Question

In the classic model given the following: Production function:

Y=3 K^.5 L^.5 Labor

(L) is 400 units

Capital (K) is 100 units

Taxes (T) are 200

Government Spending (G) is 100

Marginal Propensity to Consume is .6

Investment is determined by the following function: I(r) = 1000- 100r

where r is real interest rate.

1. a.) full formula, Y=c(Y-T)+I+G, What are the equilibrium values of C, I and r?

b.) How much are Public savings, Private savings and National Savings?

c.)  Graph the loanable funds market (Investment Demand and National Savings), show the equilibrium values based on your answers from 1(a) and (b).

Answer 1

(a)

Y = 3 x (100)^0.5 x (400)^0.5 = 3 x 10 x 20 = 600

Consumption: C = a + b(Y - T) where a: Autonomous consumption, b: MPC

In equilibrium, Y = C + I + G = a + b(Y - T) + I + G

Y = 0 + 0.6(Y - 20) + 1000 - 100r + 100 [Since value of Autonomous consumption is not given, it is assumed zero]

Y = 1,100 + 0.6Y - 120 - 100r

(1 - 0.6)Y = 980 - 100r

0.4Y = 980 - 100r

0.4 x 600 = 980 - 100r

240 = 980 - 100r

100r = 740

r = 7.4

C = 0.6 x (600 - 200) = 0.6 x 400 = 240

I = 1,000 - (100 x 7.4) = 1,000 - 740 = 260

(b)

Private savings (Sp) = Y - C = 600 - 240 = 360

Public savings (Sg) = T - G = 200 - 100 = 100

National savings (S) = Sp + Sg = 360 + 100 = 460

(c)

In loanable funds market, I is the demand curve and S is the supply curve.

From Investment function,

When I = 0, r = 1,000/100 = 10 (Vertical intercept) & when r = 0, I = 1,000 (Horizontal intercept).

In following graph, r (interest rate) and S,I (saving and investment) are measured vertically and horizontally. D0 and S0 are demand (investment) curve for loanable funds and supply (saving) curve of loanable funds, intersecting at point A with equilibrium interest rate r0 (= 7.4) and quantity of saving and investment S0 (= 460).