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Difficulty: Very hardRevenue Concepts and Relationships

A monopolist faces a market demand curve defined by the price function P=100−4QP = 100 - 4Q, where PP is the unit price in Naira (₦\text{₦}) and QQ is the quantity of output sold. If the firm increases its production and sales from 1111 units to 1212 units, what is the marginal revenue generated by the 12th12^{\text{th}} unit?

  1. ₦8\text{₦}8Answer
  2. B
    ₦52\text{₦}52
  3. C
    ₦56\text{₦}56
  4. D
    ₦48\text{₦}48

Answer

The marginal revenue of the 12th12^{\text{th}} unit is ₦8\text{₦}8.
The correct answer is derived by finding the difference in Total Revenue when output increases from 1111 to 1212 units. At Q=11Q=11, Total Revenue is 11×₦56=₦61611 \times \text{₦}56 = \text{₦}616. At Q=12Q=12, Total Revenue is 12×₦52=₦62412 \times \text{₦}52 = \text{₦}624. The marginal revenue is ₦624−₦616=₦8\text{₦}624 - \text{₦}616 = \text{₦}8.

Step-by-Step Solution

1
Calculate Total Revenue at 11 units (TR11TR_{11})
Price at 1111 units: P11=100−4(11)=₦56P_{11} = 100 - 4(11) = \text{₦}56. TR11=56×11=₦616TR_{11} = 56 \times 11 = \text{₦}616.
Total Revenue is calculated as Price multiplied by Quantity (TR=P×QTR = P \times Q).
2
Calculate Total Revenue at 12 units (TR12TR_{12})
Price at 1212 units: P12=100−4(12)=₦52P_{12} = 100 - 4(12) = \text{₦}52. TR12=52×12=₦624TR_{12} = 52 \times 12 = \text{₦}624.
Evaluating the new price and total revenue after increasing sales by one unit.
3
Compute Marginal Revenue (MR12MR_{12})
MR12=TR12−TR11=624−616=₦8MR_{12} = TR_{12} - TR_{11} = 624 - 616 = \text{₦}8.
Marginal Revenue represents the change in Total Revenue resulting from selling one additional unit of output (MR=ΔTR/ΔQMR = \Delta TR / \Delta Q).

Key Concept

Revenue Relationships in Imperfect Competition
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Topics

Revenue Concepts and Relationships

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