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
your answer.
(d) Solve for Jane’s optimal choice of savings, and how much to consume in periods one and
two. Hint: see the solution to the two good problem at the end of this assignment.

1. (15 marks) This question relates to the problem of moral hazard. Watch this Seinfeld clip
   and answer the following two questions. Limit your answer to half a page (typed and single
   spaced).
   (a) In this principal-agent problem who is the principal and who is the agent? Explain your
   answer carefully.
   (b) What is the source of the information asymmetry in this scene and what is the moral
   hazard? Again explain your answer carefully.
2. (15 marks) What does the concept of adverse selection predict about the existence of “all
   you can eat” restaurants?

Sample Solution