Question 1
Mary has income of $120 and she spends all of this income on either shoes (price of a pair of
shoes is $40) or shirts (price of a shirt is $10).
a. Draw Mary’s budget line, BL1, on a graph with shoes on the horizontal axis and shirts on
the vertical axis.
b. Write an equation for Mary’s BL1.
c. Then, suppose that Mary’s income doubles: on your graph draw Mary’s BL2 based on
this information. Write an equation for Mary’s BL2.
d. In words describe any similarity between BL1 and BL2: explain why this similarity
exists.
Question 2
Susan has $150 to spend on sandwiches (S) and milk (M). The price of sandwiches is $5 per
sandwich and the price of milk is $2 per carton.
a. Given this information draw Susan’s budget line, BL1, on a graph with sandwiches on
the horizontal axis and milk on the vertical axis.
b. Suppose the price of sandwiches increases to $10 while everything else is held constant.
Draw this new budget line, BL2, on your graph.
c. Explain in words the effect of a change in the price of sandwiches on this budget line.
Write equations for both BL1 and BL2.
Question 3
Consider the budget line depicted below:
a) What is the price of good A?
b) What is the price of good B?
c) Write the equation of the line in slope-intercept form. What is the slope of the budget line?
d) How is the slope of the budget line related to the ratio of the two prices?
Question 4
The utility function for an individual is given by the equation U = XY where U is the total
amount of utility the individual gets when they consume good X (X) and good Y (Y). Thus, if U
= 10 then the individual can get 10 units of utility from consuming 1 unit of X and 10 units of Y
(U = XY = (1)(10)) or from consuming 5 units of X and 2 units of Y or any other combination of
X and Y whose product is equal to 10. Given this utility function, the MU from good X is equal
to Y (that is, MUx = Y) and the MU from good Y is equal to X (that is, MUy = X). You are also
told that this individual’s income is $100 and that the price of good X is $2 and the price of good
Y is $4. From this information answer the following set of questions.
a. What is the budget line for this individual given the above information?
b. What is the consumption bundle of good X and good Y that maximizes this individual’s utility
given their income, prices of the two goods, and their tastes and preferences as measured by their
utility function?
c. Verify the answer you got in part (b) to make sure the individual can afford to buy this
consumption bundle.
d. What is the level of utility this individual gets when they maximize their utility given the
above information?
Suppose that the price of good X increases to $4 and nothing else changes. Use this new
information to answer this next set of questions.
e. What do you predict will happen to the consumption of good X and good Y now that the price
of good X has increased?
f. What do you predict will happen to the level of utility this person has relative to the level they
had in part (d) now that the price of good X has increased?
g. Find the new consumption bundle that maximizes this individual’s utility now that the price of
good x has increased.
h. Verify that the individual can afford the consumption bundle you found in part (g).
i. What is the level of utility this individual has when he maximizes his utility now?
Question 5
Suppose Joe’s income is $500 and he spends all of his income of either books or pizza.
Joe’s budget line is depicted in the graph below. Assume all books sells at the same price.
a. Given the above information, what is the price of a book?
b. Given the above information, what is the price of a pizza?
c. Provide an equation for Joe’s budget line recalling that the budget line can generally
be written as I = PxX + PyY where I is income, Px is the price of good X, X is the
quantity of good X, Py is the price of good Y, and Y is the quantity of good Y.
d. Suppose Joe’s income doubles as do the prices for books and pizzas. Describe the
effect of these changes on Joe’s budget line.
e. Assume that Joe’s income is at the initial level and his budget line is the one depicted
in the above graph. Suppose Joe devotes 60% of his income to the purchase of books
in order to maximize his satisfaction. How many books and pizzas will Joe consume
given this information?
f. Now, suppose the price of books increases by $5 while the price of pizza is
unchanged. Draw a graph that depicts Joe’s initial budget line (BL1) and his new
budget line (BL2). Can Joe afford his initial consumption bundle? Explain your
answer.
g. What is the equation for Joe’s new budget line given the information in part (f)?
