The Mankiw-Romer-Weil (1992) model. As mentioned in this chapter, the extended Solow model that we have considered differs slightly from that in Mankiw, Romer, and Weil (1992). This problem asks you to solve their model. The key difference is the treatment of human capital. Mankiw, Romer, and Weil assume that human capital is accumulated just like physical capital, so that it is measured in units of output instead of years of time. Assume production is given by Y = KaHb(AL)1-a-b, where a and b are constants between zero and one whose sum is also between zero and one. Human capital is accumulated just like physical capital: H # = sHY - dH, 13See Quah (1993) and Friedman (1992).

where sH is the constant share of output invested in human capital. Assume that physical capital is accumulated as in equation (3.4), that the labor force grows at rate n, and that technological progress occurs at rate g. Solve the model for the path of output per worker y K Y>L along the balanced growth path as a function of sK, sH, n, g,

d, a, and

b. Discuss how the solution differs from that in equation (3.8). (Hint: defi ne state variables such as y>A, h>A, and k>A.)