The McGraw-Hill Series

Managerial Economics ThomasMauriceeighth edition

Chapter 14

Advanced Techniques for Profit Maximization

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Advanced Techniques for Profit Maximization

• Multiplant firms• Cost-plus pricing• Multiple markets

• Price discrimination

• Multiple products• Strategic entry deterrence

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Multiple Plants

• If a firm produces in 2 plants, A & B• Allocate production so MCA = MCB

• Optimal total output is that for which MR = MCT

• For profit-maximization, allocate total output so that MR = MCT = MCA = MCB

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A Multiplant Firm (Figure 14.1)

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Cost-Plus Pricing

• Common technique for pricing when firms do not wish to estimate demand & cost conditions to apply the MR = MC rule for profit-maximization

• Price charged represents a markup (margin) over average cost:

P = (1 + m)ATC Where m is the markup on unit cost

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Cost-Plus Pricing

• Does not usually produce profit-maximizing price• Fails to incorporate information on

demand & marginal revenue• Uses average, not marginal, cost

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Practical Problems with Cost-Plus Pricing (Figure 14.3)

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Cost-Plus Pricing (Constant Costs)

• Yields profit-maximizing price when optimal markup, m*, is applied to AVC:

P = (1 + m*)AVC• And optimal markup is chosen

according to the following relation:

Where E* is price elasticity at profit-maximizing point of firm’s demand

mE

1

1

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Cost-Plus Pricing (Constant Costs)

• When demand is linear & costs are constant (SMC = AVC), profit-maximizing value for E* is:

Where A is price-intercept of linear demand curve & AVC is constant

AE

. ( AVC A )

10 5

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Multiple Markets

• If a firm sells in two markets, 1 & 2• Allocate output (sales) so MR1 = MR2

• Optimal total output is that for which MRT = MC

• For profit-maximization, allocate sales of total output so that MRT = MC = MR1 = MR2

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Price Discrimination

• Method in which firms charge different groups of customers different prices for the same good or service

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Deriving Total Marginal Revenue (Figure 14.4)

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Profit-Maximization with Two Markets (Figure 14.5)

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Multiple Products

• Related in consumption• For two products, X & Y, produce &

sell levels of output for which

MRX = MCX and MRY = MCY

• MRX is a function not only of QX but

also of QY (as is MRY) -- conditions must be satisfied simultaneously

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Multiple Products

• Related in production as substitutes• For two products, X & Y, allocate

production facility so that

MRPX = MRPY

• Optimal level of facility usage in the long run is where MRPT = MC

• For profit-maximization:

MRPT = MC = MRPX = MRPY

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Multiple Products

• Related in production as complements• To maximize profit, set joint marginal

revenue equal to marginal cost:

MRJ = MC• If profit-maximizing level of joint

production exceeds output where MRJ kinks, units beyond zero MR are disposed of rather than sold

• Profit-maximizing prices are found using demand functions for the two goods

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Profit-Maximizing Allocation of Production Facilities (Figure 14.7)

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Profit-Maximization with Joint Products (Figure 14.9)

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Strategic Entry Deterrence

• Established firm(s) makes strategic moves designed to discourage or prevent entry of new firm(s) into a market

• Two types of strategic moves• Limit pricing• Capacity expansion

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Limit Pricing

• Established firm(s) commits to setting price below profit-maximizing level to prevent entry• Under certain circumstances, an

oligopolist (or monopolist), may make a credible commitment to charge a lower price forever

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Limit Pricing: Entry Deterred (Figure 14.11)

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Limit Pricing: Entry Occurs (Figure 14.12)

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Capacity Expansion

• Established firm(s) can make the threat of a price cut credible by irreversibly increasing plant capacity

• When increasing capacity results in lower marginal costs of production, the established firm’s best response to entry of a new firm may be to increase its own level of production• Requires established firm to cut its price

to sell extra output

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Excess Capacity Barrier to Entry (Figure 14.13)

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Excess Capacity Barrier to Entry (Figure 14.13)