Questions

1. (40 marks) 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
∂C =
1
C
and his marginal utility from leisure is given by:
MUL =
∂U
∂L =
θ
L
Bob has 120 hours to allocate between working and leisure time. For every hour that he works
he earns a wage of W. The value of this wage was determined by your student number. In
addition to any income he gets from working Bob also gets \$10 from his Grandmother. He
spends all of his income (that is, what he gets from working plus the \$10 from Grandma) on
beer which costs \$1 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 half his time
interest rate. Jane gets utility from consumption in period one (given by C1) and in period
two (given by C2) according to the following utility function:
U(C1, C2) = ln(C1) + β ln(C2)
where the value of β ws determined by your student number. Given this utility function
Jane’s marginal utility from consumption in period one is given by:
MUC1 =
∂U

# ∂C1

1
C1
and her marginal utility from consumption in period two is given by:
MUC2 =
∂U

# ∂C2

β
C2
The parameter β describes how impatient Jane is. The lower the value of β the more she
prefers consumption in the present (period one) to consumption when retired (period two).
(a) What is Jane’s budget constraint in period one? What is her budget constraint in period
two?
(b) Combine these two budget constraints in order to have a single budget constraint that
relates C1 and C2 to Jane’s income and the interest rate.
(c) Assume Jane is currently saving exactly 40% of her income in period one. Could she
increase her utility by increasing or decreasing the amount she saves? Carefully explain