Question

Suppose you are given the following information about a particular industry:

QD = 6500 - 100P Market demand

QS = 1200P Market supply

C(q) = 722 + q2/200 Firm total cost function

MC(q) =2q/200Firm marginal cost function

Assume that all firms are identical and that the market is characterized by perfect competition.

a. Find the equilibrium price, the equilibrium quantity, the output supplied by the firm, and the profit of each firm.

b. Would you expect to see entry into or exit from the industry in the long run? Explain. What effect will entry or exit have on market equilibrium?

c. What is the lowest price at which each firm would sell its output in the long run? Is profit positive, negative, or zero at this price? Explain.

Short answer

1. The equilibrium price is $5, the equilibrium quantity is 6000 units, the output supplied by each firm is 500 units, and the profit of each firm would be $528.

2. There will be an entry of firms into the industry in the long run. The market equilibrium will move to a lower point.

3. The lowest price at which the firm would run is $2.5. The profit at this price would be negative.

Step-by-step solution

Determining the equilibrium price, the equilibrium quantity, the output, and the firm's profit

Since the market is perfectly competitive, the equilibrium price can be determined by equating demand and supply.The profit is calculated below:

Q_D = Q_S

6500 - 100P = 1200 P

1300P=6500

P=5

Thus, the equilibrium price is $5.

The equilibrium quantity is determined by putting the value of price.

Q_S= 1200P

= 1200 x 5

=6000

Thus, the equilibrium quantity is 6000 units.

Each firm will supply the output at which the marginal cost (MC) equals the price (P).

The output supplied by each firm is calculated below by equating MC with P.

$$\begin{gathered} MC=P \\ \frac{2q}{200}=5 \\ 2q=1000 \\ q=500 \end{gathered}$$

Thus, the output supplied by each firm is 500 units.

The profit of each firm is determined by subtracting the total revenue from the total cost. The value of TC and TR is calculated below:

$$\begin{gathered} TC\left(\$\right)=722+\frac{q^2}{200} \\ =722+\frac{{500}^2}{200} \\ =722+1250 \\ =1972 \\ TR\left(\$\right)=p\times q \\ =5\times 500 \\ =2500 \\ Profit(\$)=TR-TC \\ =2500-1972 \\ =\$528 \end{gathered}$$

Thus, the profit earned by each firm is $528.

Explanation for entry of exit of in the market and effect on market equilibrium

The firms are earning positive profit. It shows a high return on financial investment which will cause other investors to invest resources into this industry. There will be an entry of firms in the industry.

The entry of new firms in the industry will increase the total output level of the industry. The supply curve will of the product moves rightwards, causing a change in market equilibrium. The equilibrium position will move to a lower point on the demand curve. The price will decrease, and output will increase. Eventually, all the positive profits will vanish, and the firms will earn zero economic profits.

The lowest price at which firms would sell their output

The price which can cover the long-run average variable cost of the production is the last price at which the firm will sell its output.The lowest price is calculated below:

$$\begin{gathered} P=minLAC \\ =\frac{TVC}{Q} \\ =\frac{1250}{500} \\ =\$2.5 \end{gathered}$$

The lowest price at which the firms would sell their output is $2.5.

At this price level, the profit would be:

Profit($) = TR - TC

= 2.5 x 500 - 1972

= 1250 - 1972

= -722

At this price, the firms will earn negative profits.