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Unformatted text preview: Managerial Economics Class 5 1. SR versus LR costs 2. Profit maximization revisited 3. Monopoly 4. Profit maximization for PC firms and the supply curve revisited 5. LR Supply 6. LR Equilibrium in PC Markets 1 Profit Maximization We previously examined profit maximization when a firm was limited to a small set of production options. How about when the firm can produce at any output level (not just a finite set of options)? Key assumptions: 1. A firm produces a single good. 2. The firm must charge a single price for each unit of the good. 3. The firm faces some sort of inverse demand function. 4. There are lots of buyers. Remark: These assumptions are broad enough to cover perfect competition, monopoly and monopolistic competition, but not oligopoly (we will cover that setting later). 2 Profit Maximization The firms profit function yields the profit associated with each level of firm output. Profit is total revenue less total cost. Mathematically, ( ) ( ) ( ) Q TR Q TC Q = The goal is to find the output level Q * that maximizes profit. Hill climbing analogy: If we are at an optimal production level, then taking a step in any direction will not increase profit, i.e., we must be at the top of the hill. 3 Profit Maximization What characterizes a hilltop on the profit function? Slope (derivative) of the profit function must be zero Equivalently  the slope of the total revenue and total cost curves are equal Slope of the total revenue curve = marginal revenue Slope of total cost curve = marginal cost Pictorial argument behind the MR = MC rule: Marginal revenue exceeds marginal cost. Profit is increasing in output. Cannot be optimal. (=> r aise output ) Marginal cost exceeds marginal revenue. Profit is decreasing in output. Cannot be optimal. (=> l ower output ) Marginal revenue equals marginal cost. Profit may not be increased through either an increase or decrease in output. => output is optimal The hilltop problem translated to profit maximization (blue line represents profit as a function of quantity) 4 Profit Maximization How to solve profit maximization problems: The Ingredients: 1. The total cost function TC(Q) and its associated marginal cost function MC(Q). 2. The total revenue function TR(Q) = P(Q)Q and its associated marginal revenue function MR(Q). The Recipe: 1. Set MR(Q) = MC(Q) to determine candidates for the profit maximizing output level Q*. 2. If setting MR = MC delivers more than one candidate point, compare profitability at each and choose the highest. 3. Check that shutting down (Q=0) is not actually optimal. Emphasizes that price depends on the quantity through the demand curve....
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This note was uploaded on 04/30/2011 for the course MBA 862 taught by Professor Phi during the Fall '11 term at Clemson.
 Fall '11
 phi
 Economics, Monopoly

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