Question

Brittanys preferance for money income and leisure can be exoressed as U(Y,L)= (Y-200)*(L-50). This utitlity function implies that Brittany's marginal utility of leisure is (Y-200) and her marginal utility of money income is (L-50). There are 168 hours in the week available to split between work and leisure. Brittany earns $20 per hour after taxes. She also recieves $400 worth of welfare benefits each week regardless of how much she works.

A) Graph Brittany budget line.

B) Find Brittanys optimal amount of income, leisure and work

Answer 1

Utility function is U(Y,L)= (Y-200)*(L-50). There are 168 hours in the week available Brittany earns $20 per hour after taxes. She also recieves $400 worth of welfare benefits each week

Now budget line has an equation Y = (168 - L)*wage rate + non-labor income

Y = (168 - L)*20 + 400

Y = 3360 - 20L + 400

Y + 20L = 3760

From the utility function |MRS| = (L - 50)/(Y - 200). Optimum choice has |MRS| = slope of budget

(L - 50)/(Y - 200) = 1/20

20L - 1000 = Y - 200

Y = 20L - 800

Substitute this in the budget line

20L - 800 + 20L = 3760

40L = 4560

L = 114

Labor hours = (168 - 114) = 54 hours and leisure hours = 114. Optimal income Y = 20*54 + 400 = $1480