A country is described by the Solow growth model. It has a population growth rat

Question

A country is described by the Solow growth model. It has a population growth rate of 5 percent and a rate of technological progress of 3 percent. It is currently at the steady state.

a) What is the countryís growth rate for output and output per worker?

b) Assume that the country has to concede territory that contains 20% of its capital stock but only 2% of its population. What happens to its output and output per worker?

c) explain the time path for the growth rates of output and output per worker. explain the changes when the territory loss occurs and what happens to the growth rates in the subsequent years

Explanation / Answer

a) If the economy begins with an initial steady-state capital stock below the Golden Rule level. The immediate effect of devoting a larger share of national output to investment is that the economy devotes a smaller share to consumption; that is, “living standards” as measured by consumption fall. The higher investment rate means that the capital stock increases more quickly, so the growth rates of output and output per worker rise. The productivity of workers is the average amount produced by each worker – that is, output per worker. So productivity growth rises. Hence, the immediate effect is that living standards fall but productivity growth rises. In the new steady state, output grows at rate n+g, while output per worker grows at rate g. This means that in the steady state, productivity growth is independent of the rate of investment.

b) The production function in the Solow growth model is Y = f(K,L), or expressed in terms of output per worker, y = f(k). If the labor force is reduced , the L falls but Capital-labor ratio k = K/L rises. The production function tells us that total output falls because there are fewer workers. Output per worker increases, however, since each worker has more capital. The reduction in the labor force means that the capital stock per worker is higher.Therefore, if the economy were in a steady state, then afterwards the economy has a capital stock that is higher than the steady-state level.

c) In the Solow model, the saving rate affects growth temporarily, but diminishing returns to capital eventually force the economy to approach a steady state in which growth depends only on exogenous technological progress. By contrast, many endogenous growth models in essence assume that there are constant (rather than diminishing) returns to capital, interpreted to include knowledge. Hence, changes in the saving rate can lead to persistent growth.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.