# 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.