Chapter 9 Profit Maximization McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.

Main Topics Profit-maximizing quantities and prices Marginal revenue, marginal cost, and profit maximization Supply decisions by price-taking firms Short-run versus long-run supply Producer surplus 9-2

Profit-Maximizing Prices and Quantities In previous chapters, we have looked at: How many units can be sold Sales price per unit. In Ch. 2, the product’s demand function states how many units buyers will demand at each price. Quantity Demanded=D(Price) Holding all other factors, ie. taste, income, etc. fixed 9-3

Profit-Maximizing Prices and Quantities In addition to a product’s demand function, we can work from the inverse demand function. This function states how much a firm must charge to sell any given quantity of its product. Price = P(Quantity Demanded ) Holding all other factors, ie. taste, income, etc. fixed 9-4

Profit-Maximizing Prices and Quantities The primary goal of a firm is not to make money but to maximize its profit! A firm’s profit, P, is equal to its revenue R less its cost C P = R – C Maximizing profit is another example of finding a best choice by balancing benefits and costs Benefit of selling output is firm’s revenue, R(Q) = P(Q)Q Cost of selling that quantity is the firm’s cost of production, C(Q) Overall, P = R(Q) – C(Q) or P(Q)Q – C(Q) 9-5

Profit-Maximization: An Example Noah and Naomi face a weekly inverse demand function P(Q) = 200-Q for their garden benches Weekly cost function is C(Q)=Q2 Suppose they produce in batches of 10 To maximize profit, they need to find the production level with the greatest difference between revenue and cost 9-6

Figure 9.2: A Profit-Maximization Example 9-7

Marginal Revenue In general, marginal benefit must equal marginal cost at a decision-maker’s best choice whenever a small increase or decrease in her action is possible Here the firm’s marginal benefit is its marginal revenue: the extra revenue produced by the DQ marginal units sold, measured on a per unit basis 9-8

Marginal Revenue and Price An increase in sales quantity (DQ) changes revenue in two ways Firm sells DQ additional units of output, each at a price of P(Q), the output expansion effect Firm also has to lower price as dictated by the demand curve. This reduces revenue earned from the original (Q-DQ) (inframarginal) units of output, the price reduction effect Price-taking firm faces a horizontal demand curve and is not subject to the price reduction effect 9-9

Marginal Revenue and Price The green shaded area is due to the output expansion effect. The yellow shaded area is due to the inframarginal unit/price reduction effect because it must lower its price to sell the extra units. 9-10

Marginal Revenue and Price In this curve, the firm is a price taker in a perfectly competitive market. If you remember from our Principles course, p. comp. mkts allow a firm to sell as much as it wants at price P. In this case, only the outward expansion effect occurs. Why is the curve flat? Why cant we raise/lower the price? 9-11

Profit Max. for a Competitive Firm Quantity Costs and Revenue MC ATC AVC 1 Q 2 The firm maximizes profit by producing the quantity at which marginal cost equals marginal revenue. MAX P = MR AR If the firm produces Q1, marginal cost is MC1. If the firm produces Q2, marginal cost is MC2. Suppose the market price is P.

Marginal Revenue and Price In this curve, the demand curve slopes downwards. Any additional unit sold must be sold at a reduced price. What kind of market would this be for? 9-13

Profit Max. for a Monopoly Costs and 2. . . . and then the demand curve shows the price consistent with this quantity. Revenue 1. The intersection of the marginal-revenue curve and the marginal-cost curve determines the profit-maximizing quantity . . . Marginal revenue Demand Monopoly price QMAX B Marginal cost Average total cost A Q Q Quantity

Profit-Maximizing Sales Quantity Two-step procedure for finding the profit-maximizing sales quantity Step 1: Quantity Rule Identify positive sales quantities at which MR=MC If more than one, find one with highest P Step 2: Shut-Down Rule Check whether the quantity from Step 1 yields higher profit than shutting down 9-15

Supply Decisions Price takers are firms that can sell as much as they want at some price P, but nothing at any higher price Face a perfectly horizontal demand curve Firms in perfectly competitive markets, e.g. MR = P for price takers Use P=MC in the quantity rule to find the profit-maximizing sales quantity for a price-taking firm Shut-Down Rule: If P>ACmin, the best positive sales quantity maximizes profit. If P<ACmin, shutting down maximizes profit. If P=ACmin, then both shutting down and the best positive sales quantity yield zero profit, which is the best the firm can do. 9-16

Figure 9.6: Profit-Maximizing Quantity of a Price-Taking Firm 9-17

Comp. Firm’s S-R Supply Curve Costs Firm ’ s short-run supply curve If P > ATC, the firm will continue to produce at a profit. MC ATC If P > AVC, firm will continue to produce in the short run. AVC Firm shuts down if P < AVC Quantity

Supply Function of a Price-Taking Firm A firm’s supply function shows how much it wants to sell at each possible price: Quantity supplied = S(Price) To find a firm’s supply function, apply the quantity and shut-down rules At each price above ACmin, the firm’s profit-maximizing quantity is positive and satisfies P=MC At each price below ACmin, the firm supplies nothing When price equals ACmin, the firm is indifferent between producing nothing and producing at its efficient scale (why?) What about firms with sunk costs? Does the above rule apply? 9-19

Supply Curve of a Price-Taking Firm Where is the most efficient place to produce in each graph? Why? Where is the minimum place of production? Why? 9-20

Figure 9.9: Law of Supply Law of Supply: when market price increases, the profit-maximizing sales quantity for a price-taking firm never decreases. If Q* is the rev. max point before the price increase, can we sell any less after the price increase? Note: This doesn’t nec. work though in regards to the final quantity supplied. 9-21

Change in Input Price and the Supply Function How does a change in an input price affect a firm’s supply function? Increase in price of an input that raises the per unit cost of production AC, MC curves shift up Supply curve shifts up Increase in an unavoidable fixed cost AC shifts upward MC unaffected Supply curve does not shift 9-22

Figure 9.10: Change in Input Price and the Supply Function b. The curve has shifted by $5 and essentially, if the farmer receives exactly $5 more per bushel, he is willing to supply the same amount of wheat. 9-23

Change in Avoidable Fixed Cost B. As the only increase is in avoidable fixed costs, the MC and AC curves have not changed. Therefore the supply curve hasn’t changed. The only real change in this situation is that with the rise in avoidable fixed cost, the producer has to receive a higher price to stay in business. 9-24

Short-Run versus Long-Run Supply Firm’s marginal and average costs may differ in the long and short run This affects firm response over time to a change in the price it faces for its product Suppose the price rises suddenly and remains at that new high level Use the quantity and shut-down rules to analyze the long-run and short-run effects of the price increase on the firm’s output 9-25

Figure 9.13(a): Quantity Rule Firm’s best positive quantity: Q*SR in short run Q*LR in long run, a larger amount 9-26

Figure 9.13(b): Shut-Down Rule New price is above the avoidable short-run average cost at Q*SR and the long-run average cost at Q*LR Firm prefers to operate in both the short and long run 9-27

Producer Surplus A firm’s producer surplus equals its revenue less its sunk costs P = producer surplus – sunk cost Sunk Fixed costs are no considered as they are incurred no matter what, so can be ignored in making economic decisions. Avoidable fixed costs though are considered. Represented by the area between firm’s price level and the supply curve 9-28

Figure 9.16: Producer Surplus 9-29

Producer Surplus Common application: investigate welfare implications of various policies Can focus on producer surplus instead of profit because the policies can’t have any effects on sunk costs 9-30

Supply by Multi-Product Price Taking Firms When a firm’s marginal cost of production for one product changes with the quantity of a second product it produces, an increase in the price of the second product can change the firm’s supply of the first product. Why? 9-31