In the late [9905, the U.S. passed sweeping legislation retorrnmg tne Iunction and practice of providing welfare benets to the poor. Though simplied, this question asks you to examine the potential effects of this law on the behavior of Billy and Charlie (two representative welfare recipients) based on theories we've used in our unit on consumer theory. Suppose, as indicated in the diagrams at the end of this problem set, Billy and Charlie face the usual tradeoffs between leisure and all other goods (AOG's), and they view both of those goods as normal goods. In addition, each is able to use welfare benets when not working to purchase some subsistence level of all other goods. Assume, initially, both of our representative welfare recipients optimize at point \"A\" in the diagram, choosing to consume, for example, $100 worth of all other goods and 24 hours of leisure daily. Assume the initial wage is $10 at hour, and that the price of all other goods is ill 1' unit of A00. Reproduce a SINGLE COPY of the diagram above and show either consumer's optimization at point \"A". You may assume heishe has the usual \"bowed in\" indifference curve shape, and that preferences are strictly convex and strictly monotonic. Is it possible for this consumer's MRS (out of AUG and into leisure) to be different from the real wage here? Why or why not? i. Which diagram shows Billy's or Charlie's optimization at point \"A\" where hefshe is consuming IDO units of AUG and 24 hours of leisure daily. a. A b. B c. C d. D ii. At this optimum, it is possible for the MRS to be the real wage. Greater than Less than a. b. :2. Both (a) and (h) are true. d Neither (a) nor (b) is true. b. Analyze the combined effects of the following tenets of that welfare reform law on Billy's and Charlie's behaviors: (1) A reduction from $100 to $50 of the welfare benefits going to those not working. (2) An increase in the EITC (Earned Income Tax Credit) that effectively acts as a wage subsidy to the working poor. Draw TWO NEW diagrams [one for Billy and one for Charlie], each similar to the one in (a) above. Demonstrate in your diagrams how these two changes in the law may cause: *Billy to begin working *Charlie to continue not working i. Which of the diagrams correctly portrays Charlie's documented response to the changes in the law? a b. C. ii. Which of the diagrams is a possible response of Billy to the changes in the law? a I only b. I and II only C . I, II, or IV only II, III, or IV only Does the reform law make either individual better off? iii. The reform law Charlie's utility and Billy's utility. a Decreases ; increases b . Increases ; decreases C . Decreases ; has an indeterminate effect on Has an indeterminate effect on ; decreasesONLY for Billy's case, use a table to document the substitution effect and income effect of these reform law changes on his behavior. Show Billy's substitution effect and income effect in your diagram as well. iv. The direction of the for Billy varies, because we cannot know the law's effect on his a. Substitution effect ; real income b . Income effect ; real income C. Substitution effect ; real wage Income effect ; real wage 3. Let's consider the two-period Fisher (named after economist Irving Fisher) model of consumption today, consumption tomorrow and saving that we will discuss in lecture. Irving has preferences for consumption today ( Ci ) and consumption tomorrow ( C2 ) according to the following: U ( CI, C2 ) = C12 + (1/2)* C21/2 Irving's income today is In and his income tomorrow is 12 . a. Assume you can lend any amount of your current income and borrow against any amount of your future income (tomorrow's income) at the same interest rate r . Derive an expression for your budget constraint, essentially in present value terms. Use that constraint to find the optimal consumption pattern Ci*( r, I1, 12 ) and C2*( r, It , Iz ). i. This consumer's budget constraint is: a. Ci + [Ca/ ( 1+ r) ] = h+ [ha/(1+r)] b . Ci + C2 = h + [12/(1+r)] C. Ci + Cz = 1 + 12 Ci + [C/(1+ r) ] = h + Iz 11. This consumer's utility-maximizing level of consumption today ( C1 ) is: C* = (4/5) {h + [12/(1+r) ] } = [4/(5+r)]{ h + [12/(1+r) ]} CI* = [(4+r)/5} {h + [12/(1+r)] } C* = [5/(4+r)] {hi + [12/(1+r) ]}iii. This consumer's utility-maximizing level of consumption tomorrow ( C2 ) is: a. C2* = (1/5) [ In (1 +r) + 12] b . C2* = [(1+r)/5] [h (1+r) + 12] C . Cz* [(1+r)/(5+r)] [h (1+r) + 12] d C2* = [1/ (5+r) ] [ h (1+r) + 12] b. Consider two proposals before Congress: a tax rebate today of $10,000 and a bill to make a $10,000 per year tax cut permanent. How might these plans affect current consumption [Ci*( r, I1 , 12 )] ? Namely, the tax rebate would increase only In by $10,000 but the permanent tax cut would increase both In and 12 by $10,000. Essentially, you're computing the marginal propensity to consume out of current income and also out of permanent income. Which plan would have the more stimulative effect on spending today? How might this analysis inform the debate as to how to stimulate an economy coming out of recession? [ For those interested, Milton Friedman won the Nobel Prize in economics in part for his work on the permanent income hypothesis - which you're addressing here! ] i. The plan has the more stimulative effect on spending today, because this consumer's level of Ci depends a Tax rebate ; only on income today b . Tax rebate ; on both income today and income tomorrow C . Permanent tax cut ; only on income today Permanent tax cut ; on both income today and income tomorrow C. Using your answers from (a), write down Irving's optimal consumption bundle for the special case where r= .20, I1 = $17,000 and 12 = $42,000 i. Irving's optimal consumption bundle in this case is to consume today and tomorrow. a. $40,000 ; $2,000 b. $17,000 ; $42,000 C. $40,000 ; $14,400 $17,000 ; $14,400 ii. In order to achieve this optimum, Irving today, and tomorrow. a. Neither borrows nor lends today ; consumes only his income b. Borrows today ; consumes less than his income C. Lends today ; consumes more than his income d. None of the aboved. Suppose your incomes are as in (c) but that now you can borrow at r = .40 but that your interest rate on savings is only .10. Banks have to make money too! Write down your budget constraint under these conditions. Be precise and piecewise. Calculate Irving's optimal consumption bundle now and show in a diagram - rough is fine, provided it shows the proper budget constraint modification. i. For levels of C1 above 1 = $17,000 (namely if Irving borrows!), his budget constraint would be: a. Ci + [ C2 / (14)] = h + [12/(1.4) ] b. Ci + C = In+ [12/ (1.4) ] C. CI + C = 1+ 12 d. C + [C/ (14)] = h + 12 ii. For levels of C1 below In = $17,000 (namely if Irving lends/saves!), his budget constraint would be: a. Ci + [C/(1.1)] = h + [12/(1.1)] b . Ci + C2 = 1 + [12/ (1.1)] C. Ci + C2 = 1 + 12 d. Ci + [ C2/ (1.1 ) ] = 1 + 12 iii. Irving's optimal consumption bundle given the different borrowing and lending rates here is to consume today and tomorrow. a. $36,344 ; $12,498 b. $17,000 ; $42,000 C. $34,815 ; $17,059 d. $42,000 ; $17,000