Consider the endogenous growth model in which time can be used for work (u) or human capital accu- mulation (1 u). Output is produced according to Y = zuH, where z is total factor productivity and H is the current stock of human capital. The future human capital stock is given by H = b(1 u)H, where b represents efficiency in producing new human capital. The initial (current) human capital stock is H = 100. The economy is characterized by the following parameters: b = 3.1, z = 60, and u = 0.67.

1. Calculate future human capital (H), and the growth rate of human capital.

2. Calculate current output (Y ), future output (Y ), and the growth rate of output. How does the growth rate of output compare to the growth rate of human capital?

3. Suppose there is a decrease in the share of time spent working to u = 0.66. Calculate the growth rate of output following this change.

4. Are the growth rates you found in parts 1 and 3 the same or different? Explain intuitively why the increase in u did or did not affect the economy's growth rate.

5. Explain how a decrease in u will affect (if at all) the current levels of human capital, output, and consumption: H, Y , and C. If there is no effect, explain why.

6. Explain how a decrease in u will affect (if at all) the future levels of human capital, output, and consumption: H, Y , and C. If there is no effect, explain why.

7. Draw one graph in which you illustrate log-output, ln(Y ), over time under three possible scenarios: (i) a "benchmark" in which u = 0.67 forever; (ii) a temporary decrease to u = 0.66 that only lasts one period, after which u returns to u = 0.67 forever; (iii) a permanent decrease to u = 0.66 forever.

8. Related to your graph above, explain how the level of output and the growth rate of output would compare in each of the three scenarios. Explain your answer.