Advanced Techniques for Profit Maximization Chapter 14 Advanced Techniques for Profit Maximization

Advanced Techniques for Profit Maximization Multiplant firms Cost-plus pricing Multiple markets Price discrimination Multiple products Strategic entry deterrence

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

A Multiplant Firm (Figure 14.1)

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

Cost-Plus Pricing Does not usually produce profit-maximizing price Fails to incorporate information on demand & marginal revenue Uses average, not marginal, cost

Practical Problems with Cost-Plus Pricing (Figure 14.3)

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

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

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

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

Deriving Total Marginal Revenue (Figure 14.4)

Profit-Maximization with Two Markets (Figure 14.5)

Multiple Products Related in consumption MRX = MCX and MRY = MCY 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

Multiple Products Related in production as substitutes MRPX = MRPY 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

Multiple Products Related in production as complements MRJ = MC 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

Profit-Maximizing Allocation of Production Facilities (Figure 14.7)

Profit-Maximization with Joint Products (Figure 14.9)

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

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

Limit Pricing: Entry Deterred (Figure 14.11)

Limit Pricing: Entry Occurs (Figure 14.12)

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

Excess Capacity Barrier to Entry (Figure 14.13)

Excess Capacity Barrier to Entry (Figure 14.13)