1 Question- 4 parts

(30 points) Fertility and the Economy: You have been selected as a special advisor to Texas Governor Greg Abbott to participate in a special task force related to the current pandemic. Instead of epidemiology, though, Governor Abbott would like you to do economics. Specifically, he would like a long-run economic analysis of the pandemic lock down. There is a debate about the effect of the pandemic: did causing people to stay home during the pandemic increase or decrease the birth rate? Your job is not to take a side, but rather to document the effects on real output per capita of each side of the debate. In this question, you will use the Augmented Solow Model to compare the effects of either an increasing or decreasing birth rate on an economy in the long run. Assume a Cobb-Douglas production function. Assume that current n - .2, and either increases or decreases by 0.1. Other key figures in this economy: A - 5, 8 - .1, z - 0.3, and s - .05. Assume the economy is initially in a steady state. (a) Explain, using the Augmented Solow Model, where the economy currently sits, both graphically and with equations, in the steady state. Explain where birth rate enters the model, and derive the central equation. What is the current level of steady-state capita per capita and income per capita? Does this economy grow? At what rate? (b) How do we know the Cobb-Douglas production function is appropriate to represent production in the Solow Model? (c) Explain the effects of an increased or decrease birth rate on the long-run steady state of this economy. Document the effects in general (algebraic expressions) and specific (calculated fig- ures based on values) terms. Address output, capital stock, output per capita, capital stock per capita, consumption per capita, rental rate of capital, and wages. Trace out the effects dynamically, as well as calculate the specific figures before and after the changes. (d) In which situation is the economy better off? Why