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# slides_class5 - Managerial Economics Class 5 1 2 3 4 5 6 SR...

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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

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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 firm’s 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 π = - 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

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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. 5

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Computing Marginal Cost Total cost – takes as input the level of output (e.g., 6-packs of Saint Arnold) and returns the (minimum) total cost associated with producing that level of output Marginal cost – additional cost associated with increasing production by ΔQ , where ΔQ should be thought of as a “small” increase More formally, marginal cost is the
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slides_class5 - Managerial Economics Class 5 1 2 3 4 5 6 SR...

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