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.

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

              = 5.33

(c) L = 110

C = 320

Reservation wage:

= 3.14

(d) At optimal level,

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

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public property refers to the property that can be used by all legal citizens in a certain country. the public property was created and maintain using the government budget that allocated specifically for it. the budget itself come from the citizen's income tax payment.