Lecture by: Jacinto Fabiosa

Fall 2005

How Firms Make Decisions:

Profit Maximization

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The Goal Of Profit Maximization

• To analyze decision making at the firm, let’s start with a very basic question– What is the firm trying to maximize?

• A firm’s owners will usually want the firm to earn as much profit as possible

• We will view the firm as a single economic decision maker whose goal is to maximize its owners’ profit

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Definition of Profit

• Profit is defined as the firm’s sales revenue minus its costs of production

• If we deduct only costs recognized by accountants, we get one definition of profit– Accounting profit = Total revenue – Accounting costs

• A broader conception of costs (opportunity costs) leads to a second definition of profit– Economic profit = Total revenue – All costs of production– Or Total revenue – (Explicit costs + Implicit costs)

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Understanding Profit

• Proper measure of profit for understanding and predicting firm behavior is economic profit

– Unlike accounting profit, economic profit recognizes all the opportunity costs of production—both explicit and implicit costs

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Why Are There Profits?

• Risk-taking– Someone—the owner—had to be willing to take

the initiative to set up the business• This individual assumed the risk that business might

fail and the initial investment be lost

• Innovation• In almost any business you will find that some sort of

innovation was needed to get things started

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The Firm’s Demand Constraint

• Demand curve facing firm is a profit constraint– Curve that indicates for different prices, quantity of

output customers will purchase from a particular firm

• Can flip demand relationship around– Once firm has selected an output level, it has also

determined the maximum price it can charge

• Leads to an alternative definition– Shows maximum price firm can charge to sell any given

amount of output

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The Demand Curve Facing The Firm

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Total Revenue

• The total inflow of receipts from selling a given amount of output

• Each time the firm chooses a level of output, it also determines its total revenue– Why?

• Because once we know the level of output, we also know the highest price the firm can charge

• Total revenue—which is the number of units of output times the price per unit—follows automatically

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The Firm’s Cost Constraint

• Every firm struggles to reduce costs, but there is a limit to how low costs can go– These limits impose a second constraint on the firm

• The firm uses its production function, and the prices it must pay for its inputs, to determine the least cost method of producing any given output level

• For any level of output the firm might want to produce– It must pay the cost of the “least cost method” of production

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The Total Revenue And Total Cost Approach

• At any given output level, we know– How much revenue the firm will earn– Its cost of production

• Loss– A negative profit—when total cost exceeds total

revenue

• In the total revenue and total cost approach, the firm calculates Profit = TR – TC at each output level – Selects output level where profit is greatest

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The Marginal Revenue and Marginal Cost Approach

• Marginal revenue–Change in total revenue from

producing one more unit of output• MR = ΔTR / ΔQ

• Tells us how much revenue rises per unit increase in output

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The Marginal Revenue and Marginal Cost Approach

• Important things to notice about marginal revenue– When MR is positive, an increase in output causes total revenue to

rise– Each time output increases, MR is smaller than the price the firm

charges at the new output level

• When a firm faces a downward sloping demand curve, each increase in output causes – Revenue gain

• From selling additional output at the new price

– Revenue loss• From having to lower the price on all previous units of output

– Marginal revenue is therefore less than the price of the last unit of output

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Using MR and MC to Maximize Profits

• Marginal revenue and marginal cost can be used to find the profit-maximizing output level– Logic behind MC and MR approach

• An increase in output will always raise profit as long as marginal revenue is greater than marginal cost (MR > MC)

– Converse of this statement is also true• An increase in output will lower profit whenever marginal

revenue is less than marginal cost (MR < MC)

– Guideline firm should use to find its profit-maximizing level of output

• Firm should increase output whenever MR > MC, and decrease output when MR < MC

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Profit Maximization Using Graphs

• Both approaches to maximizing profit (using totals or using marginals) can be seen even more clearly with graphs

• Marginal revenue curve has an important relationship to total revenue curve

• Total revenue (TR) is plotted one the vertical axis, and quantity (Q) on the horizontal axis– Slope along any interval is ΔTR / ΔQ– Which is the definition of marginal revenue

• Marginal revenue for any change in output is equal to slope of total revenue curve along that interval

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Profit Maximization

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The TR and TC Approach

• To maximize profit, firm should

– Produce quantity of output where vertical distance between TR and TC curves is greatest and

– TR curve lies above TC curve

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The MR and MC Approach

• Can summarize MC and MR approach

– To maximize profits the firm should produce level of output closest to point where MC = MR

• Level of output at which the MC and MR curves intersect

• This rule is very useful—allows us to look at a diagram of MC and MR curves and immediately identify profit-maximizing output level

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An Important Proviso

• Important exception to this rule

– Sometimes MC and MR curves cross at two different points

– In this case, profit-maximizing output level is the one at which MC curve crosses MR curve from below

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What About Average Costs?

• Different types of average cost (ATC, AVC, and AFC) are irrelevant to earning the greatest possible level of profit

– Common error—sometimes made even by business managers—is to use average cost in place of marginal cost in making decisions

• Problems with this approach– ATC includes many costs that are fixed in short-run—including cost of all fixed inputs such as

factory and equipment and design staff– ATC changes as output increases

• Correct approach is to use the marginal cost and to consider increases in output one unit at a time

– Average cost doesn’t help at all; it only confuses the issue

• Average cost should not be used in place of marginal cost as a basis for decisions

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Two Points of Intersection

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Dealing With Losses: The Short Run and the Shutdown Rule

• You might think that a loss-making firm should always shut down its operation in the short run– However, it makes sense for some unprofitable firms to continue operating

• The question is– Should this firm produce at Q* and suffer a loss?

• The answer is yes—if the firm would lose even more if it stopped producing and shut down its operation

• If, by staying open, a firm can earn more than enough revenue to cover its operating costs, then it is making an operating profit (TR > TVC)– Should not shut down because operating profit can be used to help pay

fixed costs

– But if the firm cannot even cover its operating costs when it stays open, it should shut down

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Dealing With Losses: The Short-Run and the Shutdown Rule

• Guideline—called the shutdown rule—for a loss-making firm

– Let Q* be output level at which MR = MC

– Then in the short-run• If TR > TVC at Q* firm should keep producing• If TR < TVC at Q* firm should shut down• If TR = TVC at Q* firm should be indifferent between shutting

down and producing

• The shutdown rule is a powerful predictor of firms’ decisions to stay open or cease production in short-run

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Loss Minimization

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Shut Down

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The Long Run: The Exit Decision

• We only use term shut down when referring to short-run

• If a firm stops production in the long-run it is termed an exit

• A firm should exit the industry in long- run – When—at its best possible output level—it has

any loss at all

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Using The Theory: Getting It Wrong—The Failure of Franklin National Bank

• In the mid-1970’s, Franklin National Bank—one of the largest banks in the United States—went bankrupt

• In mid-1974, John Sadlik, Franklin’s CFO, asked his staff to compute average cost to bank of a dollar in loanable funds– Determined to be 7¢ – At the time, all banks—including Franklin—were

charging interest rates of 9 to 9.5% to their best customers

– Ordered his loan officers to approve any loan that could be made to a reputable borrower at 8% interest

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Using The Theory: Getting It Wrong—The Failure of Franklin National Bank

• Where did Franklin get the additional funds it was lending out?– Were borrowed not at 7%, the average cost of funds,

but at 9 to 11%, the cost of borrowing in the federal funds market

• Not surprisingly, these loans—which never should have been made—caused Franklin’s profits to decrease– Within a year the bank had lost hundreds of millions of

dollars– This, together with other management errors, caused

bank to fail

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Using The Theory: Getting It Right—The Success of Continental Airlines

• Continental Airlines was doing something that seemed like a horrible mistake– Yet Continental’s profits—already higher than industry

average—continued to grow

• A serious mistake was being made by the other airlines, not Continental– Using average cost instead of marginal cost to make

decisions

• Continental’s management, led by its vice-president of operations, had decided to try marginal approach to profit