Question

Consider a firm “Y” that is a monopoly.

Table 1 shows the demand schedule and marginal cost schedule for this firm.

Table 2 shows its customers and their willingness to pay (WTP) for the product sold by firm “Y”. The fixed cost for firm “Y” is $10 and this firm is maximizing profits.

For each scenario below, find: the profit-maximizing quantity sold and price. Find the profit of firm “Y”.

Scenario 1: Firm “Y” is a single-price monopolist who does not price discriminate

Scenario 2: Firm “Y” is a monopolist who perfects price discrimination.

Table 1: Demand schedule for firm “Y” product fixed cost - $10

Price($/unit) Quantity(units) Marginal cost($/hour)

40 0 -
35 1 2
30 2 5
25 3 9
20 4 12
15 5 20
Table 2
CUSTOMER WTP ($)
A 35
B 30
C 25
D 20
E 15

Answer 1

In scenario 1, the profit-maximizing quantity and price for a single-price monopolist firm can be determined by finding the quantity at which marginal revenue equals marginal cost. In scenario 2, when a monopolist perfects price discrimination, the firm should sell to customers with the highest willingness to pay first.

In scenario 1, where firm "Y" is a single-price monopolist, the profit-maximizing quantity and price can be determined by finding the quantity at which marginal revenue (MR) equals marginal cost (MC) on the demand schedule. In this case, that occurs at a quantity of 4 units, with a price of $20. To calculate the profit, subtract the total cost (which is the sum of fixed cost and variable cost) from the total revenue (which is the quantity multiplied by the price).

Profit-maximizing quantity: 4 units

Profit-maximizing price: $20

Profit of firm "Y": Total revenue - Total cost = (Quantity * Price) - Total cost

In scenario 2, where firm "Y" perfects price discrimination, it can charge different prices to different customers based on their willingness to pay (WTP). In this case, firm "Y" should sell to customers with the highest WTP first. By referring to Table 2, the firm should sell to customer A first, then customer B, and so on. By following this strategy, the firm can maximize its profit. The profit can be calculated by subtracting the total cost from the total revenue.

Profit-maximizing quantity: Sell to customers A, B, and C

Profit-maximizing price: Charge customers A, B, and C with their respective WTP

Profit of firm "Y": Total revenue - Total cost = (Quantity * Price) - Total co