Chapter 8: Problem 10

Suppose you are given the following information about a particular industry: \\[ \begin{array}{ll} Q^{D}=6500-100 P & \text { Market demand } \\ Q^{S}=1200 P & \text { Market supply } \end{array} \\] \\[ C(q)=722+\frac{q^{2}}{200} \quad \text { Firm total cost function } \\] \\[ M C(q)=\frac{2 q}{200} \quad \text { Firm 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. d. What is the lowest price at which each firm would sell its output in the short run? Is profit positive, negative, or zero at this price? Explain.

Short Answer

Expert verified

Due to the promotions' anonymity, must always consult the initial exercise for exact results. However, the resolution process is crucial: first acquire the market balance through equating supply and demand. Then find the firm's profit by subtracting the total cost from total revenues. Analyze the firm's profit to determine if new businesses will enter or exit in this perfectly competitive market. Afterwards, the long-term minimum selling price occurs when each firm's total cost equals total revenues, and the short-term minimum price occurs when the price covers the average variable cost.

Step by step solution

Solve for market equilibrium

First, equate the given supply and demand equations to find market equilibrium. This involves setting \(Q^{D}=6500-100 P\) equal to \(Q^{S}=1200P\), and solving for \(P\), the price.

Calculate Equilibrium Quantity & Individual Firm Output

Substitute the equilibrium price obtained in Step 1 to any of the two equations (Q^D or Q^S) to get the equilibrium quantity (Q*). To find the amount supplied by a single firm, divide the market equilibrium quantity by the number of firms in the industry.

Compute the Firm's Profit

The profit can be calculated by subtracting total cost from total revenue. Here, total cost is given by \(C(q)=722+\frac{q^{2}}{200}\), and total revenue is obtained by multiplying the output with the price. Subtract the total cost from total revenue to obtain the profit.

Analyze Long-Term Industry Entry or Exit

In a perfectly competitive market,, if firms make a profit, new businesses will enter the sector in the long run. Therefore, analyze the profit obtained in Step 3 and predict if the industry will see entry or exit in the long run.

Compute the long-term minimum selling price

The minimum price in the long term will occur when each firm's total cost equals the total revenue, or when the price equals the average total cost (ATC). Hence, first calculate the ATC and equate it with the price to get the long-term minimum selling price. Also, evaluate the profit at this price (Should be zero in the long-run equilibrium).

Determine the short-term minimum selling price

In the short run, a firm would keep producing as long as the price covers the average variable cost (AVC), even though the firm is making a loss. Therefore, calculate the AVC and set it equal to the price to get the short-term minimum selling price. Also, evaluate the profit at this price (Generally negative if the firm only covers variable costs).