1. Suppose the output per Worker is given by Y/L = 21k? where z; > 0 is a parameter that changes over time, 1 > a > 0 is constant , and kg > 0 is capital per unit labor. (a) What is the effect on total output of a 10% increase in the number of workers? (b) Show how to compute the growth rate gy of Y/L over time in terms of the growth rates of z; and R311. [hint begin by taking logs of the production function, and use the fact that the growth rate of any variable a- is the time derivative of the log ofm). (c) Show how to compute the growth rate of the MPk over time. (d) The government is asking you how to increase the long-run growth rate of output per capita, Y/N, where Y is output and N the pop- ulation size. One policy proposal is to look for ways to increase the number of workers L per capita; the other is to look for Ways to in- crease labor productivity. Are there other possibilities, or does this cover all possibilities? (e) Suppose only one of these tw0 strategies can be investigated; which Would you recommend? (f) Given what you learned about the Solow model is increasing the savings rate likely to be an effective solution