\fMany commentators have recently brought up concerns about rms' monopsony power in setting wages. In this question, we consider the effect of rms' monopsony power on the equilibrium of the economy considered in class. Consider an economy where there is no government spending and taxes, i.e., T : G : 0. Suppose that households' preferences are given by (C (l 02/2) and assume that total leisure time is given by h : 1. Suppose that rms production function is given by Y = N. a As in our model of households, suppose that households are prices takers, i.e., they take wages and rms' prots as given. Write the problem that the households solve and derive their optimal choice of consumption and leisure as a function of wage and rms prots. Hint: leisure should be independent ofprots 7r. b Now, suppose contrary to the model of rms in class, rms choose the amount of labor to hire N as well as their wage to. In other words, the rms know the households labor supply function that you solved for in part 1. When they change their hiring policy, they take into account the fact that this changes workers labor supply. Write the rms' problem and solve for the optimal level of labor demand and wages set by rms. Hint: The rms' problem in this case is a constrained optimization problem where they choose 11) and N subject to the fact that their choice of N must be consistent with households' choice of labor supply that you found in part 1. c Use your solution to part 2 to solve for consumption and rms' prots. Hint: Use the labor demand/supply and wage that you found in part2 and use goods market clearing to solve for consumption and prots. d Solve for the competitive equilibrium of this economy (as dened in class) and compare it with your answer to part 3. Which economy produces more output? Which one delivers a higher welfare to the consumer? Provide an intuitive explanation for your results. 6 BONUS (10 points): what policies would you recommend to increase the welfare in the economy where rms have monopsony power