Question

(15pt) Assume that GDP (Y) is 5,000. Consumption (C) is given by the equation C = 1,200 +

0.3(Y – T) – 50r, where r is the real interest rate, in percent. Investment (I) is given by the

equation I = 1,500 – 50r. Taxes (T) are 1,000, and government spending (G) is 1,500. Here,

notice that C is negatively related to the real interest rate.

a)What are the equilibrium values of C, I, and r? (3pt)

b)What are the values of private saving, public saving, and national saving? (3pt)

c)Graphically illustrate the above loanable fund market. (Warning: since C is also a function of r,

do you think the supply curve remain vertical?) (3pt)

d)Now assume there is a technological innovation that makes business want to invest more. It

raises the investment equation to I = 2,000 – 50r. What are the new equilibrium values of C, I, and r? (3pt) Also, graphically illustrate this change on the graph you draw from part (c). (1pt)

e)How would you justify the fact that C is also negatively related to r? (2

Answer 1

(a)

In equilibrium, Y = C + I + G

Y = 1,200 + 0.3(Y - 1,000) - 50r + 1,500 - 50r + 1,500

Y = 4,200 + 0.3Y - 300 - 100r

0.7Y = 3,900 - 100r

0.7 x 5,000 = 3,900 - 100r

3,500 = 3,900 - 100r

100r = 400

r = 4

I = 1,500 - 50 x 4 = 1,500 - 200 = 1,300

C = 1,200 + 0.3 x (5,000 - 1,000) - 50 x 4 = 1,200 + 0.3 x 4,000 - 200 = 1,000 + 1,200 = 2,200

(b)

Private saving (Sp) = Y - C = 5,000 - 2,200 = 2,800

Public saving (Sg) = T - G = 1,000 - 1,500 = - 500

National saving (S) = Sp + Sg = 2,800 - 500 = 2,300

(c)

Since C is inversely related to r, S is positively related to r, so supply curve of loanable funds is upward sloping.

In following graph, D0 and S0 are initial demand and supply curves of loanable funds, intersecting at point A with initial interest rate r0 and quantity of loanable funds (saving and investment) Q0.

(d)

Y = 1,200 + 0.3(Y - 1,000) - 50r + 2,000 - 50r + 1,500

Y = 4,700 + 0.3Y - 300 - 100r

0.7Y = 4,400 - 100r

0.7 x 5,000 = 4,400 - 100r

3,500 = 4,400 - 100r

100r = 900

r = 9

I = 2,000 - 50 x 9 = 2,000 - 450 = 1,550

C = 1,200 + 0.3 x (5,000 - 1,000) - 50 x 9 = 1,200 + 0.3 x 4,000 - 450 = 750 + 1,200 = 1,950

Higher investment will increase the demand for loanable funds, shifting demand curve rightward, increasing interest rate and increasing quantity of loanable funds. In above graph, D0 shifts right to D1, intersecting S0 at point B with higher interest rate r1 and higher quantity of loanable funds Q1.

(e)

If consumption is partly funded by borrowing (using loans), then the higher (lower) the interest rate, the higher (lower) the cost of borrowing, so the lower (higher) the consumption funded by borrowing, and the lower (higher) the total consumption, making total consumption inversely related to interest rate.