Question

Suppose Tom has a utility function U=C*L C= consumption L= hours of leisure Tom has 100...

Suppose Tom has a utility function U=C*L

C= consumption L= hours of leisure

Tom has 100 hours to divide between work and leisure per week

wage is $20/hr

1. Write down budget constraint in terms of consumption and hours of work

2.Tom make decisions on hours of work, leisure and consumption to max. utility. Explain why we can collapse this problem to one in which he chooses hours of leisure only

3. Find optimal hours of work and total consumption for Tom

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Homework Answers

Answer #1

1) Budget constraint focuses on how much can be consumed with the given income. Here income is Y = (100 - L)*20 or 2000 - 20L. This is because income is hours worked x wage rate and hours worked = total hours - hours of leisure. Hence C = Y or C = 2000 - 20L is the budget constraint which can be expressed as C + 20L = 2000.

2) This is because we have a utility function which has to be maximized given a budget constraint. Hence we can use Lagrangian multiplier to maximize utility with the given budget constraint

3) At the optimum choice, slope of the budget line = slope of the utility function

MUC/MUL = 1/20

L/C = 1/20

This gives C = 20L

Use this in the budget equation

20L + 20L = 2000

L = 2000/40 = 50

Hence optimum number of leisure hours = 50 and optimum number of working hours = 100 - 50 = 50.

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