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A monopolist faces an isoelastic demand curve with price elasticity ??(?) = −1.5. The monopolist’s marginal...

A monopolist faces an isoelastic demand curve with price elasticity ??(?) = −1.5. The monopolist’s marginal cost of production is constant and equal to ?. The price given the monopolist’s profit maximizing choice of output equals ? ∗ = 42. Calculate the monopolist’s marginal cost ?.

Solutions

Expert Solution

In order to maximize profit a monopolist produces that quantity at which MR = MC

where MC = Marginal cost, MR = Marginal Revenue = d(TR)/dQ = d(P*Q)/dQ = P + Q(dP/dQ) = P(1 + (Q/P)(dP/dQ) = P(1 + 1/e)

=> MR = P(1 + 1/e)

Here, P = Price, Q = quantity, TR = Total Revenue = P*Q, e = elasticity of demand = (dQ/dP)(P/Q).

Hence profit maximizing condition MR = MC => P(1 + 1/e) = MC

Here MC = Marginal cost = c, P = P* = 42 and e = elasticity of demand = ??(?) = −1.5

Hence, P(1 + 1/e) = MC => 42(1 + 1/(-1.5)) = c

=> c =  14

Hence, Marginal cost of this monopolist (c) = 14


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