1. Your preferences are summarized by the utility function U ( N , Y ) = N*Y3 where Y is a composite good and N is the number of leisure hours you consume each day. Thus, 24-N =L where L is the number of labor hours supplied each day. Also assume that you have some non-wage income Io a. Given that the price of Y is PY and your nominal wage (in $ / hour) is w derive your optimal demands for leisure and the composite good: N*( . ) & Y*(. ) and therefore L*( . ). Don't forget the 24 hour constraint, and comment on whether your optimal N*, Y*, LS* make economic sense in their arguments....namely, "as w goes down, LS* ... i . Your utility-maximizing demand for leisure ( N ) here is given by the following function: a. N* = [ 24*w + Io ] * [w /PY] N* = [24*w + Io ] / [w/ Py ] C . N* = [ 24*w2 + 10 ] / PY N* = [ 24*w + 10 ]/ [4*w ] ii . Your utility-maximizing demand for the composite good ( Y ) here is given by the following function: a. Y* = 34 * [ 24*w + Io ]/PY ] b. Y* = 34 * [ 24*w + Io]/4*w ] C. Y* = 34 * [ 24*w + 10 ] d. Y* = 34* [ 24*w + 10 ]/[ 4*PY ] iii. Your optimal labor supply ( LS ) here is given by the following function: a LS = 18 -w* Io LS = 24- w* 10 C. LS = 18 - (10/4*w ) d. LS = 24- (10 / 4*w )b. Sketch your labor supply curve from (a) and comment on its shape. i. Which diagram correctly sketches the labor supplyr curve here: a. A b. B c. C cl D ii, We can infer from that sketch that whenever the wage changes and the substitution effect and the income effect on leisure are both non-zero, a. The substitution effect dominates the income effect. b. The income effect dominates the substitution effect. c. The substitution effect just balances the income effect. d. Not enough information to tell. c. Suppose the wage rate is $20ihour. What level of non-wage income will induce you NOT to work? i. At a wage rate of $20 i hour, if non-wage income is , you will maximize utility by NOT working and taking hours of leisure a. $1920 ; 12 1). $1440 ; 24 c. $1920 ; 24 {1. $1440 ; 12 u. memo; 1.: Explain why this isomer-type solution is possible in (e). Sketch your budget constraint [ in ( N , Y ) space ] given the non-wage income you found in (o) and show your optimal oonsmnption point. i. Which diagram represents the earner-type solution in (o)? a. A h. B o. C d. D ii. As In rises, oeteris paribus, we have only effects on leisure and the composite good, eventually leading us to a. Substitution ; work all day In. Inoome ; work all day t: Substitution ; leisure all day (1 Inoorne ; leisure all day In the late 19905, the U3. passed sweeping legislation reforming the function 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 i hour, and that the price of all other goods is 3:] t' unit ofAOG. Reproduce a SINGLE COPY of the diagram above and show either consmner'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 I00 units of AUG and 24 hours of leisure daily. n-ncrtc unma- ii. At this optimum, it is possible for the MRS to be the real wage. a Greater than b. Less than c. Both (a) and (b) are true. d Neither (a) nor {b} is true. Analyze the combined effects of the following tenets of that welfare reform law on Billy's and Charlie's behaviors: {I} A reduction from $10G to $50 of the welfare benets 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 FLY-'17P B C D ii. Web of the diagrams is a possible response of Billy to the changes in the law? a. I only b. I and [I only e. I, [11 or IV only d. I], Ill, or IV only Does the reform law make either individual better off? iii. The reform law Charlie's utility and Billy's utility. Does the reform law make either individual better off? iii. The reform law Charlie's utility and Billy' 5 utility. a. Decreases ; increases b. Increases ; decreases c. Decreases ; has an indeterminate effect on d. Has an indeterminate effect on ; decreases ONLY 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 Bill}.' varies, because we cannot know the law's effect on his a. Substitution effect ; real income 13. Income effect ; real income c. Substitution effect ; real wage d. 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 , C1 ) = C12 + (1/2)* C212 Irving's income today is I, 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 Cz*( r, It , Iz ). i. This consumer's budget constraint is: a. Ci + [Ca / ( 1+ r) ] = hi+ [12/(1+r) ] b. Ci + C2 = h + [12/(1+r)] C. Ci + C2 = 1 + 12 d. Ci + [C /(1 + r) ] = h+ 12 ii. This consumer's utility-maximizing level of consumption today ( C1 ) is: a. C* = (4/5) {h + [12/(1+r) ] } b. C* = [4/(5+r)] {h + [b/(1+r)]} C. C* = [(4+r)/5}{h + [12/(1+r)]} CI* = [5/(4+r)] { h + [ 12/(]+r) ]} ili. This consumer's utility-maximizing level of consumption tomorrow ( C2 ) is: a. C2* = (1/5) [ In (1 +r) + 12] b. C2* = [(1+r)/5] [hi (1+r) + 12] C . C* = [(1+r)/(5+r)] [ hi (1+r) + 12] C* = [1/ (5+r) ] [ hi (1+r) + 12]