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# dominant strategy

Chapter 11 Problem 4
The Madison Corporation, a monopolist, receives a report from a consulting firm
concluding that the demand function for its product is:
Q = 78 - 1.1P + 2.3Y = 0.9A
Where Q is the number of units sold, P is the price of its product (in dollars), Y
is per capita income (in thousands of dollars), and A is the firm's advertising
expenditure (in thousands of dollars). The firms average variable cost function
is:
AVC = 42 - 8Q = 1.5Q^2
Where AVC is average variable cost (in dollars).

Can one determine the firm's marginal cost curve? (notes: Since AVC = 42 - 8Q =
1.5^2 we can estimate the total cost curve to be TC=AVC x Q Fixed Costs = 42 A -
8Q^2 = 1.5Q^3 = FC) therefore, marginal cost MC = dTC/dQ =
Can one determine the firm's marginal revenue curve? (notes: Total revenue, TR =PQ)
If Q = 79 - 1.1P = 2.3Y = 0.9A, we can rearrange as P =
TR=
Marginal revenue, MR = dTR/dQ =

If per capital income is \$4000 and advertising expenditure is \$200,000, can one
determine the price and output where marginal revenue equals marginal cost? If so,
what are they? (notes: Setting MR = MC when Y = 4,000 and A = 200,000 And then
solving for Q using the quadratic formula, we get Q =
Therefore, P =

Chapter 14 Problem 2
The Ulysses Corporation and the Xenophon Company are the only producers of a very
sophisticated type of camera. They each can engage in either a high or a low level
of advertising in trade journals. The payoff matrix is as follow:

Low Level High Level
Low level Xenophon's profit \$13 million Xenophon's profit \$12
million
Ulysses' profit \$12 million Ulysses' profit \$11
million

High level Xenophon's profit \$12 million Xenophon's profit \$11 million
Ulysses' profit \$13 million Ulysses' profit \$12
million

Will Ulysses engage in a high or a low level of advertising in trade journals?

Will Xenophon engage in a high or a low level of advertising in trade journals?

Is there a dominant strategy for each firm?

#### Solution Summary

Determine average variable costs.

\$2.19