𝑌 = 𝐶 + 𝐼 + 𝐺 𝐶 = 100 + 0.75(𝑌 − 𝑇) 𝐼 = 500 − 50𝑟 𝐺 = 125 𝑇 = 100 Where Y is the GDP, C is consumption, I is investment, G is Government Purchases, T is taxes, and is interest rate. If the economy were at full employment (that is, at its natural level of output), GDP would be 2,000. (21 marks) A. Explain the meaning of each of these equations. (3 marks) B. What is the Marginal Propensity to Consume and Marginal Propensity to Save? (4 marks) C. Suppose the Central Bank adjusts the money supply to maintain the interest rate at 4 percent, so r=4. Solve for GDP. How does it compare to the full employment level? (4 marks) D. Assuming no change in monetary policy, what change in Government Purchase would restore full employment? (5 marks) E. Assuming no change in fisc63al policy, what change in interest rate would restore full employment? (

5 marks)

Answer

A. Explain the meaning of each of these equations.

The equation Y=C+I+G represents the equation for Gross Domestic Product (GDP). GDP is the total value of goods and services produced in a country in a given year. The equation C=100+0.75(Y-T) represents the equation for consumption, which is the total amount of spending by households. The equation I=500-50r represents the equation for investment, which is the total amount of spending by businesses. The equation G=125 represents the equation for Government Purchases, which is the total amount of spending by the government. The equation T=100 represents the equation for taxes, which is the total amount of revenue collected by the government.

B. What is the Marginal Propensity to Consume and Marginal Propensity to Save?

The marginal propensity to consume (MPC) is a measure of how much additional income is allocated to consumption. It is calculated by taking the change in consumption divided by the change in income. The marginal propensity to save (MPS) is a measure of how much additional income is allocated to savings. It is calculated by taking the change in savings divided by the change in income.

C. Suppose the Central Bank adjusts the money supply to maintain the interest rate at 4 percent, so r=4. Solve for GDP. How does it compare to the full employment level?

If the interest rate is maintained at 4%, then the equation I=500-50r can be rewritten as I=500-200, or I=300. This means that the equation for GDP can be rewritten as Y=100+0.75(Y-100)+300+125, which can be simplified to Y=725+0.75Y. Solving for Y, we get Y=1000. This GDP of 1000 is lower than the full employment level of 2000.

D. Assuming no change in monetary policy, what change in Government Purchase would restore full employment?

Assuming no change in monetary policy and a GDP of 1000, the equation for GDP can be rewritten as Y=100+0.75(Y-100)+300+125, which can be simplified to Y=725+0.75Y. Solving for Y, we get Y=1000. To restore full employment, Government Purchases (G) will need to be increased by 875, so that the equation for GDP is Y=1000+0.75(Y-100)+300+1000, or Y=2000. This means that Government Purchases should be increased to 2000.

E. Assuming no change in fiscal policy, what change in interest rate would restore full employment?

Assuming no change in fiscal policy and a GDP of 1000, the equation for GDP can be rewritten as Y=100+0.75(Y-100)+300+125, which can be simplified to Y=725+0.75Y. Solving for Y, we get Y=1000. To restore full employment, the interest rate (r) will need to be decreased by 10%, so that the equation for GDP is Y=1000+0.75(Y-100)+500+125, or Y=2000. This means that the interest rate should be decreased to 0%.