Exam 8: Economic Growth I: Capital Accumulation and Population Growth

If an economy with no population growth or technological change has a steady-state MPK of 0.1, a depreciation rate of 0.1, and a saving rate of 0.2, then the steady-state capital stock:

Assume that a country's per-worker production is y = k^1/2, where y is output per worker and k is capital per worker. Assume also that 10 percent of capital depreciates per year (= 0.10). a. If the saving rate (s) is $0.4$ , what are capital per worker, production per worker, and consumption per worker in the steady state? (Hint: Use $s y = \delta k$ and $y = k ^ { 1 / 2 }$ to get an equation in $s , \delta , k$ , and $k ^ { 1 / 2 }$ , and then solve for $k$ ) b. Solve for steady-state capital per worker, production per worker, and consumption per worker with $s = 0.6$ . c. Solve for steady-state capital per worker, production per worker, and consumption per worker with $s = 0.8$ . d. Is it possible to save too much? Why?

If a larger share of national output is devoted to investment, then living standards will:

In an economy with population growth at rate n, the change in capital stock per worker is given by the equation:

In the Solow growth model with population growth, but no technological progress, if in the steady state the marginal product of capital equals 0.10, the depreciation rate equals 0.05, and the rate of population growth equals 0.03, then the capital per worker ratio ____ the Golden Rule level.

Examination of recent data for many countries shows that countries with high saving rates generally have high levels of output per person because:

Assume that two countries both have the per-worker production function y = k^1/2, neither has population growth or technological progress, depreciation is 5 percent of capital in both countries, and country A saves 10 percent of output whereas country B saves 20 percent. If A starts out with a capital-labor ratio of 4 and B starts out with a capital-labor ratio of 2, in the long run:

In the Solow growth model, increases in capital ______ output and ______ the amount of output used to replace depreciating capital.

What are the two main ingredients and assumptions of the Solow model?

Larger quantities of steady-state capital have both a positive and negative effect on consumption per worker in the Solow model (assume no population growth or technological progress). Explain.

The formula for the steady-state ratio of capital to labor (k*) with population growth at rate n but no technological change, where s is the saving rate, is s:

The economies of two countries, Thrifty and Profligate, have the same production functions and depreciation rates. There is no population growth or technological progress in either country. The economies of each country can be described by the Solow growth model. The saving rate in Thrifty is 0.3. The saving rate in Profligate is 0.05. a. In which country is the level of steady-state output per worker larger? Explain. b. In which country is the steady-state growth rate of output per worker larger? c. In which country is the growth rate of steady-state total output greater?

With a per-worker production function y = k^1/2, the steady-state capital stock per worker (k*) as a function of the saving rate (s) is given by:

If the production function exhibits decreasing returns to scale in the steady state, an increase in the rate of population would lead to:

Exhibit: Steady-State Consumption I The Golden Rule level of the capital-labor ratio is:

In the Solow growth model of Chapter 8, the demand for goods equals investment:

In the Solow growth model, with a given production function, depreciation rate, no technological change, and no population growth, a higher saving rate produces a:

Assume two economies are identical in every way except that one has a higher population growth rate. According to the Solow growth model, in the steady state the country with the higher population growth rate will have a ______ level of output per person and ______ rate of growth of output per worker as/than the country with the lower population growth rate.

When does a steady state occur?

An increase in the saving rate starting from a steady state with less capital than the Golden Rule causes investment to ______ in the transition to the new steady state.