Modified version of problem 6.15 from Nechyba text Assume Mr. T gets utility from consuming leisure (l) and consumption goods (c). He can choose anywhere between 0 and 24 hours of leisure per day. He can purchase consumption goods (priced at $1 per unit) by giving up leisure and working for $5 per hour. You drew this graph for problem #5 in the homework for Chapter 2 and Chapter 3.

Extra Credit Question Modified version of problem 6.15 from Nechyba text Assume Mr. T gets utility from consuming leisure (1) and consumption goods (@). He can choose anywhere between 0 and 24 hours of leisure per day. He can purchase consumption goods (priced at $1 per unit) by giving up leisure and working for $5 perhour. You drew this graph for problem #> in the homework for Chapter 2 and Chapter 3. Now the goverment decides to offer to Mr. T their AFDC cash payment of up to $25 per day. If he earns $5 or less per day (by working 1 hour or less) he receives the full $25. Ifhe earns more than $5 per day ( by working more than 1 hour per day), his cash payment is reduced by $1 for every dollar he earns over $5. So once he earns a total of $30 (or works 6 hours) his cash payment will fall to zero. Ifhe works more than 6 hours his income is $5 x the number of hours worked (with no government payment received). You drew this budget line line also in problem #5 in the homework for Chapter 2 and Chapter 3. Here is that budget line. ADG AFDC - stupe= - 5 (23, 34) 30 (18, 30) (14 25) 16 18 14 leisure a. In the budget line, you see that you have two line segments with slope = -5 separated by aAFOC - slope = -5 (23 34) 30 (18, 30) (24 25 ) 16 18 leisure a. In the budget line, you see that you have two line segments with slope = -5 separated by a horizontal line. There is an outward protruding kink at &= 23 and c= $30 and an invard protruding kink at & = 18 and c = $30. What is the equation of the line between 0 and 1 hours of work (i.e. between 23 and 24 hours of leisure? c= (ii) What is the equation of the line for hours of work greater than 6 (i. e., for leisure of less than 18)? C=. b. Assume that Mr. T's utility function is given by U(L, () = cl Calculate U(24, 25) for the comer solution with 24 hours of leisure. (ii) Calculate U(23, 30) for the kink with 23 hours of leisure. Will Mr. T prefer to work 1 hour per day or zero hours per day, if those are his only two choices? iii) Why won't Mr. T ever choose to work more than 1 hour but less than 6 hours per day! (iv Find Mr. T's utility-maximizing choice by looking for any tangency points on the two lime segments with slope = -5 (between 23 and 24 hours of leisure and between 0 and 18 hours of leisure) and comparing the utility at those points with the utility at the kink (23 hours of leisure) and the corner solution (24 hours of leisure.) Would Mr. T have chosen to work more hours without the AFDC program? C. Assume that Mr. W's utility function is given by V(, () = cal (i) Calculate V(24, 25) for the comer solution with 24 hours of leisure. (ii) Calculate V(23, 30) for the kink with 23 hours of leisure. Will Mr. W prefer to work 1 hour per day or zero hours per day, if those are his only two choices? (iii) Why won't Mr. W ever choose to work more than 1 hour but less than 6 hours per day?(iv) Find Mr. W's utility-maximizing choice by looking for any tangency points on the two line segments with slope = -5 (between 23 and 24 hours of leisure and between 0 and 18 hours of leisure) and comparing the utility at those points with the utility at the kink (23 hours of leisure) and the corner solution (24 hours of leisure.) (V) Would Mr. W have chosen to work more hours without the AFDC program? d. Reproduce the graph from above and then draw in two of Mr. T's indifference curves, one through the kink point and one through the tangency point with &