Suppose that there are two types of human capital

that an individual can accumulate. During the currentperiod, individual i has Hi1 units of type 1 humancapital, and Hi2 units of type 2 human capital. If individual i chooses to allocate 1u units of time to accumulating type 1 humancapital, then the quantity of type 1 human capital the individual has in the future period is

Hi1=b1(1u)(a(Hi1+Hi2)+(1a)H1),

where H1 is the average level of type 1 human capital in the economy.Alternatively, if individual i allocates 1u units of time to accumulating type 2 humancapital, then the quantity of type 2 human capital the individual has in the future period is

Hi2=b2(1u)(Hi1+Hi2).

Assume that b2>b1.

a. Suppose that all individuals choose to accumulate type 1 human capital. What happens to the distribution ofincome, consumption, and human capital across the population in the longrun, and at what rates doindividuals' incomes,consumption, and human capital grow in the longrun?

If all individuals choose to accumulate type 1 human capital

A.

then the growth rates ofindividuals' incomes,consumption, and human capital will be equal to b1(1u)1 throughout current and future periods. The current period differences in levels ofincome, consumption, and human capital will persist into the long run.

B.

then, in the longrun, all individuals will have the same quantity of humancapital, H1. Current period differences in levels of income and consumption amongst individuals will persist. The growth rates of human capital amongst all individuals will eventually be equal to b1(1u)1 after human capital levels have converged to H1. The growth rates of income and consumption will be consistently equal to b1(1u)1 throughout.

C.

then, in the longrun, it is impossible to determine the distribution ofincome, consumption, and human capital across thepopulation, as well as the growth rates ofincome, consumption, and human capital without the knowledge of values for the efficiency of human capitalaccumulation, b1, and the parameter for the prevalence human capital externalities a.

D.

then, in the longrun, all individuals will have the same quantity ofincome, consumption, and human capital. The growth rates ofincome, consumption, and human capital will eventually all be the same amongst individuals across the population and equal to b1(1u)1.

b. Suppose instead that all individuals choose to accumulate type 2 human capital. What happens to the distribution ofincome, consumption, and human capital across the population in the longrun, and at what rates doindividuals' incomes,consumption, and human capital grow in the longrun?

If all individuals choose to accumulate type 2 human capital

A.

then, in the longrun, the levels of humancapital, income, and consumption will converge and individuals across the population will have the same levels of humancapital, income, and consumption. The growth rates of humancapital, income, and consumption will eventually taper off and approach a growth rate of zero as the economy gets closer to maximum output potential.

B.

then, in the longrun, the levels of humancapital, income, and consumption will converge and eventually the levels of each will be the same amongst individuals across the population. The growth rates for humancapital, income, and consumption will differ for a period of time until the levels have converged. In the longrun, growth rates will be equal to b2(1u)1 and the same amongst individuals and the same across humancapital, consumption, and income.

C.

then, in the longrun, it is impossible to determine the distribution ofincome, consumption, and human capital across thepopulation, as well as the growth rates ofincome, consumption, and human capital without the knowledge of values for the efficiency of human capitalaccumulation, b2.

D.

then the growth rates of humancapital, consumption, and income will be b2(1u)1 for eachindividual, forever. As aresult, the differences inincome, consumption, and human capital in the current period will also persist forever.

c. Explain any differences between your results in parts(a) and(b) and discuss.

Accumulating

type 2 human capital

type 1 human capital

is more efficient than accumulating

type 2 human capital.

type 1 human capital.

However,

type 2 human capital

type 1 human capital

generates human capital externalities that reduce income inequality. This comparison outlinesreal-world tradeoffs that may exist between achieving high rates of growth and achieving low inequality in income.