# Homework 5 - Solution sheet.pdf - Intermediate...

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Intermediate MicroeconomicsHomework Set 5: SolutionsExercise 1First, let’s rewrite the Walrasian demand function:p*(x) = 30-2xWe know that consumer is currently consuming 10 units of good at a price \$10 (notethat this point is indeed on consumer’s demand curve:p*(x*= 10) = 30-2·10 = 10).1. The amount of money the consumer would be willing to pay to have 10 units ofgood x rather than no units at all is equal to the value of his total surplus, whichin turn is equal to the area below his demand curve on (x, p) plane (the sum ofviolet and blue areas on the left graph).Net surplus is equal to total surplusminus amount of money consumer is paying (area of violet triangle on the leftgraph).In order to compute the surplus, we integrate the demand equation from 0 to thevalue of quantity demanded (minus the price when computing net surplus):CStotal=Z100(30-2x)dx= (30x-x2)100= 200CSnet=Z100(30-2x-10)dx=Z100(20-2x)dx= (20x-x2)100= 1002. First, we need to know the new quantity demandedx0(p0= 14) = 15-14/2 = 81
Now we can compute new value of net consumer surplus in the same way as wedid before:CS0net=Z80(30-2x-14)dx=Z80(16-2x)dx= (16x-x2)80= 64ΔCS=CSnet-CS0net= 100-64 = 36

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