Due to the recession that lowered income the market price of

Due to the recession that lowered income, the market price of good X got lower. For good X, we assume that Qd(P) = 1000 P +Y/20 , and Qs(P) = 2P Y/20 , where Y is the income, and P is the price of good X. (a) Derive the equilibrium price P in terms of Y . (b) Use your answer at (a) to show the effect of income on equilibrium price, that is, find dP/dY .

Solution

(a)

Demand function [Qd(P)]:

Q = 1000 - P + (Y / 20)

Supply function [Qs(P)]:

Q = 2P - (Y / 20)

In equilibrium, demand = supply

1000 - P + (Y / 20) = 2P - (Y / 20)

1000 + 2 x (Y / 20) = 3P

1000 + (Y / 10) = 3P

P = (1000 / 3) + (Y / 30) ...... (1)

(b)

dP/dY = (1/30) [Differentiating (1) with respect to Y]

So, with 1 unit change in Y, market price increases by (1/30) units.