Question

Question 1: General Equilibrium in closed and open economies [50 marks]

Consider the following closed Keynesian economy

Desired consumption, Cd = 1000 + 0.6(Y-T) - 300r;

Desired investment, Id = 600 - 300r;

Money deman d, L = 0.6Y - 300r;

Output, Ȳ = 4000;

Expected inflation, πe = 0;

1. Assume that we are in a closed economy. Suppose that T = G = 300 and M = 8000. Find the equilibrium values of output, consumption, investment, the real interest rate, and the price level. The following are the steps to help you find them:

   1. Find an equation describing the IS curve in the following format: r = f(Y)

   2. Find an equation describing the LM curve in the following format r = g(Y, P)

   3. What is the value of output at the FE line?

   4. Given the value, use the IS curve to find the real interest rate. Calculate the investment and consumption.

   5. Given the values of output and real interest rate, find the price level.

2. Suppose M decreases to 6000. Find the short-run equilibrium. The following are the steps to help you find it:

   1. Find an equation describing the IS curve in the following format r = f(Y)

   2. Given the price level found in a), find an equation describing the LM curve in the following format r = g(Y, P)

   3. What is the new value of output? Given that value, find the new real interest rate

Calculate the investment and consumption.

c. Find the new long-run equilibrium by taking M = 6000 and the price level as flexible (repeat part a). The following are the steps to help you find it:

(i) Find an equation describing the IS curve in the following format: r = f(Y)

(ii) Find an equation describing the LM curve in the following format: r = g(Y, P )

(iii) What is the value of output at the FE line?

(iv) Given that value, use the IS curve to find the real interest rate. Calculate the investment and consumption.

(v) Given the values of output and real interest rate, find the price level.

Assume that we are in an open economy with a flexible exchange rate. Add the following equations to those presented before part a:

Taxes, T =20 + 0.2Y;

government purchases, G = 100;

net exports, NX = 150 − 0.1Y − 400r;

money supply, M = 1000;

output, Y ̄ = 2000;

d. Find the equilibrium values of output, the real interest rate, consumption, investment, net exports, and the price level. The following are the steps to help you find them:

(i) Find an equation describing the IS curve in the following format: r = f(Y)

(ii) Find an equation describing the LM curve in the following format: r = g(Y, P)

(iii) What is the value of output at the FE line?

(iv) Given that value, use the IS curve to find the real interest rate. Calculate the investment, the consumption and the net exports.

(v) Given the values of output and real interest rate, find the price level.

e. Suppose that G decreases to 50. Explain with graphs (ONLY) what will happen to the economy. Explain your graphs with words.

f. Suppose that M decreases to 750. Explain with graphs (ONLY) what will happen to the economy. Explain your graphs with words.

Answer 1