Managerial Economics
eighth edition
Thomas
Maurice
Chapter 14
Advanced Techniques for
Profit Maximization
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Managerial Economics
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
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(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 profitmaximizing 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:
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m  
1 E 
Where E* is price elasticity at profit-maximizing
point of firm’s demand
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Cost-Plus Pricing (Constant Costs)
• When demand is linear & costs are
constant (SMC = AVC), profitmaximizing value for E* is:
A
E  1 
0.5( AVC  A )
Where A is price-intercept of linear demand curve
& AVC is constant
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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 profitmaximizing 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)
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