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destinybonmer
destinybonmer
07.04.2020 • 
Business

Two countries, Richland and Poorland, are described by the Solow growth model. They have the same Cobb-Douglas production function

2. Two countries, Richland and Poorland, are described by the Solow growth model. They have the same Cobb-Douglas production function, F(K, L) = AKL1-u, but with different quantities of capital and labor. Richland saves 3200 ofits income, while Poor!and saves 10%. Richland has a population growth of 1% per year, and Poor!and has a population growth of 3% per year. (The numbers in this problem are chosen to be approximately realistic descriptions of rich and poor nations). Both nations, have technological progress at a rate of 2% per year, and depreciation at a rate of 5% per year

a. What is the per-worker production function f (k)? (2 pts)
b. Solve for the ratio of Richlands steady state income per worker to Poorlands. (Hint: The parameter α will play a role in your answer). (4 pts)
c. If the Cobb-Douglas parameter α takes the conventional value of about 1/3,how much higher should income per worker be in Richland compared to Poorland? (2 pts)
d. Income per worker in Richland is actually 16 times that of income per worker in Poor!and. Can you explain this fact by changing the value of parameter α? what must it be? Can you think of any way of justifying such a value for this parameter? (3 pts)

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