Question

Consider a monopolist with a constant marginal cost of 120 . The demand function of a representative consumer is Q(P)=150−P/4

(a) Suppose the monopolist uses standard monopoly pricing. Determine the profit-maximizing quantity and price. Calculate total profit.
(b) Draw and label a graph showing the demand, marginal revenue, and marginal cost curves. Indicate the profit maximizing points and draw a box showing the profit.
(c) Suppose the monopolist is able to use nonlinear pricing. They charge two different prices: P₁ for the first q₁ units sold and P₂ for the next q₂ sold. Determine the profit-maximizing quantities and prices (there will be two of each). Calculate the total profit (it may be helpful to draw the graph first).
(d) Draw and label a graph showing the demand and marginal cost curves. Indicate q₁ and q₂ on the graph and draw a shape showing the profit.
(e) Suppose the monopolist uses two-part pricing. Determine the profit-maximizing quantity, unit price, and fixed fee. Calculate total profit.
(f) Suppose the monopolist uses block pricing. Determine the profit-maximizing quantity and block price. Calculate total profit.

Answer 1

In standard monopoly pricing, the profit-maximizing quantity and price are determined by setting marginal revenue equal to marginal cost. In nonlinear pricing, the monopolist charges different prices for different quantities. In two-part pricing, the monopolist charges a fixed fee in addition to the unit price.

Step-by-step explanation:

In standard monopoly pricing, the profit-maximizing quantity and price can be determined by setting the marginal revenue equal to the marginal cost. The monopolist will produce the quantity where MR = MC. In this case, the marginal revenue can be calculated by taking the derivative of the demand function, Q(P), and multiplying it by the price. The profit-maximizing quantity and price can then be found by solving the equation MR = MC. To calculate the total profit, multiply the profit-maximizing price by the profit-maximizing quantity and subtract the total cost.

In nonlinear pricing, the monopolist charges different prices for different quantities. To find the profit-maximizing quantities and prices in this case, set the marginal revenue equal to the marginal cost for each quantity level and solve the system of equations. Total profit can be calculated by multiplying each price by its corresponding quantity and subtracting the total cost.

In two-part pricing, the monopolist charges a fixed fee in addition to the unit price. The profit-maximizing quantity can be found by setting the marginal cost equal to the surplus value. The unit price can be calculated by subtracting the unit cost from the maximum willingness to pay. Total profit can be calculated by multiplying the unit price by the profit-maximizing quantity and adding the fixed fee.

In block pricing, the monopolist charges a different price for different blocks of quantity. The profit-maximizing quantity can be found by setting the marginal cost equal to the surplus value for each block. The block price can be calculated by subtracting the unit cost from the maximum willingness to pay for each block. Total profit can be calculated by multiplying each block price by its corresponding quantity and subtracting the total cost.