Two countries, Richland and Poorland, are described by the Solow growth model. They have the same Cobb–Douglas production function, F(K, aL) = A KaL1−a, but with different quantities of capital and labour. Richland saves 32 percent of its income, while Poorland saves 10 percent. Richland has population growth of 1 percent per year, while Poorland has population growth of 3 percent. (The numbers in this problem are chosen to be approximately realistic descriptions of rich and poor nations.) Both nations have techno-logical progress at a rate of 2 percent per year and depreciation at a rate of 5 percent per year.
a. What is the per worker production function f(k)?
b. Solve for the ratio of Richland’s steady-state income per worker to Poorland’s.
c. If the Cobb–Douglas parameter a takes the conventional value of about one-third, how much higher should income per worker be in Richland compared to Poorland?
d. Income per worker in Richland is actually 16 times income per worker in Poorland. Can you explain this fact by changing the value of the parameter a? What must it be? Can you think of any way of justifying such a value for this parameter? How else might you explain the large difference in income between Richland and Poorland?