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 \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

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).

Key concepts

Market Equilibrium

Market equilibrium is a condition where the quantity demanded by consumers equals the quantity supplied by producers, resulting in a stable market price. In our given scenario, we start by equating the market demand function, \(Q^D = 6500 - 100P\), with the market supply function, \(Q^S = 1200P\). This equality helps us to find the equilibrium price (P*) where both supply and demand are balanced.
By solving this equation, we determine the price point at which these two curves intersect. This process is crucial in perfect competition as it reflects how price and quantity reach a point of balance.

Once the equilibrium price is found, we substitute it back into either the demand or supply function to calculate the equilibrium quantity (Q*). This value represents the total amount of goods bought and sold in the market at the equilibrium price.
Finding the market equilibrium is essential because it sets the foundation for analyzing other economic factors such as firm profitability, industry dynamics, and pricing strategies.

Firm Total Cost

In a perfectly competitive market, understanding the total cost incurred by a firm is vital for analyzing its operations and profitability. The total cost function given is \(C(q) = 722 + \frac{q^2}{200}\). This equation comprises two components: fixed costs and variable costs.
The fixed cost is represented by 722, which does not change with the level of output (q). Variable costs, in contrast, depend on the output and are captured by the term \(\frac{q^2}{200}\). As production increases, variable costs will rise, impacting the overall cost structure of the firm.

Calculating the total cost for different output levels helps firms make crucial production decisions. For example, knowing how costs increase with output allows firms to determine their break-even point or to strategize on ways to enhance efficiency in production.
Understanding the total cost is not only essential for daily operations but also plays a role in the firm's long-term strategic planning, including investment and market positioning.

Profit Maximization

Profit maximization is the goal for any firm in a perfectly competitive market. It involves finding the level of output where total revenue exceeds total cost by the largest amount. Profit for a firm is calculated as total revenue minus total cost.
To find total revenue, multiply the price (which is set by market equilibrium) by the quantity of output sold. In our exercise, we first compute profit by using the equilibrium price and quantity, followed by analyzing revenue and cost functions.

A critical part of profit maximization comes down to the differentiation of cost and revenue. When marginal revenue is equal to marginal cost (\(MR = MC\)), a firm is said to be maximizing its profits. This condition ensures no additional profit can be made by changing production levels, so resources are optimally allocated.
Understanding how to maximize profits ensures firms can survive and flourish in competitive environments, guiding them toward better pricing and output strategies.

Long-term Industry Dynamics

The dynamics of industry behavior in the long term help to determine the overall health and direction of the market in which a firm operates. In a perfectly competitive market, firms can freely enter or exit the industry based on profit opportunities.
If firms are making a profit in the short term, this signals other potential entrants to join the market, thus increasing supply and ultimately driving the price down. Conversely, if firms experience losses, some may exit the market, reducing supply and allowing the price to rise.

Over time, these adjustments lead the industry towards long-term equilibrium, where firms earn normal profits (zero economic profit). This stabilization occurs when the price equals the minimum average total cost (ATC).
Understanding these industry dynamics is critical, as it helps predict whether in the long run, the market will see more competition or consolidation. It also enables firms to strategize for future growth or identify optimal timing for strategic market exits.