1. Country A and country B both have the production function Y=F(K,L) = K1/2 L1/2
a. Does this production function have constant returns to scale? Explain
b. What is the per-worker production function, y=f(k)?
c. Assume neither country experiences population growth or technological progress and that 5% of capital depreciates each year. Assume further that country A saves 10% of output each year and country B saves 20% of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady state level of capital per worker for each country. Then find the steady state levels of income (aka output) per worker and consumption per worker.

2. Consider an economy described by the production function: Y=F(K,L)= K3/10 L7/10.
a. What is the per worker production function?
b. Assuming no population growth or technological progress, find the steady state capital stock per worker, output per worker, and consumption per worker as a function of the savings rate and the depreciation rate. (Hint: Your answer will be in terms of the variables s and δ.)
c. Assume the depreciation rate is 10%. Make a table showing steady state capital per worker, output per worker, and consumption per worker for savings rates of 0%, 10%, 20%, 30%....all the way to 100%. What savings rate maximizes output per worker? What savings rate maximizes consumption per worker?

3. An economy described by the Solow growth model has the following production function:
y = √k

a. Solve for the steady state value of y as a function of s, n, g and δ.
b. A developed country has a saving rate of 28% and a population growth rate of 1%. A less developed country has a savings rate of 10% and a population growth rate of 4%. In both countries, g=.02 and δ=.04. Find the steady state value of y for each country.
c. What policies might a less developed country pursue to raise its level of income?