Macro I
Spring 2005, Shanghai University of Finance and Economics
Instructor: Guan Gong
Problem Set #5 – Due on 6/3
Consider model of representative agents with a constant population N,
who maximize their utility function given by
where ct and lt denote the consumption and supplied labor at period t by
agent, and 0 < ρ < 1.
There is a constant amount of A land in this economy which is
distributed equivalently at period 0 between agents. These agents supply
their labor and land to a competitive market with production function AαL1-α
( A and L denote total supplied land and labor). The agent can by and sell
land without need for money, on credit base, but for consumption good, she
needs to carry money from the previous period, or equivalently she is subject
to cash in advance constraint
where mt − 1 represents the money balance of agent at the end of period t − 1,
p represents the price level, and st represents a nominal lump-sum subsidy
paid by government from the expansion of the fiat money. The money stock
Mt grows at the constant rate Mt = z Mt-1.
a) Setup representative agent’s problem and find out its FOCs.
b) What will be land’s rate of return in the steady-state equilibrium?
Compare money’s rate of return with land’s rate of return in the steady-state
equilibrium.
c) Now setup the problem for a benevolent social planner, solve it and
find out the optimal value for money expansion rate. What does it mean?
d) Now suppose in order to buy land, agent also has to carry money from
the previous period. Setup the new cash in advance problem and find the
new land’s rate of return in steady-state. Will it be less or more than
previous case? What about when we are in the optimal value for money
expansion rate?