QUESTION 2 Consider an economy in which the consumption, investment and producti

Question

QUESTION 2 Consider an economy in which the consumption, investment and production functions are as follows C=10+0.8(Y-T) 1-40-2.5 KL)- K1/32/3 Suppose government spending is 20, taxes equal 25 and the supply of factors is KL125. Answer the following questions 1. What is the equilibrium level of real GDP.? 2. What is the equilibrium real interest rate? 3. Find the level of national savings. How much of that savings is from the private agents? 4. Find the level of investment in equilibrium. 5. Suppose taxes increase to 35. What is its effect on private savings? (Give numerical answer) Attach File Browse My Computer

Explanation / Answer

(1) In short run, K = 125 and L = 125. Substituting in production function,

Short run output (Y) = K1/3L2/3 = (125)1/3(125)2/3 = 125

(2) In short-run equilibrium,

Y = C + I + G

Y = 10 + 0.8(Y - 25) + 40 - 2.5r + 20

Y = 70 + 0.8Y - 20 - 2.5r

(1 - 0.8)Y = 50 - 2.5r

0.2Y = 50 - 2.5r

0.2 x 125 = 50 - 2.5r

25 = 50 - 2.5r

2.5r = 25

r = 10

(3) When short run Y = 125, substituting in consumption function,

C = 10 + 0.8 x (125 - 25) = 10 + 0.8 x 100 = 10 + 80 = 90

National saving = Private saving + Public saving = (Y - C) + (T - G) = (125 - 90) + (25 - 20) = 35 + 5 = 40

Saving from private agents (= Private savings) = Y - C = 125 - 90 = 35

(4) When equilibrium r = 10,

I = 40 - (2.5 x 10) = 40 - 25 = 15

(5) With new value of Tax = 35,

C = 10 + 0.8(Y - 35) = 10 + 0.8Y - 28 = (0.8 x 125) - 18 = 100 - 18 = 82

New value of Private savings = Y - C = 125 - 82 = 43

Increase in private savings = 43 - 35 = 8

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