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workouts chapter 14 solutions

# workouts chapter 14 solutions - 182 CONSUMERS SURPLUS(Ch 14...

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Chapter 14 NAME Consumer’s Surplus Introduction. In this chapter you will study ways to measure a con- sumer’s valuation of a good given the consumer’s demand curve for it. The basic logic is as follows: The height of the demand curve measures how much the consumer is willing to pay for the last unit of the good purchased—the willingness to pay for the marginal unit. Therefore the sum of the willingnesses-to-pay for each unit gives us the total willingness to pay for the consumption of the good. In geometric terms, the total willingness to pay to consume some amount of the good is just the area under the demand curve up to that amount. This area is called gross consumer’s surplus or total benefit of the consumption of the good. If the consumer has to pay some amount in order to purchase the good, then we must subtract this expenditure in order to calculate the (net) consumer’s surplus . When the utility function takes the quasilinear form, u ( x ) + m , the area under the demand curve measures u ( x ), and the area under the demand curve minus the expenditure on the other good measures u ( x ) + m . Thus in this case, consumer’s surplus serves as an exact measure of utility, and the change in consumer’s surplus is a monetary measure of a change in utility. If the utility function has a different form, consumer’s surplus will not be an exact measure of utility, but it will often be a good approximation. However, if we want more exact measures, we can use the ideas of the compensating variation and the equivalent variation. Recall that the compensating variation is the amount of extra income that the consumer would need at the new prices to be as well off as she was facing the old prices; the equivalent variation is the amount of money that it would be necessary to take away from the consumer at the old prices to make her as well off as she would be, facing the new prices. Although different in general, the change in consumer’s surplus and the compensating and equivalent variations will be the same if preferences are quasilinear. In this chapter you will practice: Calculating consumer’s surplus and the change in consumer’s surplus Calculating compensating and equivalent variations Example: Suppose that the inverse demand curve is given by P ( q ) = 100 10 q and that the consumer currently has 5 units of the good. How much money would you have to pay him to compensate him for reducing his consumption of the good to zero? Answer: The inverse demand curve has a height of 100 when q = 0 and a height of 50 when q = 5. The area under the demand curve is a trapezoid with a base of 5 and heights of 100 and 50. We can calculate 182 CONSUMER’S SURPLUS (Ch. 14) the area of this trapezoid by applying the formula Area of a trapezoid = base × 1 2 (height 1 + height 2 ) .

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