# What is the rational number of hotdogs x* for Ralph to consume?

DEPARTMENT OF ECONOMICS
WINTER 2016
ECONOMICS 1A: PRINCIPLES OF MICROECONOMICS
PROF. ZELDER
PROBLEM SET 1
Due in class on Tuesday January 19
where necessary or useful.
(1) Ralph consumes hotdogs (x), and his marginal benefit from consuming x is MB = A â€“ Bx, while
his marginal cost of consuming hotdogs is MC = F Gx.
(a) What is the rational number of hotdogs x* for Ralph to consume? Answer as specifically
as possible based on the information given.
(b) How much does Ralph enjoy the last hotdog he consumes?
(c) Now, assuming that A = 100, B = 10, F = 40, and G = 2, answer parts (a) and (b)
again, being as specific as possible.
(d) Now, suppose again that A = 100, B = 10, and G = 2, but that we now have F = 120.
What is x*? [In answering, think about what is realistic in terms of the value of x.]
(2) Consider the following table representing Clemâ€™s utility from consuming cookies (x):
x
0
1
2
3
4
5
6

U(x
)
0
64
U(2
)
152
186
U(5
)
228

In the table, the numbers in the U(x) column represent the total utility he gets from consuming
that particular number of cookies. The entries U(2) and U(5) indicate that we donâ€™t specifically
know what his utility level is if he consumes 2 cookies or 5 cookies, respectively.
(a) What two properties does Clemâ€™s utility function for x exhibit?
(b) Given your answer to (a), what restrictions can you place on U(2)? On U(5)? Be sure to
(c) Suppose that, in addition to cookies, Clem spends the rest of his income on ice cream.
As Clem consumes more cookies, what happens to his total utility from ice cream? And,
as he consumes more cookies, what happens to his marginal utility from ice cream?
(d) Suppose, contrary to your answers to parts (a)-(c), that Clem feels so bloated by his 7 th
cookie that he is less happy when he consumes it than when he consumes only 6
cookies. What is true about his total utility after his 7 th cookie? Is total utility still a
monotonic function? What is true about the marginal utility of the 7 th cookie? Is
marginal utility still a monotonic function?
(3) Explain the rational basis for the following choices by Jojo, a college student. Be specific.
(a) Jojo stays up later on Friday and Saturday nights than he does on weekday nights.
(b) When Jojo is out on Friday night, he sometimes takes a taxi home, and sometimes
walks home.

(c) Jojoâ€™s shampoo bottle instructs him as follows: â€œLather. Rinse. Repeat.â€ What
determines whether he follows the instruction to â€œRepeatâ€?
(d) Jojo chooses to major in Economics rather than in Psychology.
(4) Humphrey is choosing which nightclub to visit on Saturday, Bunnyâ€™s or Fefeâ€™s, or whether to
stay home. Bunnyâ€™s has no cover charge, but Fefe does charge a cover. At Bunnyâ€™s, however,
there is a line to get in, whereas thereâ€™s no waiting at Fefeâ€™s. Specifically, suppose that it will take
40 minutes of waiting to get into Bunnyâ€™s, and suppose that the cover charge at Fefeâ€™s is \$20.
[Note that Bunnyâ€™s and Fefeâ€™s are ceteris paribus clubs, and thus do not differ in any other ways
than the cover charge and waiting time.]
(a) Suppose we know that Humphrey goes to one of the two clubs. What do we know
about the opportunity cost of Humphreyâ€™s time (in dollars per hour) if he goes to Bunnyâ€™s? If he
goes to Fefeâ€™s?
(b) Suppose that the benefit Humphrey receives from visiting either club is given by B H. If
Humphrey decides to stay home, and his opportunity cost of time is \$24 per hour, what do we
know about the size of BH?
(c) Suppose that the opportunity cost of Mauriceâ€™s time is twice that of Humphreyâ€™s,
although we donâ€™t know the exact value for either guy, and that they each get an identical
benefit of B from going to either club. If Maurice and Humphrey both go to Bunnyâ€™s, what do we
know about the value of Humphreyâ€™s time? If Maurice goes to Fefeâ€™s and Humphrey goes to
Bunnyâ€™s, what do we know about the value of Humphreyâ€™s time? If Maurice and Humphrey both
go to Fefeâ€™s, what do we know about the value of Mauriceâ€™s time?

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