The neoclassical consumption model, a retirement perspective: Consider thespecial case solved in the text where ! = 1 and utility takes the log form.Suppose the real interest rate is 5 percent. Let’s give this consumer a fnancial profle that might look like that of a middle-aged college professor contem-plating retirement: initial assets are ftoday = $50,000, and the path for labor income is ytoday = $100,000 and yfuture = $10,000.(a) What is the individual’s human wealth? Total wealth?

a. Based on only the first-order condition with respect to labor computed in part a (Based on the given Lagrangian, compute the representative consumer's first-order conditions with respect to consumption and with respect to labor). Qualitatively sketch two things in a diagram with the real wage on the vertical axis and labor on the horizontal axis. First, the general shape of the relation ship between w and n (perfectly vertical, perfectly horizontal, upward-sloping, downward-sloping, or impossible to tell). Second, how changes in / affect the relationship (shift it outward, shift it in inward, or impossible to determine). Briefly describe the economics of how you obtained your conclusions. (Note: In this question you are not to use the first-order condition with respect to consump tion nor any other conditions.) b. Now based on both of the two first-order conditions computed in part a, construct the consumption-leisure optimality condition. Clearly present the important steps and…

Consider the problem of an individual that has Y dollars to spend on consuming over wo periods. Let c1 denote the amount of consumption that the individual would like co purchase in period 1 and c2 denote the amount of consumption that the individual would like to consume in period 2. The individual begins period 1 with Y dollars and can purchase ci units of the consumption good at a price P and can save any unspent wealth. Use s1 to denote the amount of savings the individual chooses to hold at the end of period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the ndividual has at his/her disposal to purchase consumption goods in period 2 is (1+r)s1. This principal and interest on savings is used to finance period 2 consumption. Again, for simplicity, we can assume that it costs P2 dollars to buy a unit of the consumption good in period 2.

Figure 7.1 C b. 100 In Figure 7.1, all of the following is true except: An additional dollar of income always induces some additional consumption. O There is some level of consumption that is independent of income. O The marginal inclination to consume is greater than zero. O At zero income there is zero consumption.

8. The individual's budget line (in the neo-classical consumption - leisure choice model) switches from BL₁ to BL2. What change(s) could have caused this? C BL₁ BL 2 a decrease in the wage only. T l O an increase in the wage only. O an increase in non-labor income only. O an increase in both the wage and non-labor income. O a decrease in the wage, but an increase in non-labor income.

Consider the household model that you have seen in class but now assume that the household lives for 3 periods. She earns $100 in the first period, $110 in the second period, and $120 in the third period. Her goal is to consume equal amounts in all periods. The interest rate is the same in all periods. Which of the following statements are true? а. In the first period she will save b. In the first period she will borrow C. In the third period she will save In the second period her consumption is $100 d.