Question

40R1/2C1/2, where R is hours of Recreation (1) Carla's utility is described by U(R, C) and C is total consumption. The best wage that Carla can earn is $20 per hour, the price of consumption is 1 and she receives $400 per week from a divorce agreement. Carla has 100 hours per week to allocate between labor and recreation (a) How many hours will Carla work given the parameters described above? (b) How many hours would Carla work if she did not receive the weekly payment from the divorce settlement?

Answer 1

The above question is based on labour-leisure choice Of a consumer. In the first case the consumer has non labour income and in the second case, there is only labour income. The Optimality condition doesn't depend on the nature of the income C=20R , but the optimal bundle does depend on it.

R. Hewn of Richartion U CRI() = 40 R 2 Y2 C- total consumption wage - $20 per hour wont labour income - $400 per week Total Flowns available - 100 Howys for Carla Ciuen the alove information Poudget constraint will let C + 20 R = 400 + 100 (20) C+ PURE 400 + 2000 2400 C+20 R = 2400 a) marginal Rate of substinetion : MRS : 40 42122 Hox£ cl2 R42 scope of budget constscunt : 20 Equating the two f = 20 = 20R 3400 1200 - - - - R Go 100 e labour substituting C:201 in Budget 20 R+ SOR : 2400 contraint : 40R: 2000 R: 240p = 60 Yd -) C: 20X60= 1200 (62,1200) - optimal bonsumption bundle a) carla will work for 40 hours (180-60=40)

. b) if divorce she didn't receive the weekly payment from Settlement iney Audget constraint would be : CH BOR loo (20) CH 20 R 2000 MRS = & And again scope af Budget conste aint : do » 20 c=20R 2000 - 100 labore R hitting it in the Budget constraint : 20R+ 20R: 2000 UOR • dooo R= 2000 : 50 40 3 C = 20450 = 1000 rence (80, 1000) is the optimal Bundle and 100 - 50 = 50 is the labour hours.