Question

Bob is deciding how much labour he should supply. He gets utility from consumption of beer (given by C) and from leisure time (given by L), which he spends hanging out with his friend Doug. This utility is given by the following utility function:
U(C, L) = ln(C) + θ ln(L)
where the value of θ was determined by your student number and ln(C) denotes the natural logarithm of consumption etc. Given this utility function, Bob’s marginal utility from consumption is given by:
MUC = ∂U = 1 ∂C C
and his marginal utility from leisure is given by: MUL = ∂U = θ
∂L L
Bob has 12 hours each day to allocate between working and leisure time. For every hour that he works he earns a wage of W . The dollar value of this wage was determined by your student number. He spends all of his income on beer which costs $5 per unit.
(a) If Bob devotes L hours of his time to leisure, how many hours does he work? Write out Bob’s budget constraint.
(b) Suppose Bob is currently spending exactly five hours on leisure, that is L = 5.
i. Use Bob’s budget constraint to figure out how much beer he can consume.
ii. Calculate the slope of Bob’s indifference curve at this point. Is the slope of his indifference curve at this point greater than, or less than the slope of his budget constraint?
iii. At this point could Bob raise his utility by increasing or decreasing the number of hours he works? Carefully explain your answer.
(c) Solve for Bob’s optimal choice of hours worked, hours spent on leisure and beer consumption.

Answer 1