9 minute read
Recalculating expected values
Chapter 14: Increasing Revenue with Advanced Pricing Strategies
Allowing mixed bundling
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Mixed bundling allows customers to purchase the goods either together as a bundle or separately. One of the crucial differences between mixed bundling and pure bundling is that some customers purchase only a single item. These customers have a reservation price greater than the actual price for one item. However, they don’t buy the bundle because the difference between the bundle price and the price of the first item is less than their reservation price for the second item.
For example, say you’re willing to pay $30.00 for Software W and only $2.00 for Software X. In addition, the price of Software W separately is $20.00, the price of Software X separately is $15.00, and the price of the bundle is $24.00. Obviously, you’re willing to buy Software W separately — its $20.00 price is less than your reservation price of $30.00. Similarly, you’re not willing to buy Software X separately because its $15.00 price is greater than your reservation price of $2.00.
In a surprising result, you’re not willing to buy the bundle. To move from buying Software W for $20.00 to buying the bundle requires you to pay $24.00. This is $4.00 more than you have to pay to purchase Software W alone. Because your reservation price for Software X is only $2.00, it’s not worth spending the extra $4.00 to buy the bundle. The point labeled U in Figure 14-5 represents this situation.
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Figure 14-5:
Mixed bundling.
In order for you to purchase the bundle, the difference between the separate price for the first item and the bundle price must be less than your reservation price for the second item. Now assume that your reservation price for Software W remains $30.00, but your reservation price for Software X is $7.00. In this situation you’ll buy the bundle because you’re willing to pay $30.00 for Software W. That’s higher than Software W’s actual price. You can then add Software X for another $4.00 because the price of the bundle is $24.00. So, instead of purchasing Software W alone for $20.00, you can purchase the bundle including both Software W and Software X for $24.00. Because Software X is worth $7.00 to you, adding Software X to the bundle is worth it to you. You get something you’re willing to pay $7.00 for and it costs you only an extra $4.00.
In Figure 14-5, the vertical shaded area represents customers who buy only Software W. Note for this shaded area, customers’ reservation prices for Software W are higher than Software W’s $20.00 price. However, their reservation prices for Software X are less than $4.00. Because adding Software X to the bundle costs $4.00, they’re not willing to buy the bundle.
The horizontal shaded area represents customers who buy only Software X. In this horizontal shaded area, customers’ reservation prices for Software X are higher than its $15.00 price. If these customers add Software W to the bundle, it increases the price by $9.00 to $24.00. For this group of customers, their reservation prices for Software W are less than $9.00; so, they’re not willing to add Software W to their purchase of Software X.
Customers in the diagonal shaded area buy the bundle of Software W and Software X. For these customers, the reservation price of adding the second software package to the bundle is greater than the price difference. Finally, the area that isn’t shaded represents customers who don’t buy any software package.
Customers only add another good to the bundle if the actual price difference between the bundle and buying an item separately is less than the additional item’s reservation price.
Determining your total revenue with mixed bundling is very tricky. Again, assume you have 1,200 uniformly distributed customers that correspond to the area of the rectangle. Of those customers, 80 purchase just Software W at a price of $20, 135 purchase just Software X at a price of $15, and 745.5 purchase the bundle at a price of $24. The remaining 239.5 don’t purchase any software program because the price of each individual program is higher than their reservation price for that program, and the bundle’s price is higher than the customer’s reservation prices for the two programs added together. Thus, your total revenue equals $21,517 — that is, (80 × 20) + (135 × 15) + (745.5 × 24). Your revenue increases by $517 with mixed bundling as compared to selling each program separately.
Chapter 14: Increasing Revenue with Advanced Pricing Strategies
So You Want War: Pricing for Business Battles
I know a bicycle rider who once passed another bicycle rider on a hill. When passed, the second bicycle rider said, “I didn’t know it was a race.” To which the first rider responded, “It’s always a race.”
In a very real sense, businesses are always at war fighting battles with one another. Businesses compete for resources and customers. The wages one business pays for labor affect what other businesses have to pay, and the price one business charges its customers affects the price other businesses charge.
This section describes three weapons that help you fight these battles.
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Penetration pricing: Here I come
Firms use penetration pricing to quickly establish a large market share. In order to attract customers, the firm establishes a very low price. This is a useful strategy for a new firm entering a market.
Effective penetration pricing requires a very elastic demand for the good. Because customers are very responsive to price changes, establishing a low price leads to a large increase in quantity demanded. Later, if you’re successful in establishing customer loyalty, you can raise the price.
In addition to attracting new customers, an effective penetration price leads to lower per unit costs if economies of scale are present. By quickly attracting customers, you can establish a large market share leading to economies of scale that become a barrier to entry for other firms thinking about entering the market.
Penetration pricing is also used to sell complementary products. For example, a low penetration price on a game console can lead to more sales of compatible games that have high mark-ups.
You need to take into account several factors before using penetration pricing. First, consider whether your firm is able to produce enough output to satisfy customers. If you run out of product to sell, customers are likely to be dissatisfied with you. Second, price can’t be associated with quality. If customers associate a low price with poor quality, they won’t buy the product. Finally, if rivals meet the lower price you charge, the advantages of penetration pricing are negated.
Limit pricing: Keep out
Firms use limit pricing to prevent other firms from entering the market. Limit pricing occurs when the firm establishes a price below the profit-maximizing level. The lower price leads to a higher quantity demanded, leaving very little residual demand for a new firm to satisfy.
Figure 14-6 illustrates limit pricing. Initially, the market is a monopoly, so the market-demand curve, D, corresponds to the firm’s demand curve, d. As I note in Chapter 10, the marginal-revenue curve associated with a linear demand curve starts at the same point on the vertical axis and is twice as steep as the demand curve. The monopoly’s marginal-revenue curve in Figure 14-6 is labeled MR.
Figure 14-6:
Limit pricing.
Given typical average total cost and marginal cost curves, the profit-maximizing monopolist produces the quantity q0, based on marginal revenue equals marginal cost, and charges the price P0. The monopolist’s economic profit per unit is the difference between price and average total cost as represented by the double-headed arrow labeled π/q.
The positive economic profit the monopolist earns attracts new firms. If these firms enter the market, the existing firm’s profit decreases or perhaps even disappears. So, to discourage entry, the monopolist charges a lower price, PL. At this price, the monopolist must produce qL to satisfy consumer demand.
Chapter 14: Increasing Revenue with Advanced Pricing Strategies
Firms considering whether or not to enter the market now see an entirely different situation. The potential demand for an entering firm equals the market demand minus the quantity, qL, provided by the current firm. The entrant’s residual demand curve is represented by dE and the associated marginal revenue curve is MRE. The entering firm would then produce where its marginal revenue equals marginal cost. (For the moment, assume the entering firm has exactly the same costs as the current monopoly.) The entering firm’s profitmaximizing quantity and price are qE and PE. But at this output level, price equals average total cost, so the entering firm earns zero profit. Thus, the new firm has no incentive to enter the market, and the original firm has succeeded in keeping rivals out.
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Predatory pricing: Get out
Predatory pricing is used to drive existing rival firms out of a market. With predatory pricing, a firm establishes a price that’s below its marginal cost. After the rival leaves the market, the remaining firm, or predator, raises price in order to increase its profit. The predator in essence is trading a temporary short-run loss for higher future profit.
Predatory pricing depends upon the correct assessment of the relative health of the predator and prey. The predator is assuming that it’s healthier than the prey and can withstand the temporary losses better than the prey. If the predator is wrong in this assessment, predatory pricing can backfire and leave the predator vulnerable.
Predator and prey: Which is which?
In The Life and Legend of Jay Gould (published by The Johns Hopkins University Press), author Maury Klein tells the story of a price war between the owner of the New York Central Railroad, Commodore Cornelius Vanderbilt, and the Erie Railroad’s owners, Jay Gould and Jim Fisk. The price war concerned eastbound livestock traffic between Buffalo and New York City and the normal freight rate $125 a carload. Vanderbilt initiated a price war by lowering the New York Central’s rate to $100 carload. Gould and Fisk responded by lowering the Erie Railroad’s rate to $75. Vanderbilt then reduced the New York Central’s rate to $50, and Gould and Fisk dropped to $25. In a final effort to ruin the Erie Railroad’s livestock trade, Vanderbilt set his rate at $1 per carload, and as a result, the New York Central cars were full while the Erie’s cars ran empty. However, as Vanderbilt enjoyed his victory, Gould and Fisk bought every steer in Buffalo and shipped them to New York via the Central. As a result, Gould and Fisk enjoyed great profit, while Vanderbilt and the New York Central carried their cattle at tremendous cost.
