Chapter 14: Advanced Pricing Techniques McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

Advanced Pricing Techniques Price discrimination Multiple products Cost-plus pricing

Capturing Consumer Surplus Uniform pricing Charging the same price for every unit of the product Price discrimination More profitable alternative to uniform pricing Market conditions must allow this practice to be profitably executed Technique of charging different prices for the same product Used to capture consumer surplus (turning consumer surplus into profit)

The Trouble with Uniform Pricing (Figure 14.1)

Price Discrimination Exists when the price-to-marginal cost ratio differs between two markets

Price Discrimination Three conditions necessary to practice price discrimination profitably: Firm must possess some degree of market power A cost-effective means of preventing resale between lower- and higher-price buyers (consumer arbitrage) must be implemented Price elasticities must differ between individual buyers or groups of buyers

First-Degree (Perfect) Price Discrimination Every unit is sold for the maximum price each consumer is willing to pay Allows the firm to capture entire consumer surplus Difficulties Requires precise knowledge about every buyer’s demand for the good Seller must negotiate a different price for every unit sold to every buyer

First-Degree (Perfect) Price Discrimination (Figure 14.2)

Second-Degree Price Discrimination Lower prices are offered for larger quantities and buyers can self-select the price by choosing how much to buy When the same consumer buys more than one unit of a good or service at a time, the marginal value placed on additional units declines as more units are consumed

Examples of Second Degree Price Discrimination Two-part pricing Block pricing

Second-Degree Price Discrimination Two-part pricing Charges buyers a fixed access charge (A) to purchase as many units as they wish for a constant fee (f) per unit Total expenditure (TE) for q units is: Average price declines as more is purchased

Second-Degree Price Discrimination When consumers have identical demands, entire consumer surplus can be captured by: Setting f *= MC Setting A* = consumer surplus (CS) Optimal usage fee when two groups of buyers have identical demands is the level for which MRf = MCf

Inverse Demand Curve for Each of 100 Identical Senior Golfers (Figure 14.3)

Summary of Two Part Pricing Consumers will purchase product until marginal benefit = unit price Unit price will at least cover marginal cost With consumers with different preferences unit price will be above marginal cost Consumers will choose to purchase as long as consumer surplus given unit price is greater than lump-sum fee (right to purchase) With identical preferences monopolist will capture the entire consumer surplus With different preferences some consumers will retain part of their consumer surplus

Demand at Northvale Golf Club (Figure 14.4)

Second-Degree Price Discrimination Declining block pricing Offers quantity discounts over successive discrete blocks of quantities purchased

Block Pricing with Five Blocks (Figure 14.5) Compare unit price of an additional block to MC

Third-Degree Price Discrimination 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

Third-Degree Price Discrimination Equal-marginal-revenue principle Allocating output (sales) so MR1 = MR2 which will maximize total revenue for the firm (TR1 + TR2) More elastic market gets lower price Less elastic market gets higher price IF MR1 ≠ MR2 then shifting a unit of sales from the lower marginal revenue market to the higher marginal revenue market will increase revenue and leave total cost unchanged.

Allocating Sales Between Markets (Figure 14.6)

Constructing the Marginal Revenue Curve (Figure 14.7) Horizontally sum MR curves

Profit-Maximization Under Third-Degree Price Discrimination (Figure 14

Third degree price discrimination

Example of third degree price discrimination Bigsoft sells software to students and commercial users It prices the software at $100 for commercial users and $50 to students. Commercial users have a price elasticity of demand of -1.5 and students have a price elasticity of demand of -4 at the current prices. Is the firm practicing optimal third degree price discrimination?

Bigsoft example MR = P(1+1/E) Commercial users Student users MR = $50 (1-1/4) = $37.5 How much can Bigsoft increase revenues by shifting one sale? $37.5-33 = 4.5

Bigsoft example Suppose we have constant price elasticities of demand and constant marginal cost Ec = -1.5 Es = -4 MC = $40 What are optimal prices?

Bigsoft example MRc = MRs = MC MRc = $40, MRs = $40 Given that MR = P(1+1/E) then P = MR/(1+1/E) Pc = $120 and Ps = $53.33

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 Example: Disney sells DVD and complementary toys

Disney studios Disney is considering lowering the price of its latest DVD from $20 to $15. This will increase unit sales but lower profits from the sale of the DVD’s by $10 million. Increased sales of the DVDs will produce more sales of action figures. If the profit margin on an action figure is $5, how many more action figures must Disney sell to offset the decline in profits on the DVDs? Answer ($10 million/$5) = 2 million

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

JBL Plastics JBL has a vacuum press that can produce plastic cars or tanks. The marginal cost of producing two cars or one tank is $5. The marginal revenue from the sale of a toy car is $3 and the price is $6. The marginal revenue from the sale of a toy tank is $7 and the price is $14. MRPc from toy cars is $3x2= $6 MRPt from toy tanks is $7x1=$7 Should JBL readjust the ratio of cars to tanks it is producing so that MRPt= MRPc= MC

Profit-Maximizing Allocation of Production Facilities (Figure 14.9) Horizontally sum MRP curves

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-Maximization with Joint Products (Figure 14.11) Vertically sum MR curves

Farmer Jones The marginal revenue from another cow brought to market includes marginal revenue of $300 from the sale of beef at a price of $500 and a price of $50 and marginal revenue $25 from the sale of the hide. If the marginal cost of bringing another cow to market is $350, should he slaughter another cow?

Farmer Jones Product Marginal Revenue Beef $300 Hide 25 Total MR $325 Marginal Cost $350

Bundling Multiple Products When price discrimination is not possible, bundling multiple goods and charging a single price can be more profitable than charging individual prices for multiple goods Two conditions for profitable bundling Consumers must have different demand prices for each good in the bundle Demand prices must be negatively correlated across consumer types

Bundling of Tickets to Football Game Max TR =$3,300 = 2 x $1,400 + $500 Max TR = $4,000 = 2 x $2,000

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 generally produce profit-maximizing price Fails to incorporate information on demand & marginal revenue Uses average, not marginal, cost

Practical Problems with Cost-Plus Pricing (Figure 14.13) Manager assumes the firm can produce 5,000 units and sell at a 50 percent mark-up

Consider Optimal Markup Over MC Relative to Price