Problem Set 4: Aggregate Supply Economics 32OL March 28, 2021 Administrative Details: Please submit in your problem set by Saturday April 17th through Canvas. For this fourth problem set, please work on your own, that is, you cannot work in groups when developing the solutions. If you have questions regarding these problems, please contact the teaching assistants. Problems 1. Suppose that the production function had constant returns to labor (a = 0), so that the marginal product of labor is given by M PN = A. Derive the demand curve for labor. How does it differ from the one in the text? How would this affect the determination of an equilibrium in the labor market? 2. Suppose we allow for an income tax 7' on labor income. Assume workers pay for the tax out of their earnings. Thus, instead of earning W/ P per hour, they get (1 T) W/ P in aftertax income. Suppose the government lowers the income tax rate. Show graphically how this would affect labor supply and equilibrium in the labor market. Describe how this would shift the aggregate supply curve? 3. Why does the longrun aggregate supply curve not depend on expected prices, while the shortrun aggregate supply curve does? 4. Suppose that we decided to follow the labor economics literature and assume that the income and substitution effects cancel out, so that the labor supply decisions of individuals were independent of the real wage. In other words, suppose the labor supply curve is vertical. What would this imply about the slope of the shortrun aggregate supply curve? What would it imply about uctuations in output in the shortrun