Suppose there are two cities (1 and 2) and two types of citizens based on individual preferences for public goods (z): high-demand types (type A) with individual demand given by P=30-2z and low-demand types (type B) with individual demand given by P=26-2z, where Pdenotes willingness to pay.
In each city there are currently 100 citizens, but their compositions differ:
City 1: 80 type A, 20 type B
City 2: 20 type A, 80 type B
The marginal social cost per-unit of z is given by c=$400. Assume public good costs are shared equallyamong all city residents and that public good provision (z) is the only factor that may induce citizens to move to new cities if unhappy with current levels.
a) (2 points) Using the median voter method, what is the optimal level of z in each city?
b) (4 points) What is the consumer surplus for type A and type B citizens living in City 1? (Hint: diagrams help!)
c) (4 points) Assume per-capita costs per unit of z remain constant if only one citizen changes cities. What is the maximum amount one type B citizen in City 1 would pay to move to City 2?
Free-Response #2 – Consider the Stock-Flow Model. Suppose the initial demand curve for housing is given by p=8-H, where p is the per-unit rental price and H is the size of the housing stock. The flow supply curve for housing is given by p=ΔH+3, where ΔH is the change in the housing stock.
a) (2 points) Compute the equilibrium price, pe, and initial stock size H0.
b) (4 points) Suppose civil war in a neighboring country causes a wave of migration, increasing housing demand to p=14-H. Given the initial housing stock size, what’s the new higher price (p’) that results in the market? Compute the change in the housing stock as developers respond to this price change. How many periods does it take to reach equilibrium?
c) (4 points) Suppose rent control is imposed immediately after the demand shock, with the controlled price set at pc=4. How many periods does it take to reach the new equilibrium, where p=pe?