Purpose: To prove that for a monopoly firm, the marginal revenue curve lies below the demand curve. Task Instructions: This is the demand curve for Firm A’s products. The MR curve for Firm A is also shown. You must assume the firm cannot price discriminate, which means if they lower the price in order to sell more units, they are charging all consumers the same price. We can see quantity demanded, average revenue and marginal revenue from this diagram. We can also calculate total revenue. Example: When Firm A charges $137.50, the quantity demanded is 1. The firm’s Total Revenue is $137.50. Average Revenue = $137.50 = Price. Marginal Revenue of the 1st product = $137.50 Answer this question first: When Firm A charges $125, the quantity demanded is…..

Question

BlackTom AI · Accepted Answer

The demand curve shown passes through price P = 150 at Q = 0 and hits P = 0 at Q = 12, so the demand is linear with slope -150/12 = -12.5. The demand equation is therefore P = 150 - 12.5Q.

Step-by-step reasoning and calculation:
1. Identify key points from the diagram: at Q = 0, P = 150 (vertical intercept); at Q = 12, P = 0 (horizontal intercept). The example given (Q = 1, P = 137.50) confirms these intercepts.
2. Compute the slope: slope = (0 - 150) / (12 - 0) = -150/12 = -12.5.
3. Write the linear demand function using the intercept form: P = 150 + (slope)·Q = 150 - 12.5Q.
4. Set P = 125 and solve for Q:
   125 = 150 - 12.5Q
   12.5Q = 150 - 125 = 25
   Q = 25 / 12.5 = 2.

Why this is correct: plugging Q = 2 back into the demand function gives P = 150 - 12.5·2 = 150 - 25 = 125, so a price of $125 corresponds exactly to quantity demanded of 2 units. This also matches the visual reading of the plotted demand line (the point at Q = 2 aligns with P = 125).

Why other numerical guesses would be wrong: any other Q (for example 1 or 3) yields P = 137.50 or P = 112.50 respectively, not $125. Thus only Q = 2 produces P = $125.

Conclusion: The quantity demanded when Firm A charges $125 is 2, which matches the provided answer.

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