Consider a two-period production

economy consisting of consumers, rms, and a government. In the current period the consumer

allocates total time h between leisure (`) and work (Ns). Working earns the consumer a

real wage w. In addition the consumer consumes goods C, pays lump-sum taxes T to the

government, and receives dividend income from the rm . The same is true in the future

period (denote all future variables with a prime). The market real interest rate is r. The

objective of the consumer is to maximize utility from consumption and leisure over the two

periods. The rm produces output in the current period (Y ) according to the constant returns

to scale production function Y = zF(K;N), where z and K are current TFP and capital

stock respectively, which are exogenous. The same production function with primes holds

in the future period. The representative rm chooses labour in each period (N;N0) as well

as investment (I), which determines future capital (capital depreciates at rate < 1). To

undertake one unit of investment the rm has to give up one unit of the current consumption

good. The representative rm makes these choices so as to maximize the present value of

prots. Finally the government purchases G units of the current consumption good and G0 of

the future consumption good, but can borrow by issuing bonds.

1. Suppose the intertemporal economy described above is initially in a compet-

itive equilibrium in which the current labour and goods markets clear. For this question

assume that rms and consumers receive the safe interest rate r when lending, but have

to repay the risky rate r` = r + x when borrowing. Note that x is the default premium,

that captures perceived credit market uncertainty.

Suppose now that there is a wave of pessimism among agents about the future prospects

of the economy. The pessimism about the future is reected in the current period by a

joint, simultaneous \shock": (i) a decrease in expected future productivity z0; and (ii)

an increase in credit market uncertainty, captured by an increase in the default premium

faced by borrowing rms and consumers x.

(a) Using diagrams and equations show the equilibrium eects of the above

simultaneous shock on consumption, investment, the real interest rates (safe and

risky), aggregate output, employment, and the real wage.

(b) (5 marks) Are the equilibrium co-movements of real output and other macroeco-

nomic variables, consistent with the above simultaneous shock being a source of

business cycle

(c) How would your answer to part (a) change if diminishing returns to

labour in production set in at a slower rate.

(d)\Suppose that in response to the negative shock in (a) the government

is considering to: (i) increase government spending by G, or (ii) decrease taxes

by T. If the goal of the government is to boost output and employment which of

the two policies would be more eective? How does the eectiveness of the policies

depend on the size of the multiplier?