A firm has a demand curve of
𝑄
=
25
−
0.5
𝑃
. Which of the following is the correct revenue curve for this firm? Note that the horizontal axis on each graph is quantity and the vertical axis is revenue.

Question

A firm has a demand curve of 
𝑄
=
25
−
0.5
𝑃
. Which of the following is the correct revenue curve for this firm? Note that the horizontal axis on each graph is quantity and the vertical axis is revenue.

BlackTom AI · Accepted Answer

The given demand curve is Q = 25 - 0.5 P. To obtain the revenue curve, express price P as a function of quantity Q and then multiply by Q.

Step 1: Solve for P in terms of Q.
From Q = 25 - 0.5P, rearrange: 0.5P = 25 - Q, so P = 50 - 2Q.

Step 2: Revenue as a function of Q.
Revenue R(Q) = P × Q = Q(50 - 2Q) = 50Q - 2Q^2.

Step 3: Shape and key properties of the revenue function.
- It is a downward-opening quadratic (coefficient of Q^2 is -2), so the revenue curve is concave down.
- The vertex of R(Q) = 50Q - 2Q^2 occurs where dR/dQ = 50 - 4Q = 0, so Q* = 50/4 = 12.5.
- Maximum revenue at Q = 12.5 is R(Q*) = 50(12.5) - 2(12.5)^2 = 625 - 312.5 = 312.5.
- The revenue is zero at Q = 0 and at Q = 25 (since P = 50 - 2Q becomes zero when Q = 25, giving R = 0).

Step 4: How the correct graph should look.
- The curve starts at (Q, R) = (0, 0).
- It rises to a maximum around Q = 12.5 with R ≈ 312.5.
- It falls back to (Q, R) = (25, 0).
- Between these points, the curve is a smooth, symmetric downward-opening parabola.

Given that the options are not provided (the answer choices appear empty), you cannot definitively select which graph corresponds to R = 50Q - 2Q^2 without seeing the graphs. The correct graph, if present, would be the downward-opening parabola with vertex at Q = 12.5 and maximum revenue ≈ 312.5, passing through (0,0) and (25,0).

QAMO 2010-004 Fall 2025 Unit 5: Profit Maximization with Market Power Part 1 -- Short Problems

A firm has a demand curve of 𝑄 = 25 − 0.5 𝑃 . Which of the following is the correct revenue curve for this firm? Note that the horizontal axis on each graph is quantity and the vertical axis is revenue.

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QAMO 2010-004 Fall 2025 Unit 5: Profit Maximization with Market Power Part 1 -- Short Problems

A firm has a demand curve of 𝑄 = 25 − 0.5 𝑃 . Which of the following is the correct revenue curve for this firm? Note that the horizontal axis on each graph is quantity and the vertical axis is revenue.

查看解析

登录即可查看完整答案

类似问题

When a perfectly competitive firm sells additional units of output, its total revenue will

Figure 14-2Suppose a firm operating in a competitive market has the following cost curves:​Refer to Figure 14-2. If the market price is $10, what is the firm's total revenue?

Scenario 15-1A monopoly firm maximizes its profit by producing Q = 500 units of output. At that level of output, its marginal revenue is $40, its average revenue is $80, and its average total cost is $44.Refer to Scenario 15-1. At Q = 500, the firm's total revenue is

Figure 5-3​Refer toFigure 5-3. At a price of $70 per unit, sellers' total revenue equals

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Figure 5-7Refer to Figure 5-7. If, holding the supply curve fixed, there were an increase in demand that caused the equilibrium price to increase from $6 to $7, then sellers' total revenue would

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