Output, Price, and Profit: The Importance of Marginal Analysis 6 Output, Price, and Profit: The Importance of Marginal Analysis

Outline Price and Quantity: One Decision, Not Two Total Profit: Keep your Eye on the Goal Marginal Analysis and Maximization of Total Profit Generalization: The Logic of Marginal Analysis and Maximization Copyright © 2006 South-Western/Thomson Learning. All rights reserved.

Puzzle: Making Profit by Selling Below Cost Legal battle between Co. A and B who make calculators. B accused A of selling 10M for $12 each, which A knew was below cost. B claimed A was trying to drive B out of business. When A’s cost records were shown in court, looked like B was right. Direct costs of materials, L, and ads = $10.30/unit Indirect costs of admin. and R& D = $4.25 /unit So P of $12 did not cover $14.55 cost/unit.

Puzzle: Making Profit by Selling Below Cost Economists defending A showed that its calculator sales were profitable, so it wasn’t just trying to destroy B. After discussing profit-max output decisions, you’ll see why A was profitable.

Price and Quantity: One Decision, Not Two Critical decision -when Apple decides how many ipods to produce and P it will charge. P affects how consumers respond and Q affects K and L costs. When firms chose P and Q to max profits → they can pick only one –P or Q. Chose P → customers decide Q Chose Q → market determines P at which this Q can be sold

FIGURE 1. Demand Curve for Flo’s Poultry Meat Flo faces a local D curve. If she picks P = $19 → Qd = 1. If she picks Q = 9 → P = $11 to find required # of customers. A $19 Price per package B $11 D 1 9 Quantity of Chicken (20 lb-packages per week)

Price and Quantity: One Decision, Not Two Each pt on D curve corresponds to a (P,Q) pair. A firm can pick 1 pair, but it can never pick P from 1 pt on D and a different Q from another pt on D. Economists assume that firms pick (P,Q) pair that maximizes profits.

Total Profit: Keep Your Eye on the Goal Total profit (or economic profit) = TR – TC (including opportunity cost) Opportunity costs include any K or L supplied by the firm’s owners. Economic profit = Accounting profit – opportunity cost. E.g., if a talented attorney, gives up her salary of $120,000 to start her own law firm and earns $150,000 after paying for all operating costs → accounting profit = $150,000 but economic profit = $30,000 E.g., if you start a business and earn 6% on money you invested but could have earned 4% in T-Bills → economic profit = 2%.

Total Profit: Keep Your Eye on the Goal Total, Average, and Marginal Revenue: Total Revenue (TR) = P  Q Calculated from D curve Average Revenue (AR) = TR/Q = (P  Q)/Q = P AR curve = D curve Marginal Revenue (MR) =  TR when ↑output by 1 unit. Slope of TR curve

TABLE 1. Schedule of Flo’s Total, Average, and Marginal Revenue Chicken (20 lb-pack) Price (or AR) ($ per package) Total Revenue (P x Q) Marginal Revenue ----- 1 $19 2 18 36 17 3 51 15 4 16 64 13 5 75 11 6 14 84 9 7 91 8 12 96 99 10 100

FIGURE 2. Flo’s Total Revenue Curve

Total Profit: Keep Your Eye on the Goal Total, Average, and Marginal Cost: TC = P inputs x Q inputs AC = TC/Q output Per unit costs MC = ∆TC when ↑output by 1 unit. Slope of TC curve

TABLE 2. Flo’s Total, Average, and Marginal Cost Chicken (20 lb-pack) Total Cost Marginal Cost Average Cost $0.0 ----- 1 17.0 $17.0 2 26.0 9.0 13.0 3 33.0 7.0 11.0 4 40.0 10.0 5 48.0 8.0 9.6 6 57.0 9.5 7 67.2 10.2 8 80.0 12.8 9 99.0 19.0 10 125.0 12.5

FIGURE 3(a). Flo’s Total Cost Curve

FIGURE 3(b). Flo’s Average and Marginal Cost Curves

Total Profit: Keep Your Eye on the Goal Maximization of Total Profits: Profits typically increase with output, then fall. Some intermediate level of output generates max profit.

TABLE 3. TR, TC, and Profit for Flo Chicken (20 lb-pack) Total Revenue (P x Q) Total Cost Total Profit $0 $0.0 1 19 17.0 2.0 2 36 26.0 10.0 3 51 33.0 18.0 4 64 40.0 24.0 5 75 48.0 27.0 6 84 57.0 7 91 67.2 23.8 8 96 80.0 16.0 9 99 99.0 0.0 10 100 125.0 -25.0

Total Profit: Keep Your Eye on the Goal In our example: Total profit (Π) is max at 5 or 6 packages, where farm earns its highest profits of $27 per week. Any other Q level → ↓Π E.g., if Q = 3 → Π = $18 or if Q = 8 → Π = $16

Marginal Analysis and Maximization of Total Profit Use marginal analysis to find Q that max profits. Marginal profit = ∆ total profit when ↑Q by 1 unit. Slope of total profit curve Rule: if marginal Π > 0 → ↑Q if marginal Π < 0 → ↓Q Profit-max Q is reached when marginal Π = 0. Graphically, only reach top of total profit “hill” when marginal profit (its slope) = 0.

FIGURE 4(a). Profit Maximization Total Profit “hill” 27 20 Total Profit per week ($) 2 3 4 5 6 7 8 9 10 1 –20 –30 Output, Packages per week Total profit has a “hill” shape. At Q = 0, Π = 0. At larger Q levels, firm floods the market, and ↓Π. Only at intermediate Q levels is Π > 0.

Marginal Analysis and Maximization of Total Profit Like marginal Π, MR and MC can guide us to Q output where total profit is maximized. MR = slope of TR and MC = slope of TC Total profit is max when TR and TC are farthest apart. Occurs when their slopes are equal, so they are not growing closer together (Π↓) or growing further apart (Π↑). Rule: if MR > MC → Q if MR < MC → Q Profit maximizing Q is where MR = MC.

FIGURE 4(b). Profit Maximization Total Π = vertical distance between TR and TC curves TC 125 TR 99 84 Total Revenue, Total Cost per week ($) Profit 57 20 $27 1 2 3 4 5 6 7 8 9 10 Output, packages per week

TABLE 4. Maximization of Flo’s Total Profits Output (packages) Marginal Revenue Marginal Cost Marginal Profit Total Profit ----- $0.0 1 $19 $17.0 $2.0 2.0 2 17 9.0 8.0 10.0 3 15 7.0 18.0 4 13 6.0 24.0 5 11 3.0 27.0 6 9 0.0 7 10.2 -3.2 23.8 8 12.8 -7.8 16.0 19.0 -16.0 10 26.0 -25.0

Marginal Analysis and Maximization of Total Profit Finding the Optimal P from Optimal Q: Optimal Q is where MR = MC (and marg. Π = 0). E.g., at Q = 6; MR = MC = $9. Producer picks Q then demand curve  P buyers will pay to purchase that level of output. E.g., at Q = 6 → P = $14 –only P at which this Q is purchased by consumers.

Logic of Marginal Analysis & Maximization Decision makers constantly faced with problem of choosing the magnitude of some variable. E.g., how many cars to produce; how many workers to hire, or how many pints of ice cream to buy. Generally, larger the number selected → higher the total benefit. However, costs ↑ as number chosen ↑. Optimally, decision makers chose Q of some variable where difference between total benefit and total cost is greatest.

Logic of Marginal Analysis & Maximization Decide about Q of some variable, then max net benefit = total benefit – total cost by choosing the Q where marginal benefit = marginal cost. Rule is true regardless of who the decision maker is. Decision maker Marginal benefit Marginal cost Choice variable Objective consumer MU P good Q of good Max CS firm MRP input P input Q of 1 input Max Π MR output MC output Q of output

Logic of Marginal Analysis & Maximization Application: Fixed Cost and Profit-max P Suppose firm’s TFC ↑. How does this affect Π-max (P,Q) pair? E.g., If Flo’s rent doubles should she ↑P to cover ↑costs or ↑Q which will ↓P? She should do nothing! When a firm’s ↑TFC, it’s Π-max (P,Q) pair remain unchanged; assuming it pays to stay in business. TFC remain constant with ∆Q → so Flo’s TFC is the same if she produces 2 or 200 packages.

TABLE 5. Rise in Fixed Cost: Total Profits Before and After Output (packages) Total Profit with TFC = 0 Total Fixed Cost Total Profit with TFC = 5 $0.0 $5 -$5.0 1 2.0 5 -3.0 2 10.0 5.0 3 18.0 13.0 4 24.0 19.0 27.0 22.0 6 7 23.8 18.8 8 16.0 11.0 9 0.0 -5.0 10 -25.0 -30.0

FIGURE 5. Fixed Cost Does Not Affect Profit-Maximizing Output Inward shift of total profit by $5 27 22 Total Profit per week ($) 2 3 4 5 6 7 8 9 10 1 –20 –30 Output, Packages per week ↓∏ by $5 at every Q → whatever Q was most profitable before ↑TFC must still be the most profitable.

Puzzle: Making Profit by Selling Below Cost The “unprofitable” calculator: Firm B accused A of trying to drive it out of business. Firm A charged $12 per unit when its AC = $14.55. AC = $14.55 = $10.30 (direct costs) + $4.25 (indirect costs) Economist (for A) argued if calculators were really unprofitable, then firm A would be better off with Q = 0. If Q = 0 (rather than 10M), lose annual sales of $120M = $12 x 10M. And it would only save direct costs of the calculators ($10.30 x 10M) = $103M.

Puzzle: Making Profit by Selling Below Cost Indirect costs (of $4.25) –largely admin. overhead, would not be saved if A stopped making calculators. Thus, Q = 0 saves $103M and costs $120M, so A’s profits would fall by $17M. Marginal profit = MR – MC = $12 - $10.30 = $1.7 Total profit = $17M = marginal profit x Q Lesson: pay attention to MC and not AC when deciding on Q of output.