Question

(b) Consider an economy where the consumption function is given by ? = 500 + 0.8(? − ?). Investment is given by 2000 − 100? (where ? is the real interest rate), government spending is 5000, taxes are equal to 4000. Exports are 1000, while imports are given by ?? = 0.2?.

1. (i) Suppose that the real interest rate is ? = 5. Calculate the equilibrium level of real GDP for this economy. Now suppose that the Fed decides to raise the interest rate to ? = 10. Calculate the new equilibrium GDP for this economy.

2. (ii) Continue to assume that ? = 10. If the government decides to raise spending by 1000, what would be the new equilibrium level of GDP? Would you expect this change in GDP to have any impact on the interest rate? Explain why (not).

3. (iii) Someeconomistssaythatconsumptionalsodepends on the real rate of interest. If that were the case, explain in words how that would affect your answer in part (ii).

Answer 1

Given

Consumption: C = 500 + 0.8 (Y-T)

Investment: I = 2000 - 100r

Government spending: G = 5000

Taxes: T = 4000

Exports: X = 1000

Imports: M = 0.2Y

Net exports: NX = X - M = 1000 - 0.2Y

Real Gdp can be calculated using the formula below

Y = C + I + G + NX

Substituting values in the above formula

Y = 500 + 0.8 (Y - 4000) + 2000 - 100r + 5000 + 1000 - 0.2Y

Y = 8500 + 0.8Y - 0.8(4000) - 100r - 0.2Y

Y = 5300 - 100r + 0.6Y

Y - 0.6Y = 5300 - 100r

0.4Y = 5300 - 100r

Y = 13250 - 250r

(i) when r is 5

Y = 13250 - 250(5)

Y= 13250 - 1250 = 12000

when r = 10

Y = 13250 - 250(10)

Y = 13250 - 2500 = 10750

(ii) G = 5000 + 1000 = 6000

r = 10

Y = 500 + 0.8 (Y - 4000) + 2000 - 100(10) + 6000 + 1000 - 0.2Y

Y = 5300 + 0.6Y

0.4Y = 5300

Y = 13250

Change in real GDP = 13250 - 10750 = 2500

An increase in the government spending leads to an increase in the real GDP. This increase in real GDP would lead to an increase in demand for money (through the ISLM framework). The demand for money will exceed the supply of money. Assuming that the money supply in the economy is fixed, to get back the economy to the equilibrium, the interest rates would rise. Therefore, an increase in reaal GDP would lead to an increase in the interest rates.

(iii) When interest rates are high, the opportunity cost of consuming today increases. Due to this, the consumer is induces to consume less (substitution effect). On the other hand, now the interest income is higher which leads to increased consumption (income effect). The effect which dominates leads to the final decision on consumption.

If the overall effect is positive, then consumption would increase with increase in interest rate leading to an increase in the real GDP.

If the overall effect is negative, then consumption would decrease with increase in interest rate leading to a decrease in the real GDP.