Answer to Question #216635 in Macroeconomics for Collins

Question

The following parameters describe the structure of a hypothetical economy:
Autonomous consumption=240
Autonomous investment=1000
Autonomous taxes=100
Autonomous government expenditure=400
Real money supply (M/P)=600
Tax rate=0.25
Marginal propensity to consume=0.8
Interest elasticity of investment=50
Interest elasticity of demand for money=62.5
Income elasticity of demand for money=0.25
monetary policies
e) Assume a GHȼ450 million increase in government expenditure is financed by a
GHȼ300 million increase in taxes and GHȼ150 increase in money supply. Without
deriving the IS-LM equations, find the new equilibrium income and interest rate.
Explain.
f) If government wants equilibrium income and interest rate increased by 1400 and
0.8 units respectively:
i.
Determine how much government expenditure and money supply should
be changed to achieve these targets.
ii.
Determine how much autonomous taxes expenditure and money supply
should be changed to achieve these targets.

Answer 1

$Y=3,000+0.5(Y-0.2Y)+2,000+2,500+6,500-5,500-0.2Y\\Y=3,000+0.4Y+2,000+2,500+6,500-5,500-0.2Y\\ Y=14,000-5,500+0.2Y\\ Y=8,500+0.2Y\\ 0.8Y=8,500\\ Y=10,625$

$Y=3,000+0.5(Y-0.2Y)+1900+2,500+6,500-5,500-0.2Y\\Y=3,000+0.4Y+1900+2,500+6,500-5,500-0.2Y\\ Y=13900-5,500+0.2Y\\ Y=8,400+0.2Y\\ 0.8Y=8,400\\ Y=10,500$

$Y=3,000+0.5(Y-0.2Y)+2,000+2,800+6,500-5,500-0.2Y\\Y=3,000+0.4Y+2,000+2,500+6,500-5,500-0.2Y\\ Y=14,300-5,500+0.2Y\\ Y=8,800+0.2Y\\ 0.8Y=8,800\\ Y=11000$