Question

Assume that GDP (Y ) is 5,000 in a closed economy. 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.

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

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

(c) For the given consumption function, what does the relationship between consumption and the interest rate imply about the saving schedule?

Answer 1

Y=C+I+G

Y=1200+0.3(Y-1000)-50r+1500-50r+1500

5000= 4200 + 0.3(5000-1000) -100r

500-4200-0.3*4000 = -100r

800-1200=-100r

100r=400

r=4

C=1200+0.3(5000-1000)-50*4

C= 1200+1200-200

C=2200

I = 1500-50*4

I= 1300

b) public savings= T-G = 1000-1500 = -500

Private savings + public savings = I

S+ (-500) = 1300

S= 1800

National savings= Y-C = 5000-2200 = 2800

c) the relationship between consumption and interest rate implies that as interest rate increases, consumption falls. It means people reduces the consumption and increases the saving with the interest rate.