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Answer to Question #51140 in Macroeconomics for Husnyyy

Question #51140

c. Given that money supply is KSh 1400 millions, autonomous consumption is KSh120 million, while the responsiveness of consumption to changes in disposable income is estimated to be 80% by the ministry of planning. Aggregate autonomous investment is ksh 200 million investment while one % increase in interest rate changes investment by KSh10 millions. The government collected KSh 200 million as tax revenue and wishes to increase expenditure by 10% above the revenue collected. The transactionary and precautionary demand for money function is expressed as mt/p=0.1y while the speculative money demand ms/p is -100r . compute the equilibrium national income, consumption and investments.
Expert's answer
c. Money supply MS = KSh 1400 millions, autonomous consumption Ca = KSh120 million, c = 80%, aggregate autonomous investment Ia = ksh 200 million, 1% increase in interest rate changes investment by KSh10 millions. Taxes T = KSh 200 million, G = 1.1T.
The transactionary and precautionary demand for money function mt/p = 0.1y, speculative money demand ms/p = -100r 
In equilibrium money demand equals money supply Md = Ms
Md = my/p + ms/p = 0.1y - 100r
So, 0.1y - 100r = 1400
r = 0.001Y - 14
Y = C + I + G
Y = 120 + 0.8(Y - 200) + 200 - 10i + 1.1*200
0.2Y = 380 - 10i
i = 38 - 0.02Y
That's why, 38 - 0.02Y = 0.001Y - 14
0.021Y = 52
So, the equilibrium national income Y = 2476.2
Consumption is C = 120 + 0.8(2476.2 - 200) = 1940.96
Investments I = 200 - 10i = 200 - 380 + 0.2*2476.2 = 315.24

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