2. Suppose a country has the production function Yt = F(Kt,Lt). The depreciation

Question

2. Suppose a country has the production function Yt = F(Kt,Lt). The depreciation rate of capital in this country is d, and the households saving rate is s. Assume that there’s no population growth.
Using letters to answer the following questions:
a) What is total output of the country when its capital stock is Kt?
b) Since households saving rate is s, what is the investment level of the country when its capital stock is Kt?
c) When the investment in a country is just enough to cover the depreciation of the capital stock in that country, it’s in the steady state. Please write down the condition for the steady state and show it graphically.
d) If the country starts with a capital stock that is less than the amount that it would have in steady state, what would happen to its capital stock over time? What about its total output?
e) If the country starts with a capital stock that is just the amount that it would have in steady state, what would happen to its capital stock over time? What about its total output?

Explanation / Answer

Without a specific model, all I can give is answers in terms of F(Kt,Lt). If you have a specific function, substitute it in for F. a) Yt = F(Kt,Lt) this is total output b) i = s(Yt) = s*F(Kt,Lt) c) s(Yt) - d(Kt) = 0, this is where investment equals depreciation. I can't really show it graphically without a specific function, again, if you do have one, substitute it in d) If the country starts with a capital stock less than the amount that it would have in the steady state, capital stock would grow over time to reach the steady state, output would grow, very quickly at first, slowing down as it approaches the steady state, and then growing slowly after that. e_ If the country starts with the right amount of capital stock, capital stock would be constant over time (since the steady state is at the replacement level, and any additional capital would depreciate more quickly than it could be replaced). Total output would start fairly high and grow very slowly.

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