Week 7 – Check Your Understanding:
Chapter 13 Exercise 2, 13, and 15
2. Consider the following payoff matrix:
|
Player B Strategy |
|||
| 1 | 2 | ||
|
$1,000 |
– $2,000 |
||
| $2,000 |
-$1,000 |
||
|
Player A Strategy |
|||
a.
Does Player A have a dominant strategy? Explain why or why not.
b.
Does Player B have a dominant strategy? Explain why or why not.
13. Analyze the following sequential game and advise
Kodak
about whether they should introduce the new product, Picture CD.
|
New product Introduction |
Rival advertising |
Pricing policy |
Sony |
||
|
High |
$380m |
$620m |
|||
|
Moderate |
$610m |
$590m |
|||
|
Low |
$560m |
$540m |
|||
|
$710m |
$550m |
||||
|
Introduce picture CD |
|||||
|
$570m |
|||||
|
Do not introduce |
|||||
|
Increased ads |
$400m |
$720m |
|||
|
Maintain ads |
$580m |
$600m |
15. A math graduate student explains to her friend how to approach a group of smart attractive guys who have brought along famous actor Russell Crowe. What should her friend do? Ignore Russell Crowe or fixate on Russell Crowe? Explain the equilibrium reasoning underlying your answer.
Student 1
Ignore R.C.
Fixate on R.C.
No date tonight
Date with R.C.
(Worse)
(Best)
No date tonight Date
with other guys
(Better)
Student 2
Date with other guys
No date ever
(Worst)
Note:
Best payoff – date with R.C., Better – date with other guys, Worse – no date tonight, Worst – no date ever with any of these guys.
Chapter 14 Exercise 3(b, c, d), 5(a, b, c), and 8(a, b, c)
3. American Export-Import Shipping Company operates a general cargo carrier service between New York and several Western European ports. It hauls two major categories of freight: manufactured items and semi-manufactured raw material. The demand functions for these two classes of goods are
P1 = 100 – 2Q
1
P2 = 80 – Q
2
where Qi = tons of freight moved. The total cost function for American is
TC = 20 + 4(Q
1 +Q
2)
b. What are the profits-maximizing levels of price and output for the two freight categories?
c.
At these levels of output, calculate the marginal revenue in each market.
d.
What are American’s total profits if it is effectively able to charge different prices in the two markets.
5. Phillips Industries manufactures a certain product that can be sold directly to retail outlets or to the Superior Company for further processing and eventual sale as a completely different product. The demand function for each of these markets is
Retail Outlets: P
1 = 60 – 2Q
1
Superior Company: P
2 = 40 – Q
2
Where P1 and P2 are the prices charged and Q
1 and Q2 are the quantities sold in the respective markets. Phillips’ total cost function for the manufacture of this product is
TC = 10 + 8(Q
1 + Q
2)
a)
Determine Phillips’ total profit function.
b)
What are the profit-maximizing price and outlet levels for the product in the two markets?
c)
At these levels of output, calculate the marginal revenue in each market.
8. The Pear Computer Company just developed a totally revolutionary new personal computer. It estimates that it will take competitors at least two years to produce equivalent products. The demand function for the computer is estimated to be
P = 2,500 – 0.0005Q
The marginal (and average variable) cost of producing the computer is $900.
a) Compute the profit-maximizing price and output levels assuming Pear acts as a monopolist for its product.
b) Determine the total contribution to profits and fixed costs from the solution generated in Part (a).
Pear Computer is considering an alternative pricing strategy of price skimming. It plans to set the following schedule of prices over the coming two years:
Time Period Price Quantity Sold 1 $2,400 200,000 2 2,200 200,000 3 2,000 200,000 4 1,800 200,000 5 1,700 200,000 6 1,600 200,000 7 1,500 200,000 8 1,400 200,000 9 1,300 200,000 10 1,200 200,000
c. Calculate the contribution to profit and overhead for each of the 10 time periods and prices.
