Question

7. ) Shelly's preferences for consumption and leisure can be expressed as U(C, L) (C-100) x (L-40). This utility function implies that Shelly's marginal utility of leisure is C- 100 and her marginal utility of consumption is L - 40. There are 110 (non-sleeping) hours in the week available to split between work and leisure. Shelly earns S10 per hour after taxes. She also receives $320 worth of welfare benefits each week regardless of how much she works a) Graph Shelly's budget line. b) What is Shelly's marginal rate of substitution when L = 100 and she is on her budget line? c) What is Shelly's reservation wage? d) Find Shelly's optimal amount of consumption and leisure

Answer 1

U(c, L) = (c - 100) (L - y_0) MU_L = c - 100 mu_c = L - y_0 Total labor hours = 110 hours a) if shelly doesn't work she enjoys leisure for 110 hours and consumes only $320 (which is welfare benefits) And if she doesn't enjoy leisure at all she consumes $320 + $10 110 = $(320 + 1100) = $1420 by plotting these points we get shellys budget line \r\n b) when L = 100 It implies that she works for (110 - 100) = 10 hours so her consumption = $320 + $(10)(10) = $(320 + 100) = $420 MRS = MU_L/MU_C MRS = $53.33 c) Reservation wage is the MRS when she is working no hour when working no hour shelly leisure for 110 hours and consume (c) = $320 \r\n Thus MSR = c - 100/L - 40 = 320 - 100/110 - 40 = 220/70 = $3.14 Hence shellys reservation wage is $3.14 d) To find optimal amount of consumption and leisure Equate MRS with wage Budget line C = 320 + 10(110 - L) w = MRS 10 = C - 100/L - 40 10 = 320 + 10(110 - L) - 100/L - 40