1. You are given the following data for your firm, which sells a patented super-absorbent cleaning towel for use in large retail complexes (called "One Wring to Rule the Mall" ).

Q	P	TC
0	$48.00	$400.00
10	$46.50	$707.50
20	$45.00	$980.00
30	$43.50	$1,232.50
40	$42.00	$1,480.00
50	$40.50	$1,737.50
60	$39.00	$2,020.00
70	$37.50	$2,342.50
80	$36.00	$2,720.00
90	$34.50	$3,167.50
100	$33.00	$3,700.00

a. Determine equations for P=f(Q), MR=f(Q), ATC=f(Q, Q²), AVC=f(Q, Q²), MC=f(Q, Q²). Recall that your marginal equations should be derivatives of your totals!

b. Determine the profit-maximizing price and quantity. (Since MC is in terms of Q², solving with calculus and algebra can be messy. Your table should give an exact answer.)

c. How much total profit would your firm earn if you set P and Q according to part b?

d. Describe the competitiveness of the market by calculating the Lerner index.

2. For anyone interested, Massachusetts' Division of Professional Licensure can be your entry into the exciting career field of Elevator Operator. You must pay a processing fee of $25, allow access to your driver's license, provide a description of your "work experience in elevators," and (I am not making this up) pass an exam, which I assume goes beyond knowing what maybe six buttons do.

Presumably, the licensing process protects consumers (who, obviously,can make mistakes); given the information presented this week, aside from ensuring high quality elevation services, why else might existing elevator operators find it in their interest to protect the licensing system? What side effects might the fees introduce into the elevator-operator market?

3. On the way to my mother's house for Thanksgiving dinner, my wife was on her phone and noted that Old Navy was going to be open for Black Friday sales starting on Thursday at 3pm. Many people lament the fact that stores are open very early the day after Thanksgiving or, as it seems, even open on Thanksgiving day itself. The owners, managers, and employees of retail stores presumably would enjoy spending Thanksgiving with their families instead of preparing for Black Friday sales, yet almost every store announces that it will open very early on Friday morning for shoppers. How might game theory offer an explanation for this unexpected behavior?

4. The following is a payoff matrix showing profit in millions of dollars when two companies simultaneously decide on various advertising budgets ($1 million, $2 million, or $3 million):

			Pizza Hut
		$1 mill	$2 mill	$3 mill
	$1 mill	$90/ $130	75/ 135	75/ 140
Papa Johns	$2 mill	70/ 115	70/ 120	60/ 125
	$3 mill	75/ 100	80/ 95	65/ 90

a. In the first round of strategy elimination (when all three possible budgets are under consideration), which ad budget would the companies exclude?

b. After the first round of elimination (previous question), would either company make a second-round elimination?

c. What would be the likely outcome of this simultaneous advertising decision (i.e. what ad budget would each company end up choosing)?