Consider an economy in which the consumption, investment and production function
ID: 1157813 • Letter: C
Question
Consider an economy in which the consumption, investment and production functions are as follows C 10+0.8(Y-T) 1-40-2.5r FKL) K1/3L2/3 Suppose government spending is 20, taxes equal 25 and the supply of factors is KSL125. 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 Supose tanesIncreas o 35 What s ffect onprivate saving? (Give numerical answer)Explanation / Answer
(1) Equilibrium GDP (Y) = K1/3L2/3 = (125)1/3(125)2/3 = (125)1 = 125
(2) In equilibrium, Y = C + I + G
Y = 10 + 0.8(Y - 25) + 40 - 2.5r + 20
Y = 70 + 0.8Y - 20 - 2.5r
0.2Y = 50 - 2.5r
0.2 x 125 = 50 - 2.5r
25 = 50 - 2.5r
2.5r = 25
r = 10
(3) C = 10 + 0.8 x (125 - 25) = 10 + 0.8 x 100 = 10 + 80 = 90
National saving = (Y - C) + (T - G) = (125 - 90) + (25 - 20) = 35 + 5 = 40
Saving from private agents = Y - C = 125 - 90 = 35
(4) I = 40 - (2.5 x 10) = 40 - 25 = 15
(5) When Tax = 35,
C = 10 + 0.8(Y - 35) = 10 + 0.8Y - 28 = (0.8 x 125) - 18 = 100 - 18 = 82
Private savings = Y - C = 125 - 82 = 43
Increase in private savings = 43 - 35 = 8