305: Econ Midterm1
Answer Key
October 5, 2005 D. Andolfatto Name Instructions. Please write neatly and label all diagrams clearly. Limit your answers to the space provided below each question--do not write your answers on the back of the exam or in the exam booklets (which are to be used for rough work only). 1. [10 marks]. Provide two reasons why it is important for any macroeconomic theory to model individual preferences. Since preferences measure the willingness of individuals so substitute across activities, we can use preferences to help make predictions; Since preferences measure individual well-being, we can use preferences to evaluate the welfare consequences of policy. 2. [10 marks]. Should government policy be designed to maximize an economy's GDP? Explain why or why not. If people wanted to maximize GDP, they would presumably choose to do so without government coercion. People clearly value things other than GDP (like home production, leisure and schooling). Maximizing GDP would mean foregoing all of these things. It is not obvious that this would make people better off. 3. [25 marks]. Consider a model economy consisting of a representative agent with preferences u(c, l) such that M RS(c, l) = (c/l)1/2 . The agent is endowed with one unit of divisible time that can be allocated either to work (n) or non-work (l) activities; i.e., n + l = 1. Consumption (c) is generated by a technology c = y = zn, where z is an exogenous productivity parameter. (a) Write down (mathematically) the choice problem faced by a benevolent social planner (do not solve--just state the problem). Choose (c, l, n) to maximize u(c, l) subject to: c = zn and n+l = 1. (b) Write down the mathematical conditions that characterize (i.e., that would allow you to solve) the optimal allocation (c , l , n ) (again, do not solve the problem). c l
c n + l 1
1/2
= z; = zn ; = 1.
(c) Solve for the optimal allocation as a function of z. n (z) = l (z) = z ; 1+z 1 ; 1+z z2 . 1+z
c (z) = y (z) =
(d) Imagine that this economy experienced exogenous fluctuations in productivity (z). Using a diagram, show how it would be feasible for the planner to stabilize both output and employment. Would it make sense for the planner to stabilize the economy in this way? Explain.
c
A
C
B
l
Efficiency requires that output and employment fluctuate in response to changes in z (say, from A to B in the above diagram). It is feasible for the planner to stabilize both output and employment by choosing an allocation like C. While this stabilizes the business cycle, it obviously reduces economic welfare. (e) Using a diagram depicting labor supply and demand, explain how a competitive economy would react in exactly the same way to exogenous changes in productivity. [Draw diagram with upward sloping labor supply function and downward sloping labor demand function]. An increase in z would increase labor productivity and increase the demand for labor. Higher labor demand would put upward pressure on the real wage and induce households to substitute of out non-market time into market time (employment). Output would expand because more time is spent working, and because labor is more productive. This is precisely how a planner would react to the same increase in labor productivity. 2
4. [15 marks]. Imagine instead that each firm in a competitive economy faced a production technology of the following form: y = z(N )n, where N denotes aggregate (or average) employment (beyond the control of any individual firm). Assume further that productivity is an increasing function of N, so that higher aggregate levels of employment make all firms more productive. One way to model this (as explained in class) is to assume: z(N ) = zL if N NC and z(N ) = zH if N > NC , for some number NC and where zL < zH . Of course, in equilibrium it must be the case that z reflects the real wage, with employment determined entirely by labor supply (i.e., labor demand is indeterminate). Explain (a diagram would be helpful) how this economy can display two equilibria, with each equilibrium determined by a self-fulfilling prophesy. Explain further how such an economy can display business cycles that are driven by exogenous changes in expectations. Finally, why any such fluctuations would not be Pareto optimal (suggesting a potential role for government stabilization policy). Draw a diagram similar to the one in the textbook. Suppose that people expect a high level of employment (beyond the level NC ). Then it is rational to expect that labor productivity (real wage) will be high; i.e., zH . Given this expectation, it is rational to supply a lot of labor; i.e., beyond level NC . But if everyone behaves in this way, then zH will be the true level of productivity, which confirms the initial expectation. The reverse holds true if--for some reason--people initially expected em...