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The demand for a slice of pizza, expressed as QD = 6 - P, establishes a foundational relationship between price and quantity that consumers are willing to purchase. This linear demand curve indicates that when the price decreases, consumer demand increases, and vice versa. To analyze the profit-maximizing strategies for the seller, we proceed to determine the optimal price and quantity based on the firm's cost and revenue structures.
Part a: Profit-Maximizing Price and Quantity
The first step involves identifying the profit-maximizing output and price. The seller's marginal cost (MC) per slice is given as $1.00, and the marginal revenue (MR) function is specified as MR = 6 - 2Q. To maximize profit, the seller equates MR and MC:
6 - 2Q = 1
2Q = 5
Q = 2.5 slices
Since the demand function is QD = 6 - P, we can determine the price corresponding to Q = 2.5:
P = 6 - Q = 6 - 2.5 = 3.5
Therefore, the profit-maximizing price is $3.50, and the optimal quantity is 2.5 slices. This pricing strategy ensures that the seller's marginal revenue aligns with the marginal cost, leading to maximum profit under the market conditions described.
Part b: Selling at Cost with a Fixed Price
If the seller opts to sell pizza at cost—i.e., at $1.00—and charges a fixed price for customers to purchase the slices, the demand at this market price can be calculated using the demand function:
Qd = 6 - P = 6 - 1 = 5 slices
At the fixed price of $1.00, consumers demand 5 slices of pizza. The maximum fixed price the seller can charge while covering costs is exactly $1.00, since selling at any higher price would reduce demand and potentially affect total revenue negatively. Charging above this cost would turn the activity unprofitable unless subsidized or supplemented by other revenue streams.
The strategic implications of this pricing approach involve trade-offs between short-term revenue and market share. Selling at cost with a fixed price may be beneficial for market penetration or elimination of competition, but it minimizes per-unit profit margins. This strategy can be valuable in scenarios where increasing market share or creating customer loyalty is prioritized over immediate profits.
From an economic perspective, setting the price at marginal cost aligns with perfect competition principles, promoting efficiency and consumer surplus. However, for a monopolist or a firm with market power, pricing above marginal cost—especially at the profit-maximizing point found previously—is typically more advantageous for maximizing profitability.
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