Chapter 9

1. Chapter 9 Profit Maximization

2. 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

3. Profit-MaximizingPrices and Quantities • A firm’s profit, Π, is equal to its revenue R less its cost C • Π = R – C • Maximizing profit • Firm’s revenue, R(Q) = P(Q)Q • Firm’s cost of production, C(Q) • Overall, • Π = R(Q) – C(Q) = P(Q)Q – C(Q)

4. Demand function:Qd=D(P) • Inverse demand function:P=P(Qd) • it shows how much the firm must charge to sell any given Q

5. Profit-Maximization: An Example • Noah and Naomi face 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

8. Figure 9.2: A Profit-Maximization Example

9. Marginal Revenue • Marginal Revenue: the extra revenue produced by the ΔQ marginal units sold, measured on a per unit basis

11. Marginal Revenue and Price • An increase in sales quantity (ΔQ) changes revenue in two ways • Firm sells ΔQ 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; reduces revenue earned from the original (Q-ΔQ) units of output, the price reduction effect • Price-taking firm faces a horizontal demand curve and is not subject to the price reduction effect 9-7

12. Figure 9.4: Marginal Revenue and Price Firm’s extra R from selling more Q P-Taker

13. Figure 9.4: Marginal Revenue and Price B A Firm’s extra R from selling more Q= A-B

14. Price-Taker firm: MR=D curve since MR=P • Downward-sloping demand curve: MR=P when sales =0 and MR<P elsewhere.

15. Figure 9.4: Marginal Revenue and Price MR= MR

16. Sample Problem 1 (9.1): • If the demand function for Noah and Naomi’s garden benches is Qd = D(P) = 1,000/P1/2, what is their inverse demand function?

17. 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 Π • Step 2: Shut-Down Rule • Check whether the quantity from Step 1 yields higher profit than shutting down

18. 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.

19. Figure 9.6: Profit-Maximizing Quantity of a Price-Taking Firm The best choice: P=MC

20. Supply Function of aPrice-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

21. Figure 9.7: Supply Curve of a Price-Taking Firm

22. 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

23. 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

24. Figure 9.10: Change in Input Price and the Supply Function

25. Figure 9.11: Change in Avoidable Fixed Cost

26. Short-Run versusLong-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

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

28. 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

29. Producer Surplus • A firm’s producer surplus equals its revenue less its avoidable costs • Π = producer surplus – sunk cost • Represented by the area between firm’s price level and the supply curve • 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

30. Figure 9.16: Producer Surplus

31. Sample Problem 2 (9.8) • Suppose Dan’s cost of making a pizza is C(Q) = 4Q + Q2/40), and his marginal cost is MC = 4 + (Q/20). Dan is a price taker. What is Dan’s supply function? What if Dan has an avoidable fixed cost of $10?