Chapter 13, Problem 7CACQ

(a)

To determine

To find the reason for less marginal cost of firm 1.

Explanation of Solution

Firm 1 is an old firm which is operating from last 1 year in industry. It is operating at economies of scale. So, its marginal cost would be lower than the new firm.

(b)

To determine

To analyze current profit of two firms.

Explanation of Solution

Industry’s inverse demand function is given as:

  $P=20-5Q$

Market price is $15. At equilibrium level of market, P = MC

  $\begin{array}{c}15=20-5Q\\ 5Q=5\\ Q=1\end{array}$

The market equilibrium quantity is 1 million. Each has 50% of the market share. Hence, each firm is producing 0.5 million.

For firm 1:

Total revenue can be calculated as:

  $\begin{array}{c}TR=P\times Q\\ =15\times 0.5\\ =\$7.5million\end{array}$

Total cost is the summation of variable cost and fixed cost. Fixed cost is $2 million. Variable cost can be calculated as:

  $\begin{array}{c}TVC=MC\times Q\\ =2\times 0.5\\ =\$1million\end{array}$

Total cost is:

  $\begin{array}{c}TC=TFC+TVC\\ =2+1\\ =\$3million\end{array}$

  $\begin{array}{c}\mathrm{Pr}ofit=TR-TC\\ =7.5-3\\ =\$4.5million\end{array}$

For firm 2,

Total revenue can be calculated as:

  $\begin{array}{c}TR=P\times Q\\ =15\times 0.5\\ =\$7.5million\end{array}$

Total cost is the summation of variable cost and fixed cost. Fixed cost is $2 million. Variable cost can be calculated as:

  $\begin{array}{c}TVC=MC\times Q\\ =10\times 0.5\\ =\$5million\end{array}$

Total cost is:

  $\begin{array}{c}TC=TFC+TVC\\ =2+5\\ =\$7million\end{array}$

  $\begin{array}{c}\mathrm{Pr}ofit=TR-TC\\ =7.5-7\\ =\$0.5million\end{array}$

(c)

To determine

To analyze the effect of decrease in price by firm 1.

Explanation of Solution

When firm 1 decreases the price to $10, he captures whole market share.

Industry’s inverse demand function is given as:

  $P=20-5Q$

For firm 1,

Price is charged $10. At equilibrium level of market, P = MC

  $\begin{array}{c}10=20-5Q\\ 5Q=10\\ Q=2\end{array}$

The equilibrium quantity for firm 1 is 2 million.

Total revenue can be calculated as:

  $\begin{array}{c}TR=P\times Q\\ =10\times 2\\ =\$20million\end{array}$

Total cost is the summation of variable cost and fixed cost. Fixed cost is $2 million. Variable cost can be calculated as:

  $\begin{array}{c}TVC=MC\times Q\\ =2\times 2\\ =\$4million\end{array}$

Total cost is:

  $\begin{array}{c}TC=TFC+TVC\\ =2+4\\ =\$6million\end{array}$

  $\begin{array}{c}\mathrm{Pr}ofit=TR-TC\\ =20-6\\ =\$14million\end{array}$

Firm 2:

Firm 2 loses its entire market share as it charges $15.

Total revenue can be calculated as:

  $\begin{array}{c}TR=P\times Q\\ =15\times 0\\ =0\end{array}$

Total cost is the summation of variable cost and fixed cost. Fixed cost is $2 million. Variable cost can be calculated as:

  $\begin{array}{c}TVC=MC\times Q\\ =2\times 0\\ =0\end{array}$

Total cost is:

  $\begin{array}{c}TC=TFC+TVC\\ =2+0\\ =\$2million\end{array}$

  $\begin{array}{c}\mathrm{Pr}ofit=TR-TC\\ =0-2\\ =\$-2million\end{array}$

Hence, firm 2 is incurring a loss of $2 million.

(d)

To determine

To analyze whether the firm 1 has incentive to raise price after the exit of firm 2 from the market.

Explanation of Solution

When the firm 2 exits the market, firm 1 is the sole producer. It has monopoly in the market. Hence, it can exploit consumers by charging higher prices.

(e)

To determine

To analyze whether the firm 1 is engaged in predatory pricing.

Explanation of Solution

Predatory pricing is the act of pricing products or services so low that other competitors are not able to compete and are forced to leave the market.

The marginal cost of firm 2 is $10. When the price was $15, both the firms were earning extra normal profits. When the firm 1 lowers its price to $10, the firm 2 can also lower its price in order to capture the equal market share. In this manner, its price would be equal to the MC. He would be on equilibrium.

Hence, the firm 1 has not done predatory pricing. Firm 2 can compete with firm 1 till $10 because the MC of firm 2 is $10.

When the firm 1 lowers the price below 10, then it would be called predatory pricing.