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;

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.

Answer 1

(i) IS curve equation

Y = C + I + G + NX

Y = 1000 + 0.6 (Y - (20+0.2 Y) -300r + 600 - 300r + 100 + 150 - 0.1Y - 400r

Y = 1000 + 0.48 Y -12 - 1000r +600 + 250 -0.1Y

Y = 1838 + 0.38Y -1000r

1000r = 1838 - 0.62Y

r = 1.838 - 0.00062Y.................. (1)

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(ii) LM Curve equation

Real Money supply = Real Money demand

1000 = 0.6Y - 300r

300 r = 0.6 Y - 1000

r = 0.002 Y - 3.33................... (2)

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(iii) Equating LS and LM curve equations, give the output

from (1) and (2)

1.838 - 0.00062Y = 0.002 Y - 3.33

0.00262Y = 5.168

Y = 1972.52

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(iv) substituting Y = 1972.52 in (1)

r = 1.838 - 0.00062Y

r = 1.838 - 1.223

r = 0.6150

I = 600 - 300 (0.6150)

I = 600 - 184.5

I = 415.50

C = 1000 + 0.6(Y-T) - 300r

C = 1000 + 0.6 (1972.5 - (20+0.2*1972.5)) - 300 (0.6150)

C = 1000 + 0.6 (1972.5 - (20+394.5) - 184.5

C = 1000 + 0.6 (1972.5 - 414.5) - 184.5

C = 1000 + 0.6 (1558) - 184.5

C = 1750.3

NX = 150 − 0.1Y − 400r

NX = 150 - (0.1) (1972.5) - 400 (0.6150)

NX = 150 - 197.25 - 246

NX = - 283.25

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(v) At Y = 1972.5 and r = 0.615, Price level, P = 1

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