In: Economics
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 ?.
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