Page 49 - Microeconomics, Fourth Edition

c01analyzingeconomicproblems 6/14/10 1:38 PM Page 23

PROBLEMS 23
a) Suppose the level of income is I 20. Graph the supply b) Which plan would you select if your instructions are
and demand relationships, and indicate the equilibrium to rent the most movies possible while spending $300
levels of price and quantity on your graph. per year?
b) Explain why the market for wool would not be in c) In this exercise, is the number of videos rented
equilibrium if the price of wool were 18. endogenous or exogenous? Explain.
c) Explain why the market for wool would not be in d) Is the choice of plan (A, B, or C) endogenous or
equilibrium if the price of wool were 14. exogenous? Explain.
1.13. Consider the market for wool described by the e) Are total expenditures on videos endogenous or ex-
supply and demand equations in Problem 1.12. Suppose ogenous? Explain.
income rises from I 1 20 to I 2 24. 1.16. A major automobile manufacturer is considering
a) Using comparative statics analysis, find the impact how to allocate a $2 million advertising budget between
of the change in income on the equilibrium price of two types of television programs: NFL football games
wool. and PGA tour professional golf tournaments. The fol-
b) Using comparative statics analysis, find the impact of lowing table shows the new sports utility vehicles (SUVs)
the change in income on the equilibrium quantity of that are sold when a given amount of money is spent on
wool. advertising during an NFL football game and a PGA
tour golf event.
1.14. You are the video acquisitions officer for your res-
idence hall. The other officers of your hall will tell you
how many videos they would like to rent during the year. New SUV Sales Generated
Your job is to find the least expensive way of renting the (thousands of vehicles per year)
required number of videos. After researching the op- Total
tions, you have found that there are three rental plans Spent (millions) NFL Football PGA Tour Golf
from which you can choose.
$0 0 0
Plan A: Pay $3 per video, with no additional fees. $0.5 10 4
Plan B: Join the Frequent Viewer Club. Here you pay a $1.0 15 6
yearly membership fee of $50, with an additional charge $1.5 19 8
of $2 for each video rented. $2.0 20 9
Plan C: Join the Very Frequent Viewer Club. In this
club you pay a yearly membership fee of $150, with an The manufacturer’s goal is to allocate its $2 million ad-
additional charge of $1 for each video rented.
vertising budget to maximize the number of SUVs sold.
a) Which plan would you select if your instructions are Let F be the amount of money devoted to advertising on
to rent 75 movies a year at the lowest possible cost? NFL football games, G the amount of money spent on
b) Which plan would you select if your instructions are advertising on PGA tour golf events, and C(F,G) the
to rent 125 movies a year at the lowest possible cost? number of new vehicles sold.
c) In this exercise, is the number of videos rented en- a) What is the objective function for this problem?
dogenous or exogenous? Explain. b) What is the constraint?
d) Is the choice of plan (A, B, or C) endogenous or c) Write a statement of the constrained optimization
exogenous? Explain. problem.
e) Are total expenditures on videos endogenous or ex- d) In light of the information in the table, how should the
ogenous? Explain. manufacturer allocate its advertising budget?
1.15. Reconsider the problem of the video acquisitions 1.17. An electricity producer has two power plants,
officer in Problem 1.14. Suppose the officers of your each of which emits carbon dioxide (CO 2 ), a greenhouse
residence hall give you a specified amount of money to gas. Each plant is currently emitting 1 million metric
spend, and want you to maximize the number of videos tons of CO 2 per year. However, new emissions rules re-
you can rent with that budget. You can choose from the strict the firm’s emissions to 1 million metric tons of
same three plans (A, B, and C) available in Problem 1.14. CO 2 per year from both plants combined. The cost of op-
a) Which plan would you select if your instructions are erating a power plant goes up as it curtails its emissions.
to rent the most movies possible while spending $125 per The following table shows the cost of operating each
year? plant for different emissions levels: