1 consider the following model of the

Question

1. Consider the following model of the economy:

Wages are determined by the following equation W = P_e (2.5 - 10u).

Price is determined by the following equation P=2W
Production function Y=N.
Labour force is fixed L=100
Consumption function C=10+0.5(Y-T)
Investment function I =12+0.3Y-100 i
Government spending G=4
Taxes T=10
The central bank is using the following Interest Rate Rule: it = in + 2(P-PT)
Where PT=10

a. Derive the AS relationship for this economy. What are the natural rate of the unemployment and natural level of output?
b. Derive the IS relationship for this economy.
c. Derive the AD relationship for this economy.
d. What are the medium run values of P, Y and i?
e. Analyse qualitatively what will happen to the economy in the short run and the medium run if the central bank decides to increase its price target from 10 to 20? Assume that the expected price for the next period is equal to the current price

2. Spending shocks and the medium run

Using the AS-AD model where the central bank uses an interest rate rule with a price level target show the effects of an increase in consumer confidence on the position of the AD, AS, IS, and LM curves in the medium run. Then show the effect on output, the interest rate, and the price level in the short run and in the medium run. Assume that before the changes, the economy was in the medium run equilibrium.

Note: If C(Y_D)=c₀ + c₁ Y_D, an increase in consumer confidence can be modelled as an
increase in c0.

3. Dynamics and the AS-AD model
Consider the following model of the economy:
AS: P_t =?P^e_td (Y_t-Y_n)
IS: Y_t = b - c it +eG-fT
Interest Rate Rule: it = in + a(Pt-PT)
where a, b, c , d, e and f are positive parameters.
a. What is the AD relation in this economy?
b. Suppose P_T =1, Y_n=100, b=101, c=100, e=2, f=1, G=T=0
What are the medium run values of P, Y and i?

c. If G increased to 1, what would happen to P, Y and i in the medium run?

4. The neutrality of money

a. In what sense is money neutral? Why is monetary policy useful if money is neutral?

b. Fiscal policy, just like monetary policy, cannot change the natural level of output.

Why then is monetary policy considered neutral but fiscal policy is not?

c. Discuss the statement: "Since neither fiscal nor monetary policy can affect the natural level of output, it follows that, in the medium run, the natural level of output is independent of all government policies."