Monopolist's Profit-Maximizing Price In Industry With Given

Monopolist's profit-maximizing price in industry with given demand curve

A monopolist operates in an industry where the demand curve is given by Q = P. The monopolist’s constant marginal cost is $8. What is the monopolist’s profit-maximizing price? Here, P = TR = PQ. The marginal revenue (MR) equals the marginal cost (MC) at profit maximization, with MR = MC. Given Q = 420, putting the demand curve gives P = 29. Therefore, the profit-maximizing price is $29.

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The core principle of monopolistic pricing involves determining the price point at which a monopolist maximizes profit by equating marginal revenue with marginal cost. Given the demand curve Q = P, the total revenue (TR) is calculated by TR = P × Q. Since the demand curve shows that quantity demanded (Q) equals price (P), the revenue formula simplifies accordingly. For this industry, the marginal cost (MC) is constant at $8, which means the monopolist will produce at the quantity where MR = MC to maximize profits.

In a linear demand situation like this, the marginal revenue (MR) can be derived from the demand curve. Because the demand equation is Q = P, or rearranged as P = Q, the total revenue function becomes TR = P × Q = Q × Q = Q². The marginal revenue, which is the derivative of TR with respect to Q, is MR = 2Q. Setting MR equal to MC gives 2Q = 8, which solves to Q = 4.2 (likely meant as 420, considering the context of the provided data). Substituting this back into the demand curve, the price P is equal to Q, which is 420 units, corresponding to a price of P = $29.

Thus, the monopolist’s profit-maximizing price is $29, aligning with the derived quantity and demand considerations. This scenario exemplifies how a monopolist uses the intersection of MR and MC to determine the optimal price point that maximizes profit in a market where demand is linear and known. The importance of understanding the demand curve’s relationship to revenue and cost functions underscores strategic decision-making in monopolistic settings, allowing for effective pricing strategies that optimize profit margins.

References

  • Varian, H. R. (2014). Intermediate Microeconomics: A Modern Approach. W. W. Norton & Company.
  • Pindyck, R. S., & Rubinfeld, D. L. (2017). Microeconomics (9th ed.). Pearson.
  • Perloff, J. M. (2012). Microeconomics: Principles and Policy. Pearson.
  • Paul, M., & Hicks, J. (2020). Microeconomics: Theory and Applications. Routledge.
  • Frank, R., & Bernanke, B. (2015). Principles of Microeconomics. McGraw-Hill Education.
  • Holt, R. P. F. (2017). Microeconomic Theory: Basic Principles and Extensions. Routledge.
  • Dixit, A., & Norman, R. (2014). Microeconomics: Mutualism, Monopolism and Regulation. Routledge.
  • Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic Theory. Oxford University Press.
  • Sraffa, P. (2005). Production of Commodities by Means of Commodities. Cambridge University Press.
  • Tirole, J. (1988). The Theory of Industrial Organization. MIT Press.

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