Suppose GDP in 2010 is USD 1.577 trillion and the average annual growth rate is 3%. a. Calculate the GDP in 2025 using both continuous and discrete compounding.
b. What is the GDP in 2025 if the average annual growth rate increases to 4.5%?
c. What must be the average growth if in 2025 GDP is USD 3.500 trillion.
Suppose that households change their preferences so that they wish to consume more and save less in the current year. That is, current consumption rises for a given interest rate, and for given current and future income. a. Show on a graph (with axes L and w/P) the effects on the labor market. What happens to labor input and
real wage rate?
b. Show on a graph (with axes K and R/P) the effects on the market for capital services. What happens to the
interest rate?
Consider Cobb-Douglass production function Y = 60K1/3L2/3 with marginal product of labor MPL = 40K1/3L-1/3 and marginal product of capital MPK = 20K-2/3L2/3.
a. Complete the following table:
K L Y
64 8
128 16
192 24
b. Explain how these results illustrate the property of constant returns to scale.
c. Find the numerical value of the marginal product of labor MPL when K = 64 and L = 8. Recall that, in equilibrium, firms will hire workers until their MPL equals the real wage w/P. If firms in the economy had decided to employ eight workers, what would the equilibrium real wage have to be?
d. Evaluate the marginal product of capital MPK when K = 64 and L = 8. Recall that, in equilibrium, firms will hire capital until the MPK equals the real rental price of capital R/P. If firms in the economy had decide to employ 64 units of capital, what would the equilibrium real rental price of capital have to be?
e. Show that this production function satisfies Euler's theorem Y = K · M P K + L · M P L algebraically and numerically using table in (a).
Write down a permanent income equation for 7 years, t=0,1,2,3,4,5,6. Suppose that Y0 = 1000 and the income doubles every year. The discount rate is 5%.
a. What is the permanent income?
b. What is the change in the permanent income if the discount rate increases to 7%. c. What is the permanent income if the income triples (not doubles) every year?