Eco317 Exam

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Intermediate Macroeconomic Theory Economics 317: Sections A & B

Pre-Midterm Exam: Spring 2014       Directions: Please answer all questions. Your answers should be as thorough and as precise

as possible. If necessary you may continue your answer to any question at the back of the page.

  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+) u(c2, l2) + 1/(1+)2 u(c3, l3) +. . . . , where c and l represent consumption and work effort and  is the subjective rate of time preference. Finally, assume that households in 317land behave in accordance with the permanent income hypothesis.

 

   

1. 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. Prove that optimizing households’ intratemporal allocation is consistent with this principle by doing the following.

(a) Derive the slope of an indifference curve in (c,l) space and provide a thorough explanation of its economic interpretation. (10 points)

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(b) Draw a properly labelled diagram that illustrates how the representative household

will choose its optimal (c, l) combination and specify the optimality condition that should prevail when the household has chosen optimally. (5 points)

(c) Thoroughly demonstrate/explain the exact sense in which this behavior is consistent with the fundamental principle stated above. (15 points)

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2. Prove that optimizing households’ intertemporal allocation of consumption is consistent with the principle articulated in the preamble to question # 1 by doing the following.

(a) Thoroughly derive the slope of the intertemporal budget constraint the household faces in (c1, c2) space and explain its economic interpretation or conceptual importance. (10 points)

(b) Thoroughly derive the slope of the representative household’s indifference curve in (c1, c2) space and explain its economic interpretation or conceptual importance. (10 points)

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(c) Draw a properly labelled diagram that illustrates how the representative household will choose its optimal (c1, c2) combination and specify the optimality condition that should prevail when the household has chosen optimally. (5 points)

(d) Thoroughly demonstrate/explain the exact sense in which this behavior is consistent with the fundamental principle stated in the preamble to question number 1. (15 points)

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3. (a) Write a clear statement in words that defines permanent income and summarize your statement with an equation. (5 points)

 

                       

(b) What is the central hypothesis, tenet, or point of the permanent income hypothesis? (5 points)

                     

(c) Suppose 317land experiences an improvement in technology and as a result the representative household’s current income increases by $1,000. Evaluate the effects of this change in the economic environment on the representative household’s current consumption by doing the following.

  (i) Assuming that households behave according to the permanent income

hypothesis, thoroughly derive the marginal propensity to consume that is applicable in this case. (N.B. Avoid vigorous assertion.) (15 points)

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(i) cont’d                                                                                    

(ii) Given your analysis in (i) above, evaluate the accuracy of the following statement. (5 points)

“Under the permanent income hypothesis, improvements in technology do not lead to

increases in savings.”