Due to a recession that lowered incomes, the 2008 market prices for last-minure

Question

Due to a recession that lowered incomes, the 2008 market prices for last-minure rentals of U.S. beach -front properties were lower than usual. Suppose that the inverse demand function for renting a beach-front property in Ocean City, New Jersey, during the first weel of August is p=1,000 - Q + Y/20, where Y is the median annual income of the people involved in this market, Q is quantity, and p is the rental price. The inverse supply function is p= Q/2 + Y/40.

A) Derive the equilibrium price, p and quantity Q in terms of Y.

B) Use a supply and demand analysis to show the effect of decreased income on the equilibrium price of rental homes. That is find dp/dY. Does a decrease in median income lead to a decrease in the equilibrium rental price?

Explanation / Answer

at equilibrium, supply=demand

1,000 - Q + Y/20 = Q/2 + Y/40

3Q/2 = 1000 + Y/20 - Y/40

3Q/2 = 1000 + Y/40

Q = 2000/3 + Y/60

P = 1000 - 2000/3 + Y/60 +Y/20

P = 1000/3 + Y/15

dP/dY = 1/15

as dP/dY is positve, it means that the median income and prices are positively related and that a decrease in the median income will lead to a decrease in the equilibrium rental price.

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