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A single price monopolist is selling purple lemons.   Demand for the lemons is P = 4...

A single price monopolist is selling purple lemons.  

Demand for the lemons is P = 4 - 0.002Q. The marginal cost of production for the firm is MC = 0.4 + 0.001Q.

Calculate the deadweight loss if this firm chooses their optimal quantity.

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Answer #1

Deadweight loss = 0.5 x (Qc - Qm) x (P - MC)

Qm is calculated using the relation: MR = MC

MR = d(PQ)/dQ = 4 - 0.004Q = 0.4 + 0.001Q

Qm = 720

P = 4 - 0.002 x 720 = 2.56

MC = 0.4 + 0.001 x 720 = 1.12

Qc is calculated using the relation : P = MC

4 - 0.002Q = 0.4 + 0.001Q

Qc = 1200

Deadweight loss = 0.5 x (1200 - 720) x (2.56 - 1.12) = 345.6

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