Question

Shelly’s preferences for consumption and leisure can be expressed as U(C, L) = (C – 100) * (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 $10 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 one her budget line?
(c) What is Shelly's reservation wage?
(d) Find Shelly's optimal amount of consumption and leisure.

Answer 1

Step-by-step explanation:

U(C, L) = (C – 100) × (L – 40)

(a) C = (w - t)[110 - L] + 320

C = 10[110 - L] + 320

C + 10L = 1420

where,

C- consumption

w - wages

t - taxes

L - Leisure

(b) Given that,

L = 100 then,

C = 420

`MRS=(MU_(L) )/(MU_(C) )`

`MRS=(C-100 )/(L-40)`

`MRS=(320)/(60)`

= 5.33

(c) L = 110

C = 320

Reservation wage:

`MRS=(C-100 )/(L-40)`

`MRS=(220)/(70)`

= 3.14

(d) At optimal level,

`(C-100)/(L-40)=(10)/(1)`

C - 100 = 10L - 400

C - 10L = -300

C = 10L - 300

Using budget constraint:

C + 10L = 1420

10L - 300 + 10L = 1420

20L = 1720

L* = 86 and C* = 560