Question #48889

(a) 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 .
(i)Solve for equilibrium real output and equilibrium interest rate
(ii) What is the effect of the new expenditure plan impact on income and consumption?

Expert's answer

MS = 1400 millions, C0 = 120 million, c = 0.8, I = 200 million investment, 1% increase in interest rate changes investment by 10 millions, T = 200 million, wishes to increase expenditure by 10% above the revenue collected. Transactionary and precautionary demand for money mt/p = 0.1y, speculative money demand ms/p = -100r .

(i)Solve for equilibrium real output and equilibrium interest rate

As money demand equals money supply in equilibrium, so MS = MD

0.1y + 100r = 1400

Output Y = C + I + G + NX, where C - consumption, I - investment, G - government purchases, NX - net export.

Y = 120 + 0.8Y + 200 + 200*0.1

0.2Y = 340

Y = 1700 million

As 0.1y + 100r = 1400, then 0.1*1700 + 100r = 1400, r = 12.3%

(i)Solve for equilibrium real output and equilibrium interest rate

As money demand equals money supply in equilibrium, so MS = MD

0.1y + 100r = 1400

Output Y = C + I + G + NX, where C - consumption, I - investment, G - government purchases, NX - net export.

Y = 120 + 0.8Y + 200 + 200*0.1

0.2Y = 340

Y = 1700 million

As 0.1y + 100r = 1400, then 0.1*1700 + 100r = 1400, r = 12.3%

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