Pete’s Pharmaceuticals has a patent on “24 Hour Energy,” a drug that serves as a perfect substitute for sleep. When taken as directed, “24 Hour Energy” makes the consumer feel as though she has just awakened from a full night of rest. There are no close substitutes for this product, meaning Pete’s Pharmaceuticals is a monopolist. The figure below captures relevant curves for Pete’s Pharmaceuticals, where D is the market demand curve for bottles of “24 Hour Energy,” MC is the firm’s constant marginal cost curve, and MR is the firm’s marginal revenue curve.

Relevant Curves for Pete’s Pharmaceuticals

Refer to the figure above. What is the deadweight loss associated with Pete’s Pharmaceuticals’ market power in this industry?

Question

Pete’s Pharmaceuticals has a patent on “24 Hour Energy,” a drug that serves as a perfect substitute for sleep. When taken as directed, “24 Hour Energy” makes the consumer feel as though she has just awakened from a full night of rest. There are no close substitutes for this product, meaning Pete’s Pharmaceuticals is a monopolist. The figure below captures relevant curves for Pete’s Pharmaceuticals, where D is the market demand curve for bottles of “24 Hour Energy,” MC is the firm’s constant marginal cost curve, and MR is the firm’s marginal revenue curve.

Relevant Curves for Pete’s Pharmaceuticals

Refer to the figure above. What is the deadweight loss associated with Pete’s Pharmaceuticals’ market power in this industry?

BlackTom AI · Accepted Answer

Set MR = MC: 10 − 0.2Q = 2 → 0.2Q = 8 → Qm = 40. (This uses the demand line P = 10 − 0.1Q and the MR line with twice the slope, MR = 10 − 0.2Q.)

1) Relevant knowledge points and concepts
- A monopolist maximizes profit where MR = MC.  
- Socially efficient (competitive) output occurs where P = MC.  
- Deadweight loss (DWL) from monopoly is the area of the triangle between the demand curve and the MC line for the units not produced by the monopolist: DWL = 1/2 × (Qc − Qm) × (Pm − MC).

2) Step-by-step reasoning
- Inverse demand from the graph: P = 10 − 0.1Q.  
- Marginal revenue (for linear demand) has twice the slope: MR = 10 − 0.2Q.  
- Given constant MC = $2, set MR = MC to find monopoly quantity: 10 − 0.2Q = 2 → Qm = 40 (as above).

3) Intermediate calculations
- Monopoly price from demand: Pm = 10 − 0.1(40) = 10 − 4 = $6.  
- Competitive (efficient) output where P = MC: 10 − 0.1Q = 2 → Qc = 80.  
- Base of DWL triangle = Qc − Qm = 80 − 40 = 40.  
- Height of DWL triangle = Pm − MC = 6 − 2 = 4.  
- DWL = 1/2 × base × height = 0.5 × 40 × 4 = $80.

4) Why this answer is correct
The DWL measures lost surplus from units 40–80 that would be produced under P=MC but are not produced under monopoly pricing. The triangular area with base 40 and height 4 is $80, matching the calculated area.

5) Why the other options are incorrect
- $160 would be 0.5 × 80 × 4 (incorrectly using base = Qc rather than Qc − Qm).  
- $320 or $500 do not match any correct triangle area given the plotted demand and MC lines.

6) Conclusion
Therefore the deadweight loss is $80, which matches the provided correct answer.

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