Suppose an economy has the following production function, Y=K^1/3 (AL)^2/3. Furthermore, suppose that that the growth rate of capital is 3%, the growth rate of the population is 4% and the growth rate of technology is 2%.

a. Derive the equation for the per capita production function.

b. Use growth accounting to determine the growth rate of aggregate GDP for this economy.

c. What is the growth rate of per capita GDP for this economy?

d. Suppose that the capital stock increased by 10%, how much would aggregate output increase by? What about per capita output?

e. Suppose that the level of technology increased by 10%, how much would aggregate output increase by? What about per capita output? Explain why it is different than in part d).