If the marginal cost(MC) of a perfectly competitive firm is as given below and the price of the product is Rs. 15, find the profit-maximizing output of the firm.

5

The correct answer is Option (3) → 5

In a perfectly competitive market, the price ($\text{P}$) is equal to the Marginal Revenue ($\text{MR}$).

Given:

• Price ($\text{P}$) = $\text{Rs }15$

• Therefore, Marginal Revenue ($\text{MR}$) = $\text{Rs }15$

The goal of a perfectly competitive firm is to maximize profit. This is achieved by producing the quantity of output where two conditions are met:

1. Price ($\text{P}$) = Marginal Cost ($\text{MC}$)

2. The $\text{MC}$ curve must be rising i.e. Marginal cost must be non-decreasing 

We need to find the output level where $\text{MC}=15$ and the $\text{MC}$ is rising.

Output 2: Here, $\text{P}=\text{MC}$ (15 = 15). However, moving from Output 1 ($\text{MC}=18$) to Output 2 ($\text{MC}=15$), the $\text{MC}$ is falling. This point corresponds to the minimum of the $\text{MC}$ curve or the intersection where $\text{MC}$ cuts $\text{MR}$ from above, which is not the profit-maximizing point.

Output 5: Here, $\text{P}=\text{MC}$ (15 = 15). Moving from Output 4 ($\text{MC}=12$) to Output 5 ($\text{MC}=15$), the $\text{MC}$ is rising. This satisfies both conditions ($\text{P}=\text{MC}$ and $\text{MC}$ is rising).