# That is output increases by 69 percent to determine

• Notes
• 7

This preview shows page 4 - 7 out of 7 pages.

That is, output increases by 6.9 percent. To determine how the increase in the labor force affects the rental price of capital, consider the formula for the real rental price of capital R/P R/P = MPK : = .
We know that = 0.3. We also know that labor ( L ) increases by 10 percent. Let ( R/P )1 equal the initial value of the rental price of capital, and ( R/P )2 equal the final rental price of capital after the labor force increases by 10 percent. To find ( R/P )2, multiply L by 1.1 to reflect the 10-percent increase in the labor force: ( R/P )1 = . ( R/P )2 = . The rental price increases by the ratio . So the rental price increases by 6.9 percent. To determine how the increase in the labor force affects the real wage, let ( W/P )1 = . (W /P )2 = . The rental price increases by the ratio . That is, the real wage falls by 2.8 percent. c. We can use the same logic as in part (b) to set Y 1 = . Y 2 = . Therefore, we have: This equation shows that output increases by about 3 percent. Notice that α < 0.5 means that proportional increases to capital will increase output by less than the same proportional increase to labor. Again using the same logic as in part (b) for the change in the real rental price of capital: . The real rental price of capital falls by 6.5 percent because there are diminishing returns to capital; that is, when capital increases, its marginal product falls. Finally, the change in the real wage is: .
Hence, real wages increase by 2.9 percent because the added capital increases the marginal productivity of the existing workers. (Notice that the wage and output have both increased by the same amount, leaving the labor share unchanged a feature of Cobb Douglas technologies.) d. Using the same formula, we find that the change in output is:
6. a. Private saving is the amount of disposable income, Y T , that is not consumed: S private = Y T C = 5,000 1,000 (250 + 0.75(5,000 1,000)) = 750. Public saving is the amount of taxes the government has left over after it makes its purchases: S public = T G = 1,000 1,000 = 0. Total saving is the sum of private saving and public saving: S = S private + S public = 750 + 0 = 750. b. The equilibrium interest rate is the value of r that clears the market for loanable funds. We already know that national saving is 750, so we just need to set it equal to investment: S = I 750 = 1,000 50 r Solving this equation for r , we find: r = 5%. c. When the government increases its spending, private saving remains the same as before (notice that G does not appear in the S private above) while government saving decreases. Putting the new G into the equations above: S private= 750 S public = T G = 1,000 1,250
= 250. Thus, S = S private + S public = 750 + ( 250) = 500. d. Once again the equilibrium interest rate clears the market for loanable funds: I r
• • • 