Math Problem Statement
For a monopolist’s product, the demand function is 𝑝 = 50/ 𝑥 and the average cost function is AC=0.5 + (1000/x). find the profit-maximizing output and price. At this level, show marginal revenue is equal to marginal cost
Solution
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Math Problem Analysis
Mathematical Concepts
Monopoly Economics
Calculus
Marginal Revenue
Marginal Cost
Profit Maximization
Formulas
Demand function: p = 50/x
Average Cost (AC): AC = 0.5 + 1000/x
Total Cost (TC): TC = 0.5x + 1000
Total Revenue (TR): TR = 50
Marginal Cost (MC): MC = 0.5
Marginal Revenue (MR): MR = 0
Theorems
Profit maximization in a monopoly: MR = MC
Suitable Grade Level
University Level (Economics, Calculus)
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