Question

# Consider two countries: Country A and Country B. Each country has the following Cobb-Douglas type production...

Consider two countries: Country A and Country B. Each country has the following Cobb-Douglas type production function:
Country A: Y = (K0.5)(EL)0.5 Country B: Y = (K0.7)(EL)0.3
Unfortunately, your knowledge of Country A is a bit limited. You have pieces of information, but you don’t know the entire picture.
o Savings rate (s): unknown for Country A and 14.29% for Country B
o Steady-state value of capital per effective worker: unknown for both countries, but you have
heard that Country A has four times the steady state value of capital per effective worker
compared to Country B.
o Population growth rate (n): 1% for Country A and 3% for Country B
o Technological progress rate (g): 2% for both Country A and Country B o Depreciation rate (δ): 5% for both Country A and Country B
a. Convert both countries’ production functions to an effective per worker production functions.
b. What is the savings rate for Country A? Needless to say, you will also need to utilize what you know about
Country B.
c. What is the current steady-state consumption per effective worker for both countries?
d. Now, please find the level of capital per worker that is associated with the Golden Rule Steady State (in
other words, find k*Gold) for both countries. Is either country at the Golden Rule Steady State level of k?
e. Choose one of the two countries (entirely up to you) and calculate the savings rate required to bring that country to the Golden Rule Steady State.

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