1. The Leyland Pitt Corporation makes small wine refrigerators. The refrigerators are differentiated (rather than commodities), so you can consider the company to be in a monopolistically competitive industry. Leyland
duped
encouraged some EMBA students to analyze his past sales as well as some customer survey data and they estimated that the demand curve for Leyland’s refrigerators is P = 1000 – 25Q ,
where P is the price (in dollars) of a refrigerator and Q is the number of refrigerators sold per month. Analysis of his expenses indicates that he has fixed costs of real estate and managerial staff of $6,000/month and that the marginal cost of producing refrigerators is a constant $150 per refrigerator.
a. To sell 20 refrigerators per month, what price would Leyland have to charge?
b. If he sets a price of $250, how many refrigerators will Leyland sell per month?
c. At what price will Leyland maximize monthly revenue?
d. What is Leyland’s average unit cost when he sells 20 units in a month?
e. At what price will Leyland maximize his monthly profit?
2. Consider the video game console market circa 2009. Sony sells its PS3 console for $399. Microsoft sells its XBox 360 at the same price point, $399. There is speculation among video gaming analysts that either Sony or Microsoft or both will cut their price another $100 in the coming quarter. (Nintendo’s Wii is priced at $249. Nintendo has not changed the price of the Wii for several years). A Wall Street analyst has estimated the expected sales for the PS3 and Xbox 360 in the next quarter under different price scenarios. The estimates are in Table 2.1 below. Using the firms’ annual reports and other information, the analyst has also estimated the consoles’ unit costs at different production volumes, shown in Table 2.2.
a. Are the PS3 and Xbox 360 complements or substitutes? How can you tell based on the data in the tables?
b. What is the mid-point own-price elasticity (aka, arc elasticity) for the PS3 between
$299 and $399?
c. Will Sony increase or decrease its revenue if it drops the PS3 price to $299?
d. Does either firm enjoy economies of scale?
e. Depict the pricing choices facing Sony and Microsoft as a simultaneous game, including the expected payoffs. (Ignore Nintendo)
f.
PS3 price
|
Xbox 360 price
|
PS3 estimated units sold (mill)
|
Xbox 360 estimated units sold (mill)
|
$299
|
$299
|
10.25
|
11.5
|
$299
|
$399
|
10.75
|
7.0
|
$399
|
$299
|
8.25
|
12.5
|
$399
|
$399
|
8.75
|
8.0
|
|
|
Is there a Nash equilibrium in this game? Table 2.1
Table 2.2
PS3
quantity produced (mill)
|
PS3 average unit cost
|
Xbox 360 quantity produced (mill)
|
Xbox 360 average unit cost
|
8.25
|
$306
|
7.0
|
$308
|
8.75
|
$281
|
8.0
|
$279
|
10.25
|
$212
|
11.5
|
$232
|
10.75
|
$198
|
12.5
|
$219
|
3. Consider the game between you and a rival depicted below:
Advertise
Me Don’t
Advertise
Rival
$5m, $5m
|
$10m, $3m
|
$1m, $3m
|
$2m, $4m
|
|
|
Advertise Don’t Advertise
a. Do you have a dominant strategy? Does your rival?
b. What is the Nash equilibrium for this game?
c. Suppose you could negotiate an enforceable contract with your rival before the game. What would you negotiate?
4. Fredrick presents Don with two new proposals for offering a graduate certificate program. Both programs will cost $60,000, for classroom and instructor time. Both programs are projected to have two possible revenue outcomes. Program 1, which focuses on accounting, is projected to have a 50% chance of generating $150,000 in revenue and a 50% chance of generating $100,000 in revenue. Project 2, which focuses on cryptocurrencies, is predicted to have a 62.5% chance of generating $200,000 in revenue or, otherwise, generating no revenue!
a. What is the expected value of each program?