2. 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. Investment (I) is given by the equation I = 1,200 – 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. Now assume there is a technological innovation that makes business want to invest more. It raises the investment equation to I = 2,100 – 50r. What are the new equilibrium values of C, I, and r?

d. What are the values of private saving, public saving, and national saving?
A
Capital receives 3/10 of income and Labour receives 7/10 of income. That is the function would be
Y = AK^0.3L^0.7 Assuming constant total factor productivity
B
Assuming A = 1

Y = L^0.3K^0.7
To find Y' Substitute L = 1.1 * L
Y' = K^0.3(1.1* L)^0.7
Y' =1.1^0.7 *K^0.3 * L^0.7
Y' =1.10.7 Y = 1.069Y
Thus total output increased by about 7%
The rental price of capital will decrease. It will decrease because the amount of capital used is increased by 10% but the output increases by only 7%
The real wage will increase as the output increases while the amount of labour employed remains the same.

(W/P)1 = MPL = 0.7AK0.3L-0.3, (W/P)2 = 0.7A(1.1K-0.7)L-0.7

(W/P)2 / (W/P)1 = 1.029

Thus output rises by 2.9%, rental rates fall by 6.5%, and wages rise by 2.9%

d. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to total output (in percent)? The real rental price of capital (in percent)? The real wage (in percent)?

So the same thing for A, and you’ll see that everything rises by