If this monopolist can price discriminate, what is the value of its profit?

Understand the Problem

The question is asking for the profit value of a monopolist who can price discriminate, based on the provided graph. The user needs to analyze the graph to determine the monopolist's profit based on the demand curve, marginal revenue, and cost curves.

Answer

The profit value of the monopolist is $20.

Steps to Solve

Identify the Quantity Produced From the graph, find the profit-maximizing quantity. The monopolist will produce where marginal revenue (MR) equals marginal cost (MC). According to the graph, this occurs at quantity $Q = 5$.
Determine the Price To find the price, look at the demand curve associated with this quantity. At $Q = 5$, the demand curve indicates a price of $P = 14$.
Calculate Average Total Cost (ATC) The average total cost (ATC) can be found where the cost curve intersects with the quantity produced. At $Q = 5$, the ATC is $10$.
Calculate Total Revenue (TR) Use the formula for total revenue: $$ TR = P \times Q $$ Substitute the values: $$ TR = 14 \times 5 = 70 $$
Calculate Total Cost (TC) Using the formula for total cost: $$ TC = ATC \times Q $$ Substitute the values: $$ TC = 10 \times 5 = 50 $$
Calculate Profit Profit is determined by subtracting total cost from total revenue: $$ \text{Profit} = TR - TC $$ Substitute the values: $$ \text{Profit} = 70 - 50 = 20 $$

The value of the monopolist's profit is $20.

More Information

The profit calculated reflects the ability of the monopolist to set prices above marginal costs, maximizing their profits through price discrimination, which allows charging different prices for different quantities sold.

Tips

Confusing total revenue with profit: Remember to subtract total cost from total revenue for profit.
Misreading the demand curve: Ensure you read the price corresponding to the quantity produced accurately.

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