HOMEWORK 1. Consumers in Queensland pay twice as much for avocados as they do for peaches.
However, avocados and peaches are equally priced in SA. If consumers in both states maximize utility (and have identical preferences), will the marginal rates of substitution of peaches for avocados be the same for consumers in both states? If not, which will be higher? (
Hint: Draw graphs.)
2. Suppose that Mimi can choose how many hours to work at a wage rate
w, and she chooses to work seven hours per day. Suppose that her boss offers her time-and-a-half wage 1.5
w for every hour she works beyond a minimum of eight hours per day.
Plot hours of leisure (24 minus working hours) on the horizontal axis and money on the vertical axis.
a. Show how her budget constraint changes because of the proposal.
b. Under what circumstances will Mimi now choose to work more than eight
hours per day if she is maximizing her utility? (Give an example of Mimi’s
indifference curves that lead her to choose to work less than 8 hours per day
without the time-and-a-half wage, but more than 8 hours with the time-anda-
half wage.)
3. Consider the following utility function:
U(
x,
y) =
x+
y1/2
a. Very carefully draw the indifference curves associated with utility numbers
64, 49, and 36. For all three indifference curves, find the quantity of
x when
y is 0, 1, 4, 9, 16, 25, and 36.
b. How does
MRS change as you move from one indifference curve to another
along the horizontal line y=2? Or y=6? Or any horizontal line?
4. The utility that Jane receives by consuming food
F and clothing
C is given by
U(F,C)=F1/2C3/4.a. Using the equations given in class calculate the marginal utility functions (
MUFand
MUC) and the marginal rate of substitution function (
MRS).
b. Suppose that food costs $5 and clothing $10. Jane has $125 to spend on food and
clothing. Write down the two rules of utility maximization for Jane.
c. Calculate her utility maximizing choice of food and clothing. (
Hint: Solve the
system of linear equations in b.)
d. Calculate the level of utility her optimal consumption bundle gives to her.