Consider an economy describe by the following equations: 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 fiscal policy, what change in interest rate would restore full employment?

Answer:

A. Explaining the Equations

The first equation, Y = C + I + G, is the equation for Gross Domestic Product (GDP), which is the total value of all goods and services produced within a given period. C stands for consumption, which is the spending of households on goods and services. I stands for investment, which is the spending of businesses on goods and services. G stands for government purchases, which is the spending of the government on goods and services.

The second equation, C = 100 + 0.75(Y – T), is the equation for consumption. Y stands for GDP and T stands for taxes. This equation states that consumption is the sum of the base level of consumption (100) plus three-fourths of the difference between GDP and taxes.

The third equation, I = 500 – 50r, is the equation for investment. r stands for the interest rate. This equation states that investment is the sum of the base level of investment (500) minus fifty times the interest rate.

The fourth equation, G = 125, is the equation for government purchases. This equation states that government purchases are always equal to 125.

The fifth equation, T = 100, is the equation for taxes. This equation states that taxes are always equal to 100.

B. Marginal Propensity to Consume and Marginal Propensity to Save

The marginal propensity to consume (MPC) is the ratio of the change in consumption to the change in disposable income. It is calculated by dividing the change in consumption by the change in disposable income. In this equation, the MPC is equal to 0.75.

The marginal propensity to save (MPS) is the ratio of the change in saving to the change in disposable income. It is calculated by dividing the change in saving by the change in disposable income. In this equation, the MPS is equal to 0.25.

C. Solving for GDP and Comparing to Full Employment Level

Given that the interest rate is 4 percent, the equation for investment can be solved for GDP. Using the equation I = 500 – 50r, GDP can be calculated as Y = 500 – 50(4) = 400. This is lower than the full employment level of 2000, indicating that the economy is not at full employment.

D. Change in Government Purchases Needed to Restore Full Employment

In order to restore full employment, the equation for GDP must be solved for government purchases. The equation for GDP is Y = C + I + G. We can rearrange this equation to solve for G: G = Y – C – I. Using the given equations, we can calculate G = 2000 – (100 + 0.75(2000 – 100)) – (500 – 50(4)) = 2000 – 1600 – 200 = 200. Thus, a change in government purchases of 200 is needed to restore full employment.

E. Change in Interest Rate Needed to Restore Full Employment

In order to restore full employment, the equation for investment must be solved for the interest rate. The equation for investment is I = 500 – 50r. We can rearrange this equation to solve for r: r = (500 – I) /50. Using the given equation, we can calculate r = (500 – 500) /50 = 0. Thus, a change in the interest rate of 0 is needed to restore full employment.

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