Let the inverse demand curve for a monopolist's product be P = 100 - 2Q and the marginal cost of production be constant at MC = 10. Suppose that the firm considers moving from a uniform pricing strategy to a two-block tariff where the first block provides 15 units at a price of P₁ = $70 and the second block provides an additional 15 units at a price of P₂ = $40. How much does the monopolist's profit rise with this scheme? A) $225 B) $337.50 C) $450.50 D) $512

Question

Quizplus · Accepted Answer

To find the monopolist's profit with uniform pricing, we need to first find the monopolist's quantity and price that maximize profit. We can do this by setting marginal revenue equal to marginal cost:

MR = 100 - 4Q = MC = 10

Solving for Q, we get:

Q = 22.5

Substituting Q back into the demand curve, we get:

P = 100 - 2(22.5) = $55

Therefore, the monopolist's profit with uniform pricing is:

π = (55 - 10) * 22.5 = $1125

Now, let's find the monopolist's profit with the two-block tariff. We need to first compute the quantity of units sold in each block. We know that the first block provides 15 units at a price of $70, so the monopolist will sell all of these units as long as the unit cost remains below $70. We know the marginal cost is constant at $10, so the monopolist will sell all 15 units in the first block:

Q1 = 15

For the second block, we need to find the quantity that maximizes profit. We know that the price in this block is $40, so we can write the revenue from this block as:

R2 = 40(Q - 15)

where Q is the total quantity sold in both blocks. We also know that the marginal cost is still $10, so the monopolist will continue to produce units in this block as long as the marginal revenue exceeds $10. We can find the monopolist's optimal quantity by setting marginal revenue equal to marginal cost:

MR2 = 100 - 4(Q - 15) = MC = 10

Solving for Q, we get:

Q = 30

Therefore, the monopolist will sell an additional 15 units in the second block:

Q2 = 15

Now we can find the monopolist's profit with the two-block tariff. The revenue from the first block is:

R1 = 70(15) = $1050

The revenue from the second block is:

R2 = 40(15) = $600

The total revenue is:

R = R1 + R2 = $1650

The total cost is:

C = 10(Q1 + Q2) = $300

Therefore, the monopolist's profit with the two-block tariff is:

π = R - C = $1350

The increase in profit is:

Δπ = π2 - π1 = $1350 - $1125 = $225

Therefore, the correct answer is B.

Let the Inverse Demand Curve for a Monopolist's Product Be