4. Given the following Keynesian model: Y = C + I + G + X - M I = 250 C = 80 + 0
ID: 1196152 • Letter: 4
Question
4. Given the following Keynesian model:
Y = C + I + G + X - M I = 250
C = 80 + 0.75Yd G = 100
Yd = Y - T X = 200
T = 0.20Y M = 0.30Y
(a) Calculate the equilibrium level of income and indicate the value of the current account balance when the economy is at its equilibrium income level.
(b) Suppose that all equations in the model above stay the same except the size of exports. Calculate the level of exports needed to yield an equilibrium income level that also has X = M, and indicate that resulting equilibrium income level.
Explanation / Answer
a. The equilibrium level of income Y, is computed by Y = C + I + G + NX
C = consumption
I = investment
G = government expenditure
NX = net exports, exports-imports.
Substituting all the values, we get,
Y = 80 + 0.75Yd + 250 + 100 + (200-0.30Y)
Also, disposable income Yd = Y-T, and T = 0.20Y
Y = 80 + 0.75(Y-0.20Y) + 250 + 100 + (200-0.30Y), solving and re-arranging we get,
Y-0.6Y+0.30Y = 630.
0.7Y = 630
Y = $900.
Current account balance of balance of payment is the difference between exports and imports.
Imports = 0.30*900 = $270
Current account balance = 200-270 = -70. The current account is in deficit. Imports are greater than exports.
b. The level of exports needed to have exports equal to imports is $270. At this, exports equals imports.
If X=M, then the net exports component of the Y equation would be zero. as X-M => X-X = 0.
New equation would be Y = C+I+G.
Substituting the values, we get,
Y = 80 + 0.75(Y-0.20Y) + 250 + 100.
Y-0.6Y = 430
0.4Y = 430
Y = $716.66
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