Question 11
50 pts
Consider the following production function: $Y_t = A_tK_t^{0.3}L_t^{0.7}$. Suppose that in year t, capital was 20,000, labor was 600, and TFP was 10.
Furthermore, assume that the saving rate is 25%, the depreciation rate is 8%, the population grows at 1% per year and TFP grows at 2% per
year.
Answer the following 3 parts showing your work and formulas.
a) (10 points) Compute aggregate output in year t. Use two decimal places.
b) (20 points) There are 4 parts to this question: (1) calculate capital next year, $K_{t+1}$, using the capital accumulation equation we learned in
class; (2) calculate labor next year, $L_{t+1}$, using the given growth rate for labor; (3) calculate TFP next year, $A_{t+1}$, using the given growth rate
for TFP; and (4) calculate aggregate output next year, $Y_{t+1}$, using the production function. Use two decimal places.
c) (20 points) According to part b), what share did each source of growth (capital, labor, and TFP) contribute to output growth? For
percentages use 2 decimal places (e.g. 6.24%).
