Walter Nicholson Christopher Snyder Amherst College Christopher Snyder Dartmouth College PowerPoint Slide Presentation | Philip Heap, James Madison University ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Profit Maximization and Supply CHAPTER 8 Profit Maximization and Supply ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chapter Preview In the last two chapters: Production: relationship between inputs and output. Costs: relationship between output and costs. In this chapter, we want to study a firm’s output decision. How much should the firm produce to maximize profits? ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

The Nature of the Firm Why do firms exist? If they did not, how would goods be produced? The role of transaction costs. Contracts within Firms Formal vs. informal contracts Contract Incentives Relationship between incentives and efficiency Firms’ Goals and Profit Maximization ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Profit Maximization Economic profit is the difference between revenue and economic cost. Economic cost includes all relevant opportunity costs. Owner’s return on her investment and normal rate of return. Economic profit (loss) and entry (exit). Marginalism How much profit can I make from making one more car or hiring one more worker? ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Profit Maximization The Output Decision π(q) = R(q) – TC(q) The firm chooses the level of output that generates the largest profit. The firm choose the level of output for which the difference between revenue and costs is the largest. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Profit Maximization: Graphical Approach Costs (TC) Costs, Revenue Revenues (R) Output per week Profits Output per week q1 q* q2 Profits ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Profit Maximization: Golden Rule At q* what condition must hold? Marginal Revenue = Marginal Cost Why? If at the current level of output, MR > MC, the firm should . . . If at the current level of output, MR < MC, the firm should . . . Therefore, if MR = MC, the firms maximizes profits. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Profit Maximization: Graphical Approach Costs (TC) Costs, Revenue Revenues (R) slope = MR slope = MC Output per week Profits Output per week q1 q* q2 Profits ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Profit Maximization: Calculus π(q) = R(q) – TC(q) To maximize a function set the first derivative equal to zero dπ(q)/dq = dR(q)/dq – dTC(q)/dq = 0 MR(q) – MC(q) = 0 MR(q) = MC(q) ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Profit Maximization: Calculus π(q) = 20q – (50 + 10q + 0.1q2) dπ(q)/dq = ? 20 – (10 + 0.2q) = 0 q* = 50 20 – (10 + 0.2q) ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Marginal Revenue Marginal revenue is the additional revenue from selling one more unit. What happens to marginal revenue as the firm sells more or less output? Price taker is a firm whose decisions have no effect on the prevailing market price of a good. For a price taking firm MR = P. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Marginal Revenue What about for a firm that faces a downward sloping demand curve? To sell one more unit the firm would have to cut the price for all units sold, not just the last one. Revenue from the last unit = new price – revenue lost from selling the other units at a lower price MR < P ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

A Numerical Example: q = 10 - P What happens to TR and MR as output increases? ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Marginal Revenue Price Loss in revenue from cutting price by $1 = $3 $7 $6 Gain in revenue from selling one more unit = $6 Marginal revenue = $3 Demand Quantity 3 4 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Marginal Revenue and Elasticity The price elasticity of demand in a market: The price elasticity of demand for a firm: ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Marginal Revenue and Elasticity What is the relationship between elasticity and marginal revenue? When demand is elastic, eq,P < -1, MR > 0 When demand is unit elastic, eq,P = 1, MR = 0 When demand is inelastic, eq, P > -1, MR < 0 In general, can show that: MR = (1 + 1/eq,P) If eq,P = -2 (elastic), MR = (1 + 1/-2) = 1/2 > 0 If eq,P = -0.5 (inelastic), MR = (1 + 1/-0.5) = -1 < 0 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Marginal Revenue and Elasticity The firm can use elasticity information to see what happens to revenue if it sells one more unit? Suppose eq,P = -2 and the current price is $10. MR = $10 x (1 + 1/-2) = $5 The firm will sell one more unit as long as MC < $5 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Marginal Revenue Curve A marginal revenue curve shows the relation between the quantity a firm sells and the revenue yielded by the last unit sold. The marginal revenue curve will lie below the demand curve or the average revenue curve. Price P1 Demand (average revenue) Quantity q1 Marginal revenue ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Marginal Revenue Curve for Linear Demand Curves Derive the marginal revenue curve for q = 10 – P. Solve for P so P = 10 – q MR = 10 – 2q For a linear demand curve, the marginal revenue curve has the same intercept but twice the slope. If P = a – bQ, MR = a – 2bQ ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Marginal Revenue Curve Price 10 MR = 10 – 2q Demand: q=10-P or P = 10-q 5 10 Quantity ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Supply Decision for a Price Taking Firm When does it make sense to assume that firms are price takers? Suppose the market demand for corn is: Q = 16,000,000,000 – 2,000,000,000P P = 8 – Q/2,000,000,000 Assume there are 1 million corn farmers who each produce 10,000 bushels per year P = $3 and Q = 1 billion bushels What if one farmer decides to stop growing corn? Q = 9,999,990,000 and P = $3.000005 If one farmer doubles output, P = $2.999995 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Supply Decision for a Price Taking Firm If there are many suppliers in the market, each producing a small percentage of total output, their decisions will have no impact on the market price. Short Run Profit Maximization A price taking firm will maximize profits by producing a level of output where ....? P* = MC The profit maximizing condition is still MR = MC. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Supply Decision for a Price Taking Firm SMC SAC P*=MR q* Quantity ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Profits for a Price Taking Firm Profit = π = Total Revenue – Total Cost = P*q* - STC(q*) Profit = π = q*(P* - STC/q*) = q*[P* - SAC(q*)] If P* > SAC(q*), then profit > 0 If P* = SAC(q*), then profit = 0 If P* < SAC(q*), then profit < 0

Economic Profit: P* > SAC Price SMC SAC P*=MR q* Quantity ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Economic Loss: P* < SAC Price SMC SAC P*=MR q* Quantity ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

The Price Taking Firm’s Supply Curve SMC P** SAC P*=MR P*** q*** q* q** Quantity

The Shut Down Decision If profits are negative, the firm must compare losses from producing some output to how much it would lose if it shut down: q = 0. If it shuts down it only loses its fixed costs. Therefore, a firm will stay open as long as it can cover its VC. P x q ≥ SVC or P ≥ SVC/q = AVC To stay open price must be greater than or equal to short run average variable cost.

The Price Taking Firm’s Supply Curve SMC P** SAC P*=MR P*** PSD qSD q*** q* q** Quantity

Summary Any firm maximizes profits by producing where MR=MC. If a firm faces a downward sloping demand curve, MR < P and the marginal revenue curve will lie below the demand curve. With many firms in the market one firm’s actions will not affect the market price. Therefore, P = MR. A price taking firm will maximize profits where P = MC, and the firm’s supply curve is its short-run marginal cost curve. If price is less than average variable cost, the firm will shut down and only incur its fixed costs. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.