Math  /  Data & Statistics

QuestionThe figure below presents the demand curve, marginal revenue, and marginal costs facing a monopolist. (A monopolist is a producer.) a. Under monopoly pricing, are profits positive, negative, or zero? Positive b. If government regulates average total cost pricing ( P=ATCP=A T C ), are profits positive, negative, or zero? (Click to selt c. If government regulates efficient pricing, are profits positive, negative, or zero? \square Click to sele d. Is this a natural monopoly? (Click to sele

Studdy Solution

STEP 1

1. The monopolist aims to maximize profit.
2. Profit is calculated as total revenue minus total cost.
3. Under monopoly pricing, the monopolist sets output where marginal revenue equals marginal cost.
4. Average total cost pricing implies setting price equal to average total cost.
5. Efficient pricing implies setting price equal to marginal cost.
6. A natural monopoly occurs when a single firm can supply the entire market at a lower cost than multiple firms.

STEP 2

1. Determine profit under monopoly pricing.
2. Determine profit under average total cost pricing.
3. Determine profit under efficient pricing.
4. Assess if the firm is a natural monopoly.

STEP 3

Identify the quantity where marginal revenue (MR) equals marginal cost (MC). Given that MC is constant at $10, find where MR intersects MC.

STEP 4

At the intersection of MR and MC, determine the corresponding price from the demand curve. This is the monopoly price.

STEP 5

Calculate profit under monopoly pricing: - Total Revenue (TR) = Price × Quantity - Total Cost (TC) = Average Total Cost (ATC) × Quantity - Profit = TR - TC

STEP 6

For average total cost pricing, set price equal to ATC ($15). Determine the corresponding quantity from the demand curve.

STEP 7

Calculate profit under average total cost pricing: - TR = Price × Quantity - TC = ATC × Quantity - Profit = TR - TC

STEP 8

For efficient pricing, set price equal to MC ($10). Determine the corresponding quantity from the demand curve.

STEP 9

Calculate profit under efficient pricing: - TR = Price × Quantity - TC = ATC × Quantity - Profit = TR - TC

STEP 10

Determine if the firm is a natural monopoly by comparing the cost structure: - If ATC is declining over the relevant range of output, it suggests a natural monopoly.
Solution: a. Under monopoly pricing, profits are positive. b. If government regulates average total cost pricing, profits are zero. c. If government regulates efficient pricing, profits are negative. d. This is a natural monopoly because ATC is constant and lower than the demand curve over the relevant range.

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