1 Due to the recession that lowered income the market price

1. 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 . Show all math steps.

Solution

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)