1.A. Given the output (Q) and price (P) data in the following table, calculate total revenue (TR) and marginal revenue (MR):

Total Revenue Marginal Revenue

Quantity Price TR=PQ MR=TR/Q

0 $10

1 9

2 8

3 7

4 6

5 5

6 4

7 3

8 2

9 1

10 0

B.What is the quantity maximizing revenue?

SOLUTION

1.Characterize each of the following statements as true or false, and explain your answer.

A.If marginal revenue is less than average revenue, the demand curve will be downward sloping.

B.Profits will be maximized when total revenue equals total cost.

C.Given a downward-sloping demand curve and positive marginal costs, profit-maximizing firms will always sell less output at higher prices than will revenue-maximizing firms.

D.Marginal cost must be falling for average cost to decline as output expands.

E.Marginal profit is the difference between marginal revenue and marginal cost and will always equal zero at the profit-maximizing activity level.

SOLUTION

2.21st Century Insurance offers mailorder automobile insurance to preferredrisk drivers in the Los Angeles area.The company is the lowcost provider of insurance in this market but doesn't believe its annual premium of $1,500 can be raised for competitive reasons.Rates are expected to remain stable during coming periods; hence, P = MR = $1,500.Total and marginal cost relations for the company are as follows:

TC=$41,000,000 + $500Q + $0.005Q²

MC=TC/Q = $500 + $0.01Q

A.Calculate the profitmaximizing activity level.

B.Calculate the company's optimal profit, and optimal profit as a percentage of sales revenue (profit margin).

SOLUTION