PRICING So far we have supposed perfect competition: the firm cannot affect the price. Whatever the firm produces is sold at the world market price. Most commodity businesses are highly competitive: regardless of how much steel, corn, or oil a firm produces, the world market price is not affected and the firm can sell everything that is produced. An oil extraction firm in Texas cannot affect the world price of oil. A key component to perfect competition is that all firms produce essentially the same product: product differentiation is minimal. Many electronics products, such as TVs, are highly competitive industries. Gas stations and internet retailing also tend to be highly competitive. Internet retailing is not a very differentiated product. In competitive industries, the firm has no pricing power: it cannot offer a price above the competition without losing all customers. However, for many goods the firm has some pricing power. Such firms have few competitors and/or produce a differentiated product. A firm with pricing power has more freedom to set a price. If the price is high, the firm makes more money on each unit, but of course sells less units: only those customers who really like the firm s product will buy it, the rest buy imperfect alternatives from competitors. Alternatively, the firm can cut prices and try to sell more units to make higher profits. Here we determine what price maximizes profits. We will also evaluate many common pricing strategies. When should we use coupons or rebates? What about setting the price equal to a fixed mark-up over costs? Why do some firms charge $1 for a coke that costs 5 cents to make and $2 for a burger that costs $1.85 to make? We will also study price wars and other games firms play against each other. I Market Demand Quantity demanded is the number of the firm s product customers wish to purchase. What affects the quantity demanded? 1. Price of the product (P). (inversely related to demand). 2. Income of consumers (I). (Can be positively or inversely related to demand). 3. Price of substitute goods. (positively related to demand). 4. Advertising (A). (positively related to demand). 5. Price of complementary goods. (inversely related to demand). 47
For example, demand for cruises is affected by the price of a cruise the firm charges, income, the price of other vacation packages, advertising, and the price of goods like sun tan lotion, which are complementary with cruises. A Market Demand Function Definition 25 The Market Demand Function is the relationship between the quantity demanded of the product and the various factors that influence the quantity demanded. Notice that the market demand is for the whole industry and not a particular firm. For example, the market demand for laptops might be: Q = 700P +500I 200S +0.01A (103) Here A is advertising, P is the price of a laptop, I is income, S is the price of software, and Q is the quantity demanded. Apparently, if the price rises by $1, then the quantity demanded falls by 700 units per year. B Market Demand Schedule Alternatively, we may have a table. Below is a table of prices and quantity of craft beer demanded: Price of craft beer Quantity Demanded $3 1000 $5 500 $7 300 $10 90 Table 10: Market demand for craft beer. A table has less information in than a market demand function. Did demand fall strictly because of the price, or did advertising or income also change? We also cannot compute what happens to demand if we change the price of a complementary product, like pizza. However, computing the actual demand curve requires more data. The appendix shows how to compute the demand function using company data and statistics. 48
II Price Elasticity and the Optimal Pricing Policy Price elasticity measures how sensitive the market demand function is to changes in the price the firm charges. A Price Elasticity of Demand Definition 26 The Own Price Elasticity of Demand is the percentage change in quantity demanded from a one percent change in price. The price elasticity is our primary measure of the firm s pricing power. Formula: e p = P Q dq dp (104) The formula is best understood using the approximate formula: e p P Q Q Q P = Q P P = percent change in Q percent change in P. (105) In equation (105) we calculate the percentage change as (new old)/old. However, we could also use (new old)/new. We might want to do this, for example, if the old sales or price is zero. In fact, dividing by the old value and dividing by the new value are two ways to approximate the true slope which is the derivative. In problems I will tell you which to use, except when you are given the percentage change, in which case you can assume I mean (new old)/old. As before, we use the derivative formula when we have the actual market demand function. We use the Delta-formula when we have a table. As price elasticity becomes more negative firms lose pricing power. Even a small rise in price would mean no goods are sold. As e p gets larger (approaches 0), pricing power increases. Such firms may increase the price quite a bit and lose few customers. 49
elasticity economics term pricing power level of competition price sensitivity e p = perfectly elastic none perfect competition very sensitive e p < 1 elastic little competitive sensitive e p = 1 unitary elastic moderate moderate competition moderate 1 < e p < 0 inelastic strong imperfect competition not very sensitive e p = 0 perfectly inelastic infinite no competition insensitive Table 11: Terminology for price elasticity. B Examples Consider the laptops example with S = A = 0 and I = 1: Q = 500 700P e p = ( P Q )( ) dq = dp P 500 700P ( 700) = 700P 500 700P (106) (107) In general, the price elasticity varies with P: if P = 0 then e p = 0. If P = 1 2 then e p = 350 = 2.33. So if P = 1 150 2 demand. a one percent increase in price causes a 2.33% decrease in We can alternatively use the table. Using the market demand for beer table 10, using new minus old over new, with P = 5: e p = P Q Q P = 5 500 500 1000 = 2.5. (108) 5 3 Continuing, we have: Price of beer Quantity Demanded e p dividing by new e p dividing by old $3 1000 NA NA $5 500-2.5-0.75 $7 300-2.33-1 $10 90-7.78-1.63 Table 12: Price elasticity for beer. 50
Note that the two methods yield very different elasticities. Both are approximations of the true elasticity which is calculated using the derivative. Because the table has very limited data, it is not surprising that one or both of the estimates might be off. Real world examples: Industry Price Elasticity Interpretation Beer -2.83 elastic/price sensitive Wine -0.198 inelastic/insensitive Domestic Cars -0.78 inelastic/insensitive Foreign Cars -1.09 elastic/sensitive Cigarettes (everyone) -0.42 inelastic/insensitive Cigarettes (young adults) -0.8 inelastic/insensitive Prescription Drugs -0.17 inelastic/insensitive Emergency Room Visits -0.37 inelastic/insensitive Legal Services -0.4 inelastic/insensitive Higher Education -1.1 elastic/sensitive Fresh Tomatoes -4.6 elastic/sensitive Economy airline tickets -1.30 elastic/sensitive First class tickets -0.45 inelastic/insensitive Table 13: Price elasticities across industries. C Determinants of Elasticity Determinants of elasticity: 1. Level of competition (decreases elasticity, e p is more negative, more price sensitive). 2. Degree of product differentiation (increases elasticity, e p less negative). 3. Level of income (increases elasticity, e p less negative). 4. Length of time (decreases elasticity, e p more negative). 5. Availability of close substitutes (decreases elasticity, e p more negative). For example, from table 13, demand for many luxury goods (first class tickets, wine) are less price sensitive. Markets with less competition (domestic cars) are more price inelastic. 51
The market for foreign cars, which is dominated by low price cars, is more competitive. Demand for beer is elastic: Products are differentiated (helped by prodigious amounts of advertising), but many competitors exist as well. Elasticities of products by an individual firm are generally more negative/lower/less pricing power. For example, the book quotes Philip-Morris price elasticity for cigarettes at -0.69. Cigarettes are addictive. One might think you can raise the price indefinitely and addicts will continue to buy the product. But it is not so: makers of discount cigarettes will take your business. In addition, teenage consumers have little income and therefore cannot afford large price increases. Determinants 1, 2, and 5 may be related. Highly differentiated products are difficult to substitute for, which decreases the level of competition. III Set the price to maximize profits Here we suppose one of two cases, either the firm is: 1. Monopoly: the sole provider of a good with few close substitutes. 2. Competitors exist, but do not react: products are highly differentiated, and a firm which raises/lowers the price will not cause the other players in the industry to raise/lower their prices. In both cases we assume other firms do not react to your price change, for example by matching your price increases or decreases. That case is covered later in the strategy section. A Profit Maximizing Price The difference from before is that the marginal revenue is not constant: higher production means the price must be lower to sell all the product. Note that we always set a price for which we can sell all of our production. To have production left over would not be profit maximizing. Here we will choose a quantity and then compute the price we need to charge to sell all the production. One can also set a price and then think about what the demand is at that price and thus how much to produce. Profits are: maxπ = TR TC, (109) 52
maxπ = P (Q)Q TC(Q) (110) Notice I have made explicit that P depends on Q. If we choose a high Q for example, we must lower the price to sell all of the product. We can therefore choose Q first, knowing that later we must choose P to sell all of the product. Take the derivative with respect to Q (here I am using an additional rule of calculus) and set equal to zero: So: P + dp Q MC = 0, (111) dq P + dp Q = MR = MC (112) dq The marginal revenue is different. The first term is the same as before: increase the quantity by one and get P revenue. But the second term (which is negative) shows that by increasing the quantity by one the firm must also lower the price slightly on all Q of the products to ensure the product gets sold, which reduces revenue. Notice that the derivative is part of the formula for elasticity: P + dp Q dqp P = MC, (113) P + 1 e p P = MC, (114) ) P (1+ 1ep = MC, (115) P = 1 1+ 1 e p MC. (116) The price is proportional to marginal costs, in a way that depends on the price elasticity. Notice that the firm never chooses a price which results in an inelastic price elasticity. If e p > 1 then marginal revenue is negative and so MR < MC. If the firm increases prices, then revenues rise because prices increase adds revenue for each unit sold, but the quantity sold falls only a little. Further costs fall since we are producing less. 53
B Mark up The price which maximizes profits is a mark-up over marginal costs. Mark up = P cost cost (117) Mark up = 1 1 ep +1MC MC MC (118) Mark up = 1 1 1 1 = e p +1 e p +1 (119) Examples. If the price elasticity is 2, then P = 1 1 +1MC, or P = 2MC, so we charge a mark 2 1 up of = 1 = 100% over marginal costs. 2+1 As e p, the firm has no pricing power and we must charge the minimum price possible, P = MC (no mark up). C Cost Plus Pricing Definition 27 Cost-Plus pricing: Charge a fixed mark-up over wholesale costs or over average costs. Many firms use cost-plus pricing. Consider a swimming pool company who charges a 100% mark up over the wholesale price (for example, if the manufacturer charges $10 for chlorine, then charge $20). This is a mistake. Our mark up should be over marginal costs, which include things like labor and shipping. Further, the firm is not taking into account the elasticity (if the pool store down the street sold the same chemicals, the price elasticity is low). IV Profit Maximization, Monopoly: Full Example A With Demand Function Suppose demand is: Q = 5 2P. (120) 54
The demand curve gives the quantity demanded as a function of the price. Suppose total costs are: TC = 1 4 1 2 Q+Q2. (121) 1 Step 1: Solve Demand Curve For P Solving for P: P (Q) = Q 5 2 (122) Given Q, there is a price we must charge to sell all we produce. 2 Step 2: Find MC and MR We are maximizing profits. Therefore, set: MR = MC. (123) We have Further, MC = dtc dq = 1 +2Q. (124) 2 TR = P Q = Q 5 2 Q = 1 2 Q2 + 5 Q, (125) 2 MR = Q+ 5 2. (126) 3 Step 3: Set MC = MR Therefore: MR = Q+ 5 2 = MC = 1 +2Q, (127) 2 3 = 3Q, (128) 55
Q = 1. (129) 4 Step 4: Compute Price, Elasticity, and Mark-up The optimal price to charge is therefore: P = Q 5 2 = 1 5 2 = 2. (130) The price elasticity is: e p = P Q dq dp = Q 5 ( 2). (131) 2Q e p = 1 5 ( 2) = 4. (132) 2 1 The markup is: Mark up = 1 1+e p = 1 1 4 = 1 3 = 33%. (133) Notice that the optimal pricing policy makes demand elastic, the firm chooses a price where further increases in P have large effects on demand. If the firm had pricing power (e p > 1) then the firm could raise prices with a relatively small decrease in sales. Thus it makes sense to raise prices when e p > 1, until the elasticity satisfies e p 1 and further increases in the price do not make up for lost sales. B Using Tables Consider the example from the costs section (table 8). I have the same table, but the price is no longer constant: 56
Typical Data Calculate this! Q P TR TC ATC MC MR P ATC π 20 70 1400 1271 63.6 6.5 129 22 69.75 1534.5 1359 61.8 44.0 67.3 8.0 175.5 24 69.25 1662 1456 60.7 48.5 63.8 8.6 206 26 68.75 1787.5 1562 60.1 53.0 62.8 8.7 225.5 28 68 1904 1675 59.8 56.5 58.3 8.2 229 30 67.25 2017.5 1797 59.9 61.0 56.8 7.4 220.5 32 66.5 2128 1928 60.3 65.5 55.3 6.3 200 34 65.75 2235.5 2067 60.8 69.5 53.8 5.0 168.5 36 65 2340 2214 61.5 73.5 52.3 3.5 126 38 64 2432 2370 62.4 78.0 46.0 1.6 62 40 63 2520 2534 63.4 82.0 44.0-0.4-14 42 62 2604 2707 64.5 86.5 42.0-2.5-103 44 60.5 2662 2888 65.6 90.5 29.0-5.1-226 46 59 2714 3077 66.9 94.5 26.0-7.9-363 48 57 2736 3275 68.2 99.0 11.0-11.2-539 Table 14: Average and marginal costs in the gas industry. Marginal costs are computed as in the notes on cost theory. To compute the marginal revenue when Q = 22: MR = TR Q = 1534.5 1400 = 67.3. (134) 22 20 I have calculated MR for the remaining values of Q in column 7 of table 14. Looking at the marginal revenue and marginal cost columns, to maximize profits we produce where MR = MC. Here MR = MC at between 28 and 30 units (probably pretty close to 28). So produce about 28 units. Notice directly from the table that the price to charge is $68. Producing 26 units maximizes profit per unit ($8.7 per unit), but leaves profits on the table. Units 27-28 do not make as much profits as the average unit, but still make profits for the firm and therefore should be produced. A competitive firm would choose higher production. Here P = MC at a little over 32 units. Firms with pricing power raise prices above the competitive level: 57
Less is sold, but the firm more than makes up for the lost revenue by getting more revenue on the units it does sell. In addition, by producing less, the firm reduces costs, which also increases profits. V Income Elasticity Definition 28 The Income Elasticity of Demand is the percentage change in quantity demanded from a 1% change in consumers income. Formula: e I = dq di I Q Q I I Q = percent change in Q percent change in I (135) We can think of income as the income of the consumer s who buy the product. But we can also think of income as the state of the economy as a whole. Table 15 shows how to interpret the income elasticity. Income Elasticity Economics Term Sensitivity e I > 1 Luxury Good, Normal Good Sensitive to income 0 < e I < 1 Necessity, Normal Good Not sensitive 1 < e I < 0 Inferior Good Not sensitive e I < 1 Inferior Good Sensitive Table 15: Meaning of income elasticity. If the income elasticity is positive, a high income elasticity corresponds to quantity demanded being very sensitive to income. If the income elasticity is negative, households will substitute away from the good as incomes rise. Examples: Milk (e I = 0.05) is a necessity. When incomes rise, households do not purchase much extra milk. European cars (e I = 1.93) are luxury goods. Higher income households purchase more European cars. Fresh potatoes (e I = 0.43) is inferior. Most food items prepared at home are inferior, since the wealthy eat out much more. 58
Suppose the economy (income) grows by 4% last year. We can expect demand for milk to rise by 4 0.05 = 0.2%, demand for European cars should rise by 4 1.93 = 7.72%, and demand for potatoes should fall by 4 0.43 = 1.72%. Income elasticity is used to forecast demand. Necessities are more recession proof, however, luxury goods tend to do better in good times. Other elasticities can also be computed, for example the advertising elasticity. VI Common Pricing Strategies Many common strategies exist for pricing goods. How do these strategies fit into the above framework? A Price Discrimination Definition 29 Price Discrimination is selling the same product at more than one price. Examples of price discrimination: coupons, rebates, college discounts, senior citizen discounts, and even selling the same product (with the same cost) at different prices in wealthy and poor neighborhoods. Consider the demand function Q = 50 2P. At P = 5, 40 units are demanded. At P = 10, 30 units are demanded. We lose 10 customers (assume each customer buys 1 unit) when we raise the price from 5 to 10. Who are the 10 price sensitive customers? Quite possibly these customers might be college students, seniors, or the poor. If we instead charge $10 but with a senior citizen discount of $5, then we can still sell to 40 customers, but raise the price for 30 of them. Notice that price discrimination is charging a different price for the same good. If the good is different, the price will of course be different. 1 Degrees of discrimination Degrees of price discrimination: 1. First degree: Charge a different price to every customer based on their willingness to pay. 2. Second degree: Charge a different price based on quantity purchased. 59
3. Third degree: Charge different prices to different groups. Examples of first degree price discrimination include negotiated prices such as cars, Priceline.com, and university tuition. In each case, the firm tries to assess the customer s willingness to pay and charge a higher price if the customer appears to be willing to pay more. The primary example of second degree price discrimination are quantity discounts (for example, buy one, get second one at half price). Typically households are willing to pay less for extra units of the good. Most price discrimination is third degree, however. Examples include senior discounts and college discounts. Coupons, rebates, and a host of similar strategies try to charge a higher price to households with less time, since these households are typically higher income. First degree discrimination has the highest revenues. However, you have to pay your sales force more when they negotiate. More information about the customers are required. 2 Pitfalls of discrimination Discrimination raises profits if you can do it. Discrimination does not always work though: 1. Discrimination requires a lack of competition. If two auto dealers exist on the same block, the customer can negotiate the price down to marginal cost. 2. Information costs exist. For example, the need to hire commission based sales people. 3. A target group is not always easy to identify. Some seniors and college students are wealthy, for example. 4. Arbitrage can sometimes result. Those with discounts can buy and resell to those who do not. 3 Example: Third Degree Price Discrimination Suppose demand for business travel (b) consumer travel (c) are: P c = 10 Q c (136) P b = 20 1.5Q b (137) Total costs are: TC = 4+2(Q c +Q b ) (138) 60
Wechooseapriceforeachtypeofcustomer tomaximizeprofits. Forthebusiness traveler: TR b = P b Q b = (20 1.5Q b )Q b = 20Q b 1.5Q 2 b, (139) MR b = dtr b dq b = 20 3Q b, (140) TC = 4+2(Q c +Q b ) = 4+2Q c +2Q b (141) MC b = dtc dq b = 2, (142) We set MR = MC as before: MR b = 20 3Q b = MC b = 2, (143) 18 = 3Q b, Q b = 6 (144) We sell 6 units to the business travelers. Similarly for consumers we have: TR c = P c Q c = (10 Q c )Q c = 10Q c Q 2 c, (145) MR c = dtr c dq c = 10 2Q c, (146) TC = 4+2(Q b +Q c ) = 4+2Q b +2Q c (147) MC c = dtc dq c = 2, (148) MR c = 10 2Q c = MC c = 2, (149) 8 = 2Q c, Q c = 4. (150) We sell 4 units to the consumer travelers. Note that we can get the same result by writing out the whole profit equation. 61
The prices are: P c = 10 4 = 6 (151) P b = 20 1.5 6 = 11 (152) We discriminate against the business traveler, by say, charging $6 dollars for a flight that stays over on a Saturday, and $11 for a flight that does not. Profits are: π = 11 6+6 4 4 2(4+6) = 66 (153) With no price discrimination, total costs are: TC = 4+2Q (154) Demand with a single price is: P = 10 Q c (155) P = 20 1.5Q b (156) Thus: Q c = 10 P (157) Q b = 40 3 2 3 P (158) Q = Q c +Q b = 70 3 5 3 P (159) P = 14 3 5 Q (160) Now doing the problem without price discrimination, we charge P = 8, sell Q = 10 units, and make profits of 8 10 4 2 10 = $56, less than in the case where we can discriminate. 62
B Up-charging (The Popcorn Problem) Sometimes the pricing of certain related products is very different. Consider popcorn at the movies. Movie tickets are sold at a relatively small markup over marginal costs, but popcorn, which costs next to nothing to produce, is sold for very high prices. Similarly for a hamburger and a coke, extra memory on an Iphone, wine at a restaurant, etc. In all of these cases, the mark-up on the up-charge far exceeds the mark-up on the base good. Let us examine the possible explanations. The obvious answer does not hold up under close examination. Unlike airports, which have a monopoly on air travel, one has a choice for restaurants and movie theaters. Movie theaters cannot charge more for popcorn because consumers are trapped at the movie theater. Competition (usually fierce) exists since most customers can go to the theater with the lowest combined price of popcorn and tickets. A theater which lowered the price of popcorn could presumably increase sales dramatically. One possible explanation is similar to price discrimination. The idea is that price sensitive customers get the movie cheaper by not buying popcorn. Less price sensitive customers buy the popcorn and so pay more. Some evidence for this exists in that popcorn demand per person goes up during periods of low movie demand, when only the die hard fans go. Note that this is not exactly price discrimination since the groups purchase two different goods. Charging extra for a better version of the product is known as upcharging. The idea here is to charge a high markup on the up-charge. Wealthier customers and loyal fans will pay a high mark up for the up-charge. The poor and other price sensitive customers will get the no-frills version of the product at a lower markup. Example: suppose a restaurant suspects wine drinkers are less price sensitive than those who drink water. In particular, the restaurant believes that the price elasticity for those ordering dinner with wine is -2. The restaurant believes that the price elasticity of those ordering dinner with water is -4. Suppose further the marginal cost of wine is $10 and the marginal cost of dinner is $60. 1. Calculate the price of the wine and the price of the dinner assuming the restaurant uses upcharge pricing. For wine drinkers we use the formula: P = 1 1+ 1 e p MC, (161) 63
P = 1 1+ 1 2 ($60+$10) = $140. (162) This is the price of dinner and wine which accounts for both marginal costs. Now for the water drinkers: P = 1 1+ 1 4 $60 = $80. (163) We want to charge the water drinkers $80. The final prices are then $80 for dinner and $60 for wine. These two values ensure the water drinkers pay $80 and the wine drinkers pay $140. 2. Calculate the markup on the wine. We can use the formula: Mark up = P cost cost (164) Mark up = $60 $10 $60 = 6 = 600% (165) The restaurant charges a huge markup on the wine (upcharge pricing), as a way of charging less price sensitive customers more. VII Evaluating Pricing Strategies: Other We will look at price matching offers and other strategies where firms react to each other s pricing strategies in the next section. VIII Estimating Demand To find the market demand function, we use the same technique as when we find the cost and production functions. We need to assemble data on quantity demanded and the various factors that affect quantity demanded, such as price and income. The data sources are similar: 64
1. Time Series Data. Get historical data on demand and price, income, etc. 2. Cross Section Data. Get data from various geographic locations. 3. Conduct a randomized study. Select a random set of consumers and change the price. Randomized trials are becoming increasingly common. A famous example is Amazon.com, which recently randomized prices offered to consumers who went to their website. This generated a lot of uproar at the time but is now common. Sophisticated software now exists which will vary prices randomly, generate demand curves, and then re-price so as to maximize profits. All automatically. Still consumers can become wise to this strategy and visit a site many times to get the best price, especially for items bought online. Market demand functions need to be constantly re-estimated. Consumers sometimes buy without shopping around, based on, say a reputation for low prices. This can make demand look inelastic. But after a price change, consumers slowly learn the firm does not have the lowest price and switch, making demand more elastic. 65