overall welfare. Consumer surplus helps us determine that.
If you look at a demand curve (see figure 4.14) we note that each point on the demand curve is actually showing what a person is willing to pay for one more unit of the good. The negative slope of the demand curve tells us that the “marginal willingness to pay” declines as a person consumes more units of a good.
Insert figure 4.13 and 4.14 here.
In figure 4.13 we are just showing the steps of a demand curve as the price changes. Figure 4.14 looks more like what we are used to seeing without the individual steps being emphasized like in figure 4.13.
The consumer is willing to pay $20 for one ticket, $19 for the second ticket and $18 for the third ticket. Thus the consumer values the third ticket less than they value the 2nd and 1st ticket. This really gives us a lot of information about a consumer’s willingness to pay for different amounts of tickets.
Suppose the market establishes the price of tickets to be $14, which is shown in figure 4.13. This simply means that the consumer will pay $14 for every ticket they buy and in this example she is willing to buy 6 tickets at $14 each.
The first ticket, which she pays $14 for, but was willing to pay $20. Thus she gets a surplus of $6. The second ticket she was willing to pay $19 but only pays $14 thus gets a surplus of $5, do this for each ticket up to 6 tickets and add up all the surpluses and we see consumer surplus is $21 = 6+5+4+3+2+1.
If we just make the demand curve a straight line without the steps then we see consumer surplus is the shaded area (triangle) above the price and below the demand curve.
Remember the area under a triangle is ½ * length * width.
The market demand is summing all the individuals demand for tickets. Figure 4.14 shows this and tickets are measured in thousands. Note at $14 the market want 6500 tickets. Thus consumer surplus is .5*6*6500= $19,500. The $6 is the difference between $20 and the price the consumers pay $14.
The concept of consumer surplus can be used in determining how much money people are willing to pay to reduce pollution.
Insert figure 4.15 here.
People are willing to pay higher prices for a house if the air in the area in which they are living is cleaner. Studies have been done to estimate how much they are willing to pay to have cleaner air. There have been many environmental laws to clean up the air and these cleanups are very expensive. Are the costs of these cleanups worth it?
Consumer surplus helps answer this. Studies show that a homeowner
is willing to pay more for their house to live in areas with a reduced
amount of certain pollutant in the air. Figure 4.15 shows that to
reduce 5 pphm of pollution from the air the consumer would be willing to
pay an extra $1000 per unit thus the consumer would be willing to pay a
total of $5000. If they could only reduce pollution by one unit the
consumer would be willing to pay $2000. Each unit reduction we see
the consumer is willing to pay less and eventually pays $1000 per unit.
The consumer values the last one unit reduction at $1000 but the first
one unit reduction is valued at $2000. Thus we see the consumer surplus
is actually $2500. If we knew the cost of the clean up we can do
a cost benefit study to show all the houses which have a consumer surplus
of $2500 each and see how much people are willing to pay for the cleanup.
Network Externalities.
When one persons demand for a product is affected by other peoples
demand for the product. This is very different than just a demand
curve which is based on income, price, tasted and price of similar
goods. Now there are externalities. A positive network
externality occurs when the quantity of a good demanded by one consumer
increases as more people buy the good. This is called the
Bandwagon Effect
When a consumer wants the good that everyone else has there is a Bandwagon effect. This would be fads and stylish goods.
Figure 4.16
If consumer thinks only 20,000 people want good then D20 is demand
curve. Not too many people want the good so there is not much of an
incentive for you to want it if you are susceptible to fads and styles.
Now suppose the consumer thinks that 40,000 want the good.
Because you are susceptible to fads and styles, the good is more
attractive to you and you want to buy more of is so D40 becomes
the new demand curve If consumers think 60,000 people then D60
becomes the new demand curve and so on.
In figure 4.16 if the price was $30 then demand would be D40 because
40,000 people want it. If the price is $20 then we see that 80,000
people would want it. The market demand curve is the Demand curve
found by joining all the points that correspond to 20,000, 40,000
60,000 etc.
Note how the market demand curve is relatively elastic. Because
of the Bandwagon effect when the price drops more people want to buy it
so it is very responsive to changes in price. For example if
price drops from $30 to $20 look what happens on demand curve D40
Quantity goes from 40,000 to 48,000. But due to
bandwagon effect the market shows the quantity demanded going from
40,000 to 80,000 as it becomes more stylish because more people want to
own it. This is because of the Bandwagon effect.
The example of DVD and Text messaging, facebook ect are good examples
of Bandwagon effects. As a business you would want to promote the
concept of the hot new product.
The Snob Effect is an example of a negative network externality.
This is when the quantity demanded for good decreases in response to
the growth of a good.
As the name implies people act like snobs because they want the good
that very few people have. Thus one of a kind artwork, $2000 hand
bags etc. There is a certain amount of prestige and status from
owning something that no one else has.
Insert figure 4.17.
The snob effect shows that the demand curve will tend to be more inelastic.
D2 is the demand curve if consumers thought only 2000 people owned the
good. If consumers believed that 4000 people owned the good it
would be less exclusive and the snob value is reduced and quantity
demanded for the snob will be reduced and the curve D4 applies.
If consumers believe 6000 people want the good then D6 applies because
the snob value is reduced.
Because of the Snob effect the market demand is less elastic.
Here is why. If the price is $30,000 then 2000 people will want
the good. If the price is lowered to $15,000 then we see if there was
no snob effect Quantity would be 14000 along D2. But because it
is a snob good it’s value is reduced because more people own
it. Thus the snob effect cuts back the demand 8000 units. The net
increase in sales is only 6000 from 2000 to 8000. Firms
want to market a good to be a snob effect (trump apartments, high end
vodka) because then with the less elastic demand curve they can raise
the price.