Temple University

Department of Economics

Solution to the Consumer Surplus Problem Set

The demand curve can be written as Q=20-.8P or as P=25-1.25Q. For purposes of drawing graphs as we conventionally do them the latter representation is more useful. The supply curve can also be written two ways: Q=-4+.4P or P=10+2.5Q. For graphing purposes the latter is easier to work with.

Setting quantity demanded equal to quantity supplied we get

20-.8P=-4+.4P

24=1.2P

P=20

Substitute P=20 back into the demand curve to get **Q**=20-.8(20)=**4**. The
equilibrium price and quantity are shown in the diagram below.

- Consumer surplus is the area under the demand curve but above the going price. In the diagram consumer surplus corresponds to the area of the yellow triangle. The area of a right triangle is found from formula area=(1/2)*base*height. In this example the base is 4, the height is 25-20=5. Therefore consumer surplus is .5*4*5=10.
- There are ten identical consumers. If total market demand at P=$20 is 4 then each consumer must have purchased .4 units. Similarly, at a price of $24 the total quantity demanded is .9, therefore each consumer must have purchased .09. At a price of $25 no one buys anything. Applying the notion of consumer surplus to the individual, gives us CS=.5*(.4)*(25-20)=1. The conclusion is that each buyer has a consumer surplus of 1. That is the most any one of them would be willing to pay to become a member.
- Having to pay a ‘membership fee’ will
**not**change any individual’s final demand for the product. Why? At a price of $25 no one would purchase anything. When the price falls to $24 then buyers will purchase .9 units. At the market clearing price of $20, those who would have paid $24 for the first .9 units feel as though they got a bargain. They ‘saved’ .9*(24-20)=$3.60 by virtue of the fact that they need only pay the market price. Suppose we now inform this group that although they only have to pay $20/unit for their purchases of .9 units they must also pool their resources and pay a membership fee of $3.60. Their total expense is 20*.9+3.60=$21.60. As far as this first group of consumers is concerned this is no different than the $24/unit they would have paid for the first .9 units in the first place, .9*24=$21.60.