Question

Calculate the steady-state level of capital in each of the following economies. Unless other- wise stated, use the standard Solow model assumptions about national production, spend- ing/saving, and capital accumulation.

a) The contribution of physical capital to national production in advanced countries such as the United States may be overstated. Some empirical estimates suggest it is closer to 20%, rather than 33% (the one-third that pops up in the production function), which implies the appropriate (per effective worker) production function for the United States is y = k1/5. (5 points)

b) Research economists at the central bank for a particular country find that a 1% increase in income causes households to increase savings by more than 1%. To account for this, they adjust their growth model by using the assumption that household savings/investment (per effective worker) is given it = syt2. (5 points)

Answer 1

A steady state economy is an economy of stable or mildly fluctuating size. The term typically refers to a national economy, but it can also be applied to a local, regional, or global economy. An economy can reach a steady state after a period of growth or after a period of downsizing or degrowth.

Assumptions
The key assumption of the neoclassical growth model is that capital is subject to diminishing returns in a closed economy.

- Given a fixed stock of labor, the impact on output of the last unit of capital accumulated will always be less than the one before.

- Assuming for simplicity no technological progress or labor force growth, diminishing returns implies that at some point the amount of new capital produced is only just enough to make up for the amount of existing capital lost due to depreciation. At this point, because of the assumptions of no technological progress or labor force growth, we can see the economy ceases to grow.

- Assuming non-zero rates of labor growth complicate matters somewhat, but the basic logic still applies – in the short-run, the rate of growth slows as diminishing returns take effect and the economy converges to a constant "steady-state" rate of growth (that is, no economic growth per-capita).

- Including non-zero technological progress is very similar to the assumption of non-zero workforce growth, in terms of "effective labor": a new steady state is reached with constant output per worker-hour required for a unit of output. However, in this case, per-capita output grows at the rate of technological progress in the "steady-state".

The production function is:

Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor?

MPL = 1/3*K1/3H1/3 L-2/3. Increase in human capital raises MPL.

Derive an expression for the marginal product of human capital. How does an increase in the amount of human capital affect the marginal product of human capital?

MPH = 1/3*K1/3H-2/3 L1/3. Increase in human capital lowers MPH.

What is the income share paid to labor? What is the income share paid to human capital? In the national income accounts of this economy, what share of total income do you think all workers would appear to receive?
1/3, 1/3, and 2/3, respectively.