Question

How can a monopolist identify the profitmaximizing level of output if it knows its marginal revenue and marginal costs?

Short answer

A monopolist can identify the profit-maximizing level of output by equating its marginal revenue (MR) and marginal costs (MC) functions, and then solving for the output level (Q*). For example, given the MR function \( MR(Q) = a - bQ \) and the MC function \( MC(Q) = c + dQ \), the monopolist will find the profit-maximizing output level (Q*) by solving the equation \( a - bQ = c + dQ \), which gives \( Q* = \frac{a - c}{b + d} \). At this output level, the monopolist maximizes its profit in the market by setting its marginal revenue equal to its marginal cost.

Step-by-step solution

Understand the basic concepts

Firstly, the student needs to have a clear understanding of the following concepts: - Monopolist: A single seller in the market with no competition and has the power to set prices in the market. - Marginal Revenue (MR): The additional revenue generated by selling one more unit of output. - Marginal Cost (MC): The additional cost incurred in producing one more unit of output.

MR and MC functions

Given the marginal revenue (MR) function and the marginal cost (MC) function, make sure both functions are in terms of output (Q), as it will be easier to find the profit-maximizing level of output. For example, Marginal Revenue: \( MR(Q) = a - bQ \) Marginal Cost: \( MC(Q) = c + dQ \) Where a, b, c, and d are constants.

Equate MR and MC functions

To find the profit-maximizing level of output, equate the marginal revenue (MR) function with the marginal cost (MC) function: \( a - bQ = c + dQ \)

Solve for the profit-maximizing output level (Q*)

Now, rearrange the equation to solve for Q* (profit-maximizing output level): \( Q* = \frac{a - c}{b + d} \)

Interpret the result

At this profit-maximizing output level (Q*), the monopolist will equate its marginal revenue to its marginal cost, and at this level, the monopolist is maximizing their profit in the market. Keep in mind, the monopolist has market power, and their pricing strategy leads to a higher price than in a competitive market.