Question

1. Suppose the following is true about Edna's utility: u = 10c0.5 p0.5 a. Calculate her utility if she consumes c = $49 and enjoys l = 12.25 hours of leisure. b. If she increases leisure to l = 16 hours, how much does she need to consume in order to maintain her level of utility in part (a)? C. If she decreases her leisure to l = 9 hours, how much does she need to consume in order to maintain her level of utility in part (a)? d. Draw her indifference curve on a graph. e. What is her marginal utility of consumption when she consumes c = $49 and enjoys f = 12.25 hours of leisure? f. What is her marginal utility of leisure at this point? 8. What is her marginal rate of substitution at this point? Provide an interpretation for your answer. h. If Edna's wealth is $2 and the wage is W = $4, what is her budget constraint? i. Draw her budget constraint on your graph in part (d). j. Show that c = $49 and l = 12.25 is feasible given her budget constraint. k. Given this budget constraint, is c = $49 and l = 12.25 Edna's optimal combination of consumption and leisure? Why or why not?

Please show steps for parts g through k

Thank you for your help!

Answer 1

491 2+ ---- - ---- (a) When c = $49 and 1= 12:25, utility = 10 (49) (12.2505 - 10x7x3.5 = 245 (b) 245 = 100°S (163.95 -> C5 - 245 -> - (125) = 37.51563 (6) 245=10 cos (agos os 245 c= 8.167 - 66.69444 (d) Refer to fig. 1 indifference curve in 10]. (Figil (c) AL (2) Muc = 4 = 345 = 2.5 (f) MU, - o - 24 - 24 = 10 o 12.25 Eseisume (9) Marginal rate of substitution (MRS) is the slope of the andifference cureve, which shows the consumption spending Edna is willing to give up for I more hour of leisure. Hence MRs = Islope of the indifference curve) = 2 » MRS = e = Mu L = 2 x 20 = & Hence, Edna is willing to give up $C) for 1 more hour of leisure. (6) Let Edna's wealth ant to wage w- $4 per har = leisure to laber hours. and et 1²-t = total available hours (e=endarment wealth), wewage) and Total expenditure on consumption=c. Total income would be wir etw (t-1) Hence the budget constraint is c= etw (t-1) When e=$2 and w=$4, it becomes et c=2+4t - 44 (2) Refer to fig 1, where ABT is the budget constraint, i.e. there is a kink corresponding to w=2 Henega û with o Consider t=24 Hence, the budget constraint becomes c=2+4 (24)-4L =98-4l. with l=12.25 c = 98-4 (12-25) = 98-49 249 fact on the Hence, c= $49 and l = 12.25 bundle is feasible and it is in budget line as shown in fig. 1 . W with c = 49 and l = 12.25, slope of indifference curcue = MRS - 12.25 49 On the other hand, at c = 49 and 1=12-25, slope of budget constraint = -4. since = 2 + 4t - 4L, Optimal bundle sclection requires slope of budget line to be equal to MRS, when (2+4t) is intercept & -4 = slope. which is not true in this case. Hence, the bundle s of c=49 and l = 12.25 is not aptimal.