The amount of education the typical person receives varies substantially among countries. Suppose you were to compare one country, called Gilder, with a highly educated labor force with another country, called Florin, with a less educated labor force. Assume that education only affects the level of the efficiency of labor. Also, assume that the countries are otherwise the same: they have the same population growth, the same saving rate, the same depreciation rate, and the same rate of technological progress. Both countries are described by the Solow model and are in their steady states. What would you predict for the following variables?
a. The rate of growth of total income.
b. The level of income per worker.
c. The real rental price of capital.
d. The real wage.

a.The rate of growth of total income:

In the steady state, the growth rate of output is n+g which is the same for both countries.

b.The level of income per worker:

The level of income per worker is higher in Gilder since it has higher A(0) education level.

c.The real rental price of capital.  

Th real rental price of capital is also same in both countries  

d.The real wage.

Real wage will be higher in Gilder which has a higher education level

Explanation:

Education is one factor affecting the efficiency of labor, which we denoted by E. Since country 1 has a more highly educated labor force than country 2, each worker in country 1 is more efficient. That is, E1 > E2. Both countries are in steady state.

a. In the Solow growth model, the rate of growth of total income is equal to n + g, which is independent of the work force's level of education. The two countries will, thus, have the same rate of growth of total income because they have the same rate of population growth and the same rate of technological progress.

b. Both countries have the same saving rate, the same population growth rate, and the same rate of technological progress, we know that the two countries will converge to the same steady-state level of capital per effective worker k*.

The output per effective worker in the steady state, which is y = f(k), is the same in both countries. But y = Y/(L E) or Y/L = y E. We know that y will be the same in both countries, but that E1 > E2. Therefore, yE1 > y*E2. This implies that (Y/L)1 > (Y/L)2. Thus, the level of income per worker will be higher in the country with the more educated labor force.

c. We know that the real rental price of capital R equals the marginal product of capital (MPK). But the MPK depends on the capital stock per efficiency unit of labor. In the steady state, both countries have k1 = k2 = k* because both countries have the same saving rate, the same population growth rate, and the same rate of technological progress. Therefore, it must be true that R1 = R2 = MPK. Thus, the real rental price of capital is identical in both countries.

d. Output is divided between capital income and labor income. Therefore, the wage per effective worker can be expressed as

w = f(k) - MPK • k.

If both countries have the same steady-state capital stock k and the same MPK. Therefore, the wage per effective worker in the two countries is equal.

However, workers are more intereted about the wage per unit of labor, not the wage per effective worker. The wage per unit of labor is related to the wage per effective worker by the equation

Wage per Unit of L = wE.

Thus, the wage per unit of labor is higher in the country with the more educated labor force.

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