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.

Consider now the full intertemporal model in which in addition to the goods

and labour markets, the money market also clears. The supply of money is determined

exogenously by the government. The demand for real money balances of consumers and

rms is given by Md

P = L(Y;R), which depends positively on real income Y (transac-

tion motive) and negatively on the nominal interest rate R (opportunity cost of holding

money). Suppose the economy is initially in long-run equilibrium. Now, suppose that

there is a war with a neighbouring country that destroys part of the economy's current

stock of capital K and reduces current productivity z at the same time.

(a) (12 marks) How will the simultaneous drops in K and z aect the current equi-

librium values of the price level, consumption, investment, the real interest rate,

aggregate output, employment, and the real wage?

(b) (8 marks) Suppose that in response to the negative shock in (a) the government

increases the money supply (known to agents) by an amount M in order to boost

employment and output. Using diagrams analyze the equilibrium eects of this

policy (in combination with the negative capital-productivity shock in (a)) on the

price level, consumption, investment, the real interest rate, aggregate output, em-

ployment, and the real wage. Is the policy eective in increasing employment and

output?

(c) (7 marks) How would your answer to part (b) change if agents did not observe

(know) that the increase in M has taken place? Analyze the eects of the unantic-

ipated increase in M in the context of the Lucas-Friedman imperfect information

model.

(d) (8 marks) How would your answer to part (b) change if the price level was xed

or \sticky"? Analyze the eects of the increase in M in the context of the New

Keynsian model, when the interest rate is the target of monetary policy.