Question

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} \\] \(C(q)=722+\frac{q^{2}}{200} \quad\) 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. 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

The equilibrium price and quantity can be calculated by equating the supply and demand functions. The firm's output and profit can be calculated, and the long-run adjustments can be predicted. The lowest prices in the long run and short run can be determined by considering the firm's costs of production.

Step-by-step solution

Find the equilibrium price and quantity.

Set the supply function \(Q^s\) equal to the demand function \(Q^D\). This gives: \(6500 - 100P = 1200P\). Solve this equation to find the equilibrium price \(P\). Substitute this price into either the supply or demand function to find the equilibrium quantity \(Q\).

Calculate firm output and profit.

Divide the market equilibrium quantity by the number of firms to find the output for each firm. Afterwards, substitute the quantity into the total cost function \(C(q)\) to get the total cost for the firm. Calculate the firm's profit using the equation: Profit = Total Revenue - Total Cost, where Total Revenue = Price * Quantity.

Determine the long run adjustment.

In the long-run, if the firm makes a positive profit, other firms will enter the market and drive the price down. If the firm is making losses, some firms will exit, which will drive the price up. If the firms are breaking even, there will be no entry or exit.

Identify the lowest price in the long run and short run.

In the long run, the lowest price at which each firm would sell its output is at its minimum average total cost. This can be found by differentiating the total cost function \(C(q)\) and setting it equal to zero. In the short run, the firm will continue to produce as long as the price covers the variable costs.

Key concepts

Market Equilibrium

Market equilibrium occurs when the quantity demanded by consumers matches the quantity supplied by producers, resulting in a stable market price. In our scenario, to find this balance you set the demand function, represented by \( Q^D = 6500 - 100P \), equal to the supply function, \( Q^S = 1200P \). Solving for \( P \), gives us the equilibrium price, and consequently using this price in either function provides the equilibrium quantity.

Understanding market equilibrium is essential because it determines the price at which goods are traded and the quantity available in the market. It also serves as a reference point for analyzing the effects of external shocks on a market, such as changes in consumer preferences or production costs.

Perfect Competition

Perfect competition describes a market structure where many firms offer a homogeneous product, there are no barriers to entry or exit, and all firms are price takers. This means no single firm can influence the market price; it is determined solely by supply and demand. Given that all firms in our example are identical and operate in a perfectly competitive market, they must accept the market equilibrium price.

In a perfectly competitive market, firms can only adjust the quantity they supply. However, in the long run, economic profits tend to zero, which ensures that no firm has a significant advantage over others, keeping the playing field level.

Firm Total Cost Function

The firm total cost function, such as \( C(q) = 722 + \frac{q^2}{200} \) in our exercise, represents the total cost incurred by a firm at different levels of output. This cost includes both fixed costs, such as rent and salaries, which do not change with the amount produced, and variable costs, which vary with production levels.

Understanding this function allows firms to calculate how much it will cost them to produce a certain amount of goods. It is vital for determining the output level that maximizes profits or minimizes losses, especially when combined with revenue information.

Marginal Cost Function

Marginal cost is the additional cost incurred by producing one more unit of a good. For the firm in question, the marginal cost function is \( MC(q) = \frac{2q}{200} \). Marginal cost is critical for decision-making as it indicates how much the total cost changes with a small increase in production.

Firms use the marginal cost to determine the optimal production point. In perfect competition, a firm will supply additional units of output up to the point where the marginal cost equals the market price, thereby maximizing profitability.

Long Run Industry Adjustment

Long run industry adjustment refers to the process by which the number of firms in the market changes in response to economic profits or losses. If firms are making economic profits, new firms will enter the industry, increasing supply, driving down prices, and thus reducing profits. Conversely, if firms are experiencing losses, some will exit the market. This reduces supply, increases prices, and potentially turns losses into profits or breakeven.

In the long run, we expect firms in a perfectly competitive market to earn zero economic profit. This is because any profit opportunity is eliminated by the entry of new firms, and losses lead to an exit of existing firms. In our exercise, determining whether firms would enter or exit the market involves analyzing profits and comparing the market price to the firm's average total cost.