Question

Country A has a capital-labor ratio that is initially twice as big as that of country B, but neither is yet in a steady state. Both countries have the same production function, f(k) = 6k0.5. Country A has a 10% saving rate, 10% population growth rate, and 5% depreciation rate, while country B has a 20% saving rate, 10% population growth rate, and 20% depreciation rate.

(a) Calculate the steady-state capital-labor ratio for each country. Does the initial capital-labor ratio affect your results?

(b) Calculate output per worker and consumption per worker for each country.

(c) Which country has the highest output per worker? Explain.

Which country has the highest consumption per worker? Explain.

Answer 1

a) Country A has a capital-labor ratio that is initially twice as big as that of country B, but neither is yet in a steady state. Both countries have the same production function, f(k) = 6k^0.5. Country A has a 10% saving rate, 10% population growth rate, and 5% depreciation rate, while country B has a 20% saving rate, 10% population growth rate, and 20% depreciation rate.

Now,

where   is the depreciation rate and is the saving rate.

At the steady state,

Thus, the steady-state capital labor ratio:

For country A, the steady-state capital-labor ratio = 16

For country B, the steady-state capital-labor ratio = 16

Thus, the initial capital-labor ratio does not affect the results.

b) At steady state,

For country A, output per worker = 24

For country B, output per worker = 24

Again, at steady state,

For country A, consumption per worker = 21.6

For country B, consumption per worker = 19.2

c) Both countries have equal output per worker at steady state but since country B has a higher saving rate, it is able to save more but consumes less.

Thus, country A has higher consumption per worker.