Intermediate Macroeconomic Theory Economics 317: Section B
Scenario:This exam is based on the following description of 317land. 317land is a monetary economy in which the typical household has production opportunities summarized by the production function yt = f(lt). In addition, households have access to a competitive commodity or goods market and to a perfect credit or bond market. The bonds in 317land are one period bonds that pay real interest at rate R. Assume that the typical household in 317land has an infinite planning horizon and seeks to maximize horizon long utility given by U = u(c1, l1) + 1/(1+r) u(c2, l2) + 1/(1+r)2 u(c3, l3) +. . . . , where c and l represent consumption and work effort and r is the subjective rate of time preference. Finally, assume that households in 317land behave in accordance with the permanent income hypothesis.
- The president of 317land believes that it is important to stimulate current economic activity in 317land and is considering a stimulus package that includes tax cuts. His advisors have provided him with two alternative policies. Under policy A, the representative household will receive a permanent tax cut that will reduce their tax liability in the current period and in every subsequent period by $100. Under policy B, the representative household will receive a one-time tax rebate of $1000.00 dollars. Under that assumption that the government’s primary goal is to encourage current consumption and that the real interest rate is 3 percent, evaluate which of these policies is most consistent with the government’s objective by doing the following.
(a) Thoroughly derive the marginal propensity to consume that is applicable for policy A and use it to predict the effect of policy A on per capita consumption. (state your final result as a dollar figure. (15 points)
(b) Thoroughly derive the marginal propensity to consume that is applicable for policy B and use it to predict the effect of policy B on per capita consumption. (state your final result as a dollar figure). Identify the policy you would recommend and explain why. (15 points)
(c) Will these policies affect work effort? Explain briefly. (10 points)
- Prove that the (c1, c2) combination that is consistent with maximization of the representative optimizing household’s lifetime utility is the (c1, c2) combination at which the marginal benefit is equal to marginal costs by doing the following.
(a) Use whatever combination of written and graphical exposition you deem necessary to demonstrate that the representative optimizing household in 317land will pick the (c1, c2) combination for which the marginal rate of substitution of consumption in period 2 for consumption in period one is equal to the intertemporal relative price of period one consumption. (15 points)
(b) Thoroughly demonstrate/explain the exact sense in which the behavior you described in your answer to question 2(a) is consistent with the fundamental principle that the optimal level of a good service or activity is the level at which marginal benefit is equal to marginal costs. (15 points)
- In class we noted that in order to maximize horizon-long utility households in an economy like 317land will have to allocate resources optimally along three dimensions. These are: intratemporal allocation (i.e. the choice of (c, l) in any period t, intertemporal allocation of consumption, and intertemporal allocation of work effort. Fundamental economic principles instruct that optimizing households’ allocation of resources along these dimensions will be guided by the fundamental principle that the optimal level of a good service or activity is the level at which marginal benefit is equal to marginal costs.
(a) Write an essay that thoroughly proves that the representative optimizing household’s intertemporal allocation of work effort will be consistent with this principle. (20 points)
(b) Thoroughly evaluate the accuracy of the following statement.
“Holding all else constant, a reduction in the intertemporal relative price of current consumption will induce optimizing households to intertemporally reallocate work effort from the future (or future periods) to the current period.” (10 points)
(c) Suppose 317land is hit by a natural disaster. Use whatever combination of written and graphical exposition you deem appropriate to explain how this change in the economic environment is likely to affect the representative household’s intertemporal allocation of work effort. (10 points)