Albany-Berkeley Clinker (ABC), LLC is the monopoly provider of ready-mix concrete in East Bay. The factory can produce a bag of concrete for a constant marginal cost of $3. Monthly demand for concrete is equal to Qd = 16, 000 2, 000P . Suppose that each bag of concrete causes $3 worth of social damages due to air pollution from the ABC plant.
a) Write out an equation for the monopolist’s marginal revenue curve (MR as a function of Q).
b) Assuming there is no policy, what price does the monopolist charge when maximizing profits?
The demand curve faced by ABC is , and their marginal cost (MC) is $3.
(a) The marginal revenue curve is the change in total revenue due to change in unit quantity. For this, inverse demand function is required, which can be found as or . The total revenue is price multiplied by quantity, ie , and putting the inverse demand function, we have or . The MR is hence or or or or .
(b) Assuming there is no policy, the monopoly charges price at quantity for which MC is equal to MR, ie at , and since MC is constant at $3, we have or or or . For quantity of 5000, the price is charged as per the demand curve (or inverse demand curve ), ie or or . Thus, monopolist charges $5.5 when maximizing profits.
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