Suppose that an economy is described by the following production function: Y t =

Question

Suppose that an economy is described by the following production function:

Yt = At*Kt^a*Lt^b*Zt^c

1

Ytis real GDP at time t, Ktis the capital stock at time t, Ltis the number of worker hours at time t, At is the efficency at time, and Zt^c is the stock of land and natural resources at time t. The parameters a, b, and c are the capital share of national income, the labor share of national income, and the land and natural resources share of national income, respectively.

Suppose that the stock of land and natural resources are constant. Also, suppose that real GDP and the capital stock are both growing at 4 percent per year and worker hours and population are growing at 1 percent per year. Suppose further that the production function exhibits constant returns to scale with capital%u2019s share of output equal to 1/3 and land and natural resources share of output equal to 1/4.

(2 points) What is the annual growth rate of labor productivity? You must show your work.

(2 points) What proportion of labor productivity growth is due to the growth of efficiency (the growth of total factor productivity)? You must show your work.

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