3 . Country A and country B both have the same production function Y = F(K; L) =
ID: 1188895 • Letter: 3
Question
3 . Country A and country B both have the same production function Y = F(K; L) = K^.47L^.53
a) Capital depreciates at the rate of 5 percent each year in both countries. Country A saves 15 percent of output while country B saves 22 percent of output each year. Find the steady-state level of capital per worker for each country. Then Önd the steady state levels of output and consumption per worker.
b) Suppose that both countries start off with a capital stock per worker of 1.5. What are the levels of output per worker and consumption per worker? Remembering that the change in the capital stock is investment minus depreciation, use a calculator to show how the capital stock per worker will evolve over time in both countries (see also p.213 in the book for what such a table would look like). How many years will it be before the consumption in country B is higher than the consumption in country A?
Explanation / Answer
a) At steady state level of capital depreciation equals investments.
dK = sY = sF(K;L) = s K.47
K/K.47 = s / d
K.53 = s / d
K* = [s / d]1/.53
Country A :
Saving(s) = 0.15; Depreciation (d) = 0.05 and Y = K.47L.53
Thus K* = [0.15 / 0.05]1/.53 = 7.94
Country B :
Saving(s) = 0.22; Depreciation (d) = 0.05 and Y = K.47L.53
Thus K* = [0.22 / 0.05]1/.53 = 16.37
Steady state level Per capita production/output: Country A : K.47 = 7.94.47 = 2.647
Steady state level Per capita production/output: Country B : K.47 = 16.37.47 = 3.720
Steady state level of per capita consumption : Country A: (1-s)Y = (1-0.15)2.64 = 2.244
Steady state level of per capita consumption : Country B: (1-s)Y = (1-0.22)3.72 = 2.901
b)
It was found that long after at least 18 years the consumption in country B is higher than the consumption in country A.
Period Per capita capital Per capita output per capita consumption Country A 0 1.5 1.062 0.9033 Country B 0 1.5 1.0933 0.852Related Questions
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