Question 1 (10 points)
Suppose that there are four bundles, A, B, C & D. Using the weak preference (%) and strict
preference (!) relations, define a consumer?s preferences such that
(a) Completeness and transitivity are both satisfied. (3 points)
(b) Completeness is satisfied but transitivity is violated. (3 points)
(c) Specify two utility function for the preferences in part (a). (4 points)
Question 2 (2 points)
What is the di?erence between ordinal utility and cardinal utility? (one to two sentences is
Question 3 (4 points)
Suppose that a utility-maximizing consider must choose between the following bundles:
Bundle Units of food Units of clothing
A 10 7
B 7 10
C 8 11
D 8 10
E 9 4
F 13 6
G 4 12
1. Which bundles can be ruled out with certainty? (2 points)
2. Why can we rule them out? (2 points)
Question 4 (10 points)
1. Which assumption is violated when indi?erence curves cross? Draw an example. (1
2. How does the indi?erence curve illustrate the marginal rate of substitution? (1 point)
3. Draw the indi?erence maps that each include three curves. One map should exhibit
the typical scenario, one should exhibit perfect substitutes, and the last perfect compliments.
Illustrate on your graph the direction of increasing utility. (8 points)
Question 5 (6 points)
Suppose that there are two goods: food and clothing. Suppose the consumer has income I,
the price of food is pf and the price of clothing is pc.
(a) Write the consumer?s budget constraint. (1 point)
(b) Reformulate the budget constraint to put it into goods space and plot it. (2 points)
(c) Interpret each term from (b). (3 points)
Question 6 (8 points)
Suppose the price of food is 7 and the price of clothing is 15.
(a) What is the relative price of food? Interpret this value. (3 points)
(b) What is the relative price of clothing? Interpret this value. (3 points)
(c) How are the two relative prices related? (2 points)
Question 7 (15 points)
Suppose a consumer has income 500. The price of food is 10 and the price of clothing is 20.
(a) Plot the budget line with food on the horizontal axis. (3 points)
(b) What happens to the original budget line if income increases by 50%? Plot this on the
same graph as (a). (3 points)
(c) What happens to the original budget line if the price of food increases by 50%. Show
on a new plot. (3 points)
(d) What happens to the original budget line if the price of clothing decreases by 50%?
Show on a new plot. (3 points)
(e) What happens to the original budget line if the price of food increases by 100% and the
price of clothing increases by 50%? (3 points)
Question 8 (5 points)
Suppose that there are two goods, football tickets and basketball tickets. Suppose the
consumer is considering two bundles on the budget line, A and B. With bundle A, the MRS
for football tickets is greater than the relative price of football tickets and with bundle B,
the MRS for football tickets is less than the relative price.
(a) Draw the budget line and corresponding convex indi?erence curve. (1 point)
(b) Should the consumer consume bundle A? Why or why not? (2 points)
(c) Should the consumer consume bundle B? Why or why not? (2 points)
Question 9 (20 points)
There are two goods. Consider a consumer with a convex indi?erence curve.
(a) Draw a utility-maximizing bundle. (2 points)
(b) Suppose that the price of the good on the horizontal axis goes down. Show the income
and substitution e?ect if the good is a normal good. (5 points)
(c) Repeat exercise (b) on a new plot, supposing that the good is an inferior good. (5 points)
(d) Repeat exercise (c) on a new plot, but show a case where the negative income e?ect is
greater than the substitution e?ect. (5 points)
(e) What is unique about the demand curve corresponding to (d)? (3 points)
Question 10 (20 points)
There are two goods, food f and clothing c. Suppose that a consumer?s utility function is
u(f, c) = f 1
The individual has income I = 16. The price of food is given by pf = 8. The price of
clothing is given by pc = 2.
(a) Solve for the consumer?s utility maximizing bundle. (5 points)
Now suppose that the price of food drops to pf = 2.
(b) Calculate the new utility maximizing bundle. (5 points)
(c) Decompose this change into an income and substitution e?ect. How large is each? (10
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