Due to a recession that lowered incomes, the 2008 market prices for last-minute rentals of U.S. beachfront properties were lower than usual. Suppose that the inverse demand function for renting a beachfront property in Ocean City, New Jersey, during the first week 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?