1 Lecture 1: Optimal Pricing for Monopoly with Multiple GoodsJacob LaRiviere

2 Composite Commodity TheoryAssume there are n goods (e.g., apples, bananas, carrots, etc…) but we really only care about one of them (e.g., apples). How do we handle this problem as economists? Lets start with the very general consumer’s problem: constrained maximization. Needed assumptions are completeness, reflexivity and transitivity.

3 Composite Commodity TheorySuggestion: Say that we only solved this optimization problem for goods 2, …, n. Take the first good as a parameter [e.g., like ‘m’ in y(x)=mx+b] max 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 𝑈 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 𝑠.𝑡. 𝑝 1 ∙ 𝑥 1 +…+ 𝑝 𝑛 ∙ 𝑥 𝑛 ≤𝐼 Assume there are n goods (e.g., apples, bananas, carrots, etc…) but we really only care about one of them (e.g., apples). How do we handle this problem as economists? Lets start with the very general consumer’s problem: constrained maximization. Needed assumptions are completeness, reflexivity and transitivity.

4 Composite Commodity TheorySuggestion: Say that we only solved this optimization problem for goods 2, …, n. Take the first good as a parameter [e.g., like ‘m’ in y(x)=mx+b] This leads to a bunch of solution functions for all of the parameters… max 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 𝑈 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 𝑠.𝑡. 𝑝 1 ∙ 𝑥 1 +…+ 𝑝 𝑛 ∙ 𝑥 𝑛 ≤𝐼 Assume there are n goods (e.g., apples, bananas, carrots, etc…) but we really only care about one of them (e.g., apples). How do we handle this problem as economists? Lets start with the very general consumer’s problem: constrained maximization. Needed assumptions are completeness, reflexivity and transitivity. max 𝑥 2 ,…, 𝑥 𝑛 𝑈 𝑥 2 ,…, 𝑥 𝑛 ; 𝑥 𝑠.𝑡. 𝑝 2 ∙ 𝑥 2 +…+ 𝑝 𝑛 ∙ 𝑥 𝑛 ≤ 𝐼

5 Composite Commodity TheorySuggestion: Say that we only solved this optimization problem for goods 2, …, n. Take the first good as a parameter [e.g., like ‘m’ in y(x)=mx+b] This leads to a bunch of solution functions for all of the parameters… NOTE: I now is 𝐼 ; we’re netting out expenditures on goods 2, 3, …, n. max 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 𝑈 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 𝑠.𝑡. 𝑝 1 ∙ 𝑥 1 +…+ 𝑝 𝑛 ∙ 𝑥 𝑛 ≤𝐼 Assume there are n goods (e.g., apples, bananas, carrots, etc…) but we really only care about one of them (e.g., apples). How do we handle this problem as economists? Lets start with the very general consumer’s problem: constrained maximization. Needed assumptions are completeness, reflexivity and transitivity. max 𝑥 2 ,…, 𝑥 𝑛 𝑈 𝑥 2 ,…, 𝑥 𝑛 ; 𝑥 𝑠.𝑡. 𝑝 2 ∙ 𝑥 2 +…+ 𝑝 𝑛 ∙ 𝑥 𝑛 ≤ 𝐼 𝑥 2 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼 , …, 𝑥 𝑛 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼

6 Composite Commodity TheoryIdea: with these “solution functions” for the goods we don’t care about, lets plug them back in to the original utility function… This reduces the problem to a function of a bunch of parameters (e.g., m and b) rather than variables (e.g., y and x). This is useful; parameters aren’t complicated but variables are!

7 Composite Commodity Theory𝑥 2 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼 , …, 𝑥 𝑛 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼 -> 𝑈 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 Idea: with these “solution functions” for the goods we don’t care about, lets plug them back in to the original utility function… This reduces the problem to a function of a bunch of parameters (e.g., m and b) rather than variables (e.g., y and x). This is useful; parameters aren’t complicated but variables are!

8 Composite Commodity TheoryCall this new function “V” and let x1 vary again: 𝑥 2 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼 , …, 𝑥 𝑛 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼 -> 𝑈 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 Idea: with these “solution functions” for the goods we don’t care about, lets plug them back in to the original utility function… This reduces the problem to a function of a bunch of parameters (e.g., m and b) rather than variables (e.g., y and x). This is useful; parameters aren’t complicated but variables are! 𝑈 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 =𝑈 𝑥 1 , 𝑥 2 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼 ,…, 𝑥 𝑛 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼 =𝑉 𝑥 1 , 𝐼 ; 𝑝 2 ,…, 𝑝 𝑛

9 Composite Commodity TheoryCall this new function “V” and let x1 vary again: Noting that the prices of goods 2, 3, …, n are fixed, consider maximizing V 𝑥 2 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼 , …, 𝑥 𝑛 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼 -> 𝑈 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 Idea: with these “solution functions” for the goods we don’t care about, lets plug them back in to the original utility function… This reduces the problem to a function of a bunch of parameters (e.g., m and b) rather than variables (e.g., y and x). This is useful; parameters aren’t complicated but variables are! 𝑈 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 =𝑈 𝑥 1 , 𝑥 2 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼 ,…, 𝑥 𝑛 ∗ 𝑝 2 ,…, 𝑝 𝑛 , 𝐼 =𝑉 𝑥 1 , 𝐼 ; 𝑝 2 ,…, 𝑝 𝑛 max 𝑥 1 , 𝐼 𝑉 𝑥 1 , 𝐼 ; 𝑝 2 ,…, 𝑝 𝑛 s.t. 𝑝 1 ∙ 𝑥 1 + 𝐼 ≤𝐼

10 Composite Commodity TheoryWe can call 𝐼 the composite commodity and evaluate “everything we don’t care about” as it and now call it x2. NOTE: Effectively we’ve normalized the cost of the composite commodity to $1

11 Composite Commodity TheoryThis problem has a solution where for different levels of p1 and I there are different solutions for 𝑥 1 and 𝑥 2 . max 𝑥 1 , 𝑥 2 𝑉 𝑥 1 , 𝑥 s.t. 𝑝 1 ∙ 𝑥 1 + 𝑥 2 ≤𝐼 We can call 𝐼 the composite commodity and evaluate “everything we don’t care about” as it and now call it x2. NOTE: Effectively we’ve normalized the cost of the composite commodity to $1 𝑥 1 ∗ 𝑝 1 ,𝐼 , 𝑥 2 ∗ 𝑝 1 ,𝐼

12 Composite Commodity TheoryThis problem has a solution where for different levels of p1 and I there are different solutions for 𝑥 1 and 𝑥 2 . Finally, plot 𝑥 1 ∗ 𝑝 1 ,𝐼 against 𝑝 1 and voila! You have a demand curve… …sum them over all consumers and you have a market demand curve! max 𝑥 1 , 𝑥 2 𝑉 𝑥 1 , 𝑥 s.t. 𝑝 1 ∙ 𝑥 1 + 𝑥 2 ≤𝐼 We can call 𝐼 the composite commodity and evaluate “everything we don’t care about” as it and now call it x2. NOTE: Effectively we’ve normalized the cost of the composite commodity to $1 𝑥 1 ∗ 𝑝 1 ,𝐼 , 𝑥 2 ∗ 𝑝 1 ,𝐼

13 How do monopolists price goods?

14 Monopolists, like all firms, should price to maximize profits.As a result, the demand curve and costs matter

15 Monopolists, like all firms, should price to maximize profits.As a result, the demand curve and costs matter Perfect Comp: MB = MC = P (other firms can undercut price otherwise)

16 Monopolists, like all firms, should price to maximize profits.As a result, the demand curve and costs matter Monopolist doesn’t have to worry about competitors -> set Q such that MC = MR

17 Monopolists, like all firms, should price to maximize profits.As a result, the demand curve and costs matter Monopolist doesn’t have to worry about competitors -> set Q such that MC = MR How to construct MR? To sell another unit, must lower the price so firm loses money on units they were selling (intensive margin) and gains money from additional units sold (extensive margin) MR = extensive gains – intensive losses

18 Monopolist’s math max 𝑞 𝜋 𝑞 =𝑃 𝑞 𝑞 −𝑇𝐶(𝑞)f.o.c.: 𝑃 ′ 𝑞 ∗ 𝑞 ∗ +𝑃 𝑞 ∗ −𝑇 𝐶 ′ 𝑞 ∗ =0 Maximizes profits (TR – TC) by setting a quantity and charging needed price to have market clear e.g., price is a function of quantity: P(q) and note the TR = P(q)*q 𝑃 ′ 𝑞 ∗ 𝑞 ∗ +𝑃 𝑞 ∗ −𝑀𝐶 𝑞 ∗ =0 𝑃 ′ 𝑞 ∗ 𝑞 ∗ +𝑃 𝑞 ∗ =𝑀𝐶 𝑞 ∗ NOTE: P’(q) < 0 since demand slopes downward 𝑃 ′ 𝑞 ∗ 𝑞 ∗ Intensive margin loss as q increases 𝑃 𝑞 ∗ Extensive margin gain as q increases

19 Monopolist’s math 𝑃 ′ 𝑞 ∗ 𝑞 ∗ +𝑃 𝑞 ∗ =𝑀𝐶 𝑞 ∗𝑃 ′ 𝑞 ∗ 𝑞 ∗ +𝑃 𝑞 ∗ =𝑀𝐶 𝑞 ∗ Note that P’(q) is the slope of the demand curve and that economists think about elasticities rather than slopes. Assume MC(q) = c for simplicity (e.g., constant MC) Lerner Equation: If demand curve is relatively inelastic, charge a high markup. NOTE 1: Assume that elasticity is constant along all portions of the demand curve for convenience. NOTE 2: “Constant Elasticity” makes demand curve non- linear but a perfectly valid assumption. NOTE 3: 𝜖 refers to own price elasticity unless otherwise noted.

20 Monopolist’s math 𝑃 ′ 𝑞 ∗ 𝑞 ∗ +𝑃 𝑞 ∗ =𝑀𝐶 𝑞 ∗𝑃 ′ 𝑞 ∗ 𝑞 ∗ +𝑃 𝑞 ∗ =𝑀𝐶 𝑞 ∗ 𝑑𝑃( 𝑞 ∗ ) 𝑑𝑞 𝑞 ∗ +𝑃( 𝑞 ∗ )=𝑐 Note that P’(q) is the slope of the demand curve and that economists think about elasticities rather than slopes. Assume MC(q) = c for simplicity (e.g., constant MC) Lerner Equation: If demand curve is relatively inelastic, charge a high markup. NOTE 1: Assume that elasticity is constant along all portions of the demand curve for convenience. NOTE 2: “Constant Elasticity” makes demand curve non- linear but a perfectly valid assumption. NOTE 3: 𝜖 refers to own price elasticity unless otherwise noted. 𝑃( 𝑞 ∗ )−𝑐=− 𝑑𝑃( 𝑞 ∗ ) 𝑑𝑞 𝑞 ∗ Divide both sides by P 𝑃( 𝑞 ∗ )−𝑐 𝑃( 𝑞 ∗ ) =− 𝑑𝑃( 𝑞 ∗ ) 𝑑𝑞 𝑞 𝑃( 𝑞 ∗ )

21 Monopolist’s math 𝑃 ′ 𝑞 ∗ 𝑞 ∗ +𝑃 𝑞 ∗ =𝑀𝐶 𝑞 ∗𝑃 ′ 𝑞 ∗ 𝑞 ∗ +𝑃 𝑞 ∗ =𝑀𝐶 𝑞 ∗ 𝑑𝑃( 𝑞 ∗ ) 𝑑𝑞 𝑞 ∗ +𝑃( 𝑞 ∗ )=𝑐 Note that P’(q) is the slope of the demand curve and that economists think about elasticities rather than slopes. Assume MC(q) = c for simplicity (e.g., constant MC) Lerner Equation: If demand curve is relatively inelastic, charge a high markup. NOTE 1: Assume that elasticity is constant along all portions of the demand curve for convenience. NOTE 2: “Constant Elasticity” makes demand curve non- linear but a perfectly valid assumption. NOTE 3: 𝜖 refers to own price elasticity unless otherwise noted. 𝑃( 𝑞 ∗ )−𝑐=− 𝑑𝑃( 𝑞 ∗ ) 𝑑𝑞 𝑞 ∗ Divide both sides by P 𝑃( 𝑞 ∗ )−𝑐 𝑃( 𝑞 ∗ ) =− 𝑑𝑃( 𝑞 ∗ ) 𝑑𝑞 𝑞 𝑃( 𝑞 ∗ ) 𝑃( 𝑞 ∗ )−𝑐 𝑃( 𝑞 ∗ ) =− 𝑑𝑃( 𝑞 ∗ ) 𝑃( 𝑞 ∗ ) 𝑑𝑞 𝑞 =− % Δ𝑃 % Δ𝑞 =− 1 % Δ𝑞 % Δ𝑃 =− 1 𝜖 𝑷( 𝒒 ∗ )−𝒄 𝑷( 𝒒 ∗ ) =− 𝟏 𝝐

22 qm p q D MC qc Monopoly Profits Dead Weight Loss MR pm

23 Choosing Quantity Marginal Revenue, the increment to revenue from a increase in quantity sold Elasticity of demand: tells you the % change in quantity for a 1% change in price 𝜖=− %Δ𝑞 %Δ𝑝 =− 𝑑𝑞 𝑞 𝑑𝑝 𝑝 =− 𝑑𝑞 𝑑𝑝 𝑝 𝑞 =− 1 𝑝′(𝑞) 𝑝 𝑞

24 Examining the elasticity functionThe demand curve. Gives the price as function of q. 𝜖=− 1 𝑝 ′ 𝑞 𝑝(𝑞) 𝑞 First derivative of the demand curve. At any point 𝑞 0 it gives the slope at that point. Relative levels of price and quantity

25 Special case: linear demandAt high prices, q is low. A 1% change in p is relatively large, especially compared to quantity. Elasticities will be relatively large. 𝜖=− 1 𝑠𝑙𝑜𝑝𝑒 𝑝(𝑞) 𝑞 First derivative is constant At low prices, p will be small and q is large. Elasticities will mechanically be low. NOTE: This is about within a demand curve. We generally talk about demand for a product generally.

26 Some general facts about elasticityAt high prices, a fixed % change in price is larger in level terms. Since q will tend to small, a given level change in q, will be a larger in percentage terms. This creates a relationship such that elasticities will tend to be high at the “top of the demand curve” and low at the bottom. When we think of “small changes” in price, the impact of raising and lowering will be symmetric. However, for larger changes, e.g. 10%, an increase and decrease need to have the same magnitude impact

27 Elasticity and total revenueTotal revenue (TR) = p(q)*q Product Rule Algebra Substituting in Translating to calculus Negative of this is elasticity

28 Elasticity and total revenueTotal revenue (TR) = p(q)*q One minus the elasticity translates a price increase in percent to a revenue increase. For example, if the elasticity is 3.5, a 1% price increase causes a -2.5% impact on revenue (a loss).

29 Elasticity and total revenueElasticity = 1  small changes in price do not impact revenue Elasticity < 1  price drops lower revenue, price increases raise revenue Elasticity>1  price drops raise revenue

30 Inverse Elasticity RuleProfit Max (MR=MC) 𝑝− 𝑐 ′ 𝑞 =−𝑞 𝑝 ′ 𝑞 𝑝−𝑐′(𝑞) 𝑝 =− 𝑞 𝑝 𝑝 ′ 𝑞 = 1 𝜖 MR MC Necessarily elasticity > 1 Markup formula widely abused as a pricing strategy Price-cost margin AKA Lerner index

31 Inverse Elasticity RuleMR MC Profit Max (MR=MC) Price-cost margin (Lerner index) = 1 over elasticity Price minus marginal costs divided by price is referred to as gross margin. Necessarily elasticity > 1 Markup formula widely abused as a pricing strategy Price-cost margin AKA Lerner index

32 Inverse Elasticity RuleSuppose MC=0. Then quantity is chosen so that elasticity is 1. Intuition: if marginal costs are zero, then optimize for revenue. Total revenue grows until elasticity = 1. If MC>0, one will “stop” before reaching elasticity = 1. Necessarily elasticity > 1 Markup formula widely abused as a pricing strategy Price-cost margin AKA Lerner index

33 qm p q D MC qc Monopoly Profits Dead Weight Loss MR pm

34 Digression on Margin FormulaPerfect competition says price=MC, or zero markup, which implies elasticity of infinity. In other words, by deviating from market price I can sell all my units. What are some examples where this is approximately true in practice? In general MC will depend on price. Cannot in general say “what are my marginal costs” to get optimal mark up

35 Markup formula cont. 𝑝= 𝜖 𝜖−1 𝑐 ′ 𝑞𝑝= 𝜖 𝜖−1 𝑐 ′ 𝑞 Seems to say “fixed markup on marginal costs”, but elasticity will depend on the demand function, so will not be fixed across a firm’s products and across customers. Optimal pricing is much more complicated than a fixed markup

36 Markup formula cont. Does not capture competitor reactions𝑝= 𝜖 𝜖−1 𝑐 ′ 𝑞 Markup > 1 Elasticity will generally depend on q, costs depend on q With constant elasticity, firm passes on more than 100% of cost or tax (a tax is like a marginal cost, firm “marks up the tax”) Works at firm level, with elasticity measured at firm, not industry Does not capture competitor reactions

37 Monopoly Pricing FormulaPrices depends on elasticity, which depends on the product, customer characteristics Offer discounts to elastic (price sensitive) customers Discounts offered on basis of factors correlated with price sensitivity Pricing can often be understood by how decision variables correlate with price sensitivity Can be converted into a markup formula Often used to justify a “constant markup” policy but it doesn’t justify that, since elasticity changes from market to market In markets with less elastic demand, price higher. This is known as price discrimination

38 Pricing Multiple Goods

39 Basic idea One firm selling multiple goodsA firm’s goods will, in general, “compete with each other” to some degree A rational firm takes this into account when setting price. Optimal price will depend on own price elasticity (what we just learned about) and cross price elasticities

40 Review: substitutes and complementsPricing Related Goods Price of Complement Sales of Good Complements and Substitute Products (Relationship) Sales of a good rise when the price of a complement falls Console and games Drinks and food at a restaurant (e.g. happy hour to attract customers) Sales of a good fall when the price of a substitute falls Games vs. other games Food at a restaurant Lower price of substitute cannibalizes demand from other product Lower price of complement promotes sales of other product Prices of substitutes (complements) are higher (lower) than standalone profit-maximizing prices Price of Substitute Sales of Good

41 Inverse Elasticity Rule 2Suppose we sell n goods indexed i=1,…,n Demands xi(p) Profit If we assume constant marginal cost, this simplification is an example of selling the same good in multiple markets or to multiple customer “types” Cross-price elasticity Note no minus sign. Positive  substitutes; Negative  complements

42 Representative Consumer AssumptionIf there is a representative consumer maximizing utility: max u(x)-px, so Thus there are symmetric cross-derivatives From the total derivative of FOC This rule need not hold in practice, but is a commonly made assumption Recall this rule from multivariate calculus

43 In Matrix Notation 0 = 1 + E L, and thus L = - E-1 1Price cost margin: Vector of ones, vector of inverse elasticities 0 = 1 + E L, and thus L = - E-1 1

44 Two Good Formula L = - E-1 1 yieldsRule for inverting a 2x2 matrix L = - E-1 1 yields 𝑳 𝟏 𝑳 𝟐 = 𝒆 𝟏𝟏 𝒆 𝟏𝟐 𝒆 𝟐𝟏 𝒆 𝟐𝟐 −𝟏 𝟏 𝟏 𝑳 𝟏 =− 𝒆 𝟐𝟐 − 𝒆 𝟏𝟐 𝒆 𝟏𝟏 𝒆 𝟐𝟐 − 𝒆 𝟏𝟐 𝒆 𝟐𝟏 = 𝟏− 𝒆 𝟏𝟐 𝒆 𝟐𝟐 𝒆 𝟏𝟏 − 𝒆 𝟏𝟐 𝒆 𝟐𝟏 𝒆 𝟐𝟐 =− 𝟏− 𝒆 𝟏𝟐 𝒆 𝟐𝟐 𝒆 𝟏𝟏 𝟏− 𝒆 𝟏𝟐 𝒆 𝟐𝟏 𝒆 𝟐𝟐 𝒆 𝟏𝟏 =− 𝟏 𝒆 𝟏𝟏 𝟏− 𝒆 𝟏𝟐 𝒆 𝟐𝟐 𝟏− 𝒆 𝟏𝟐 𝒆 𝟐𝟏 𝒆 𝟐𝟐 𝒆 𝟏𝟏 Divide top and bottom by 𝒆 𝟐𝟐 Factor out 𝒆 𝟏𝟏 Multiply top and bottom by 𝒆 𝟏𝟏

45 Two Good Formula L = - E-1 1 yields𝒆 𝟏𝟐 𝒆 𝟐𝟏 𝒆 𝟐𝟐 𝒆 𝟏𝟏 will be between 0 and 1 because 𝒆 𝟏𝟐 𝒆 𝟐𝟏 < 𝒆 𝟐𝟐 𝒆 𝟏𝟏 This is because cross price elasticities have to be smaller than the relevant own price elasticities.

46 Two Good Formula L = - E-1 1 yields=− 𝟏 𝒆 𝟏𝟏 𝟏− + − 𝟏− ++ −− =− 𝟏 𝒆 𝟏𝟏 >𝟏 𝟎−𝟏 Markup rise if goods are substitutes

47 Two Good Formula for SubstitutesL = - E-1 1 yields L 𝟏 =− 𝟏 𝒆 𝟏𝟏 𝟏− 𝒆 𝟏𝟐 𝒆 𝟐𝟐 𝟏− 𝒆 𝟏𝟐 𝒆 𝟐𝟏 𝒆 𝟐𝟐 𝒆 𝟏𝟏 =− 𝟏 𝒆 𝟏𝟏 𝟏− + − 𝟏− ++ −− =− 𝟏 𝒆 𝟏𝟏 >𝟏 𝟎−𝟏 Is positive for substitutes Markup rises

48 Two Good Formula for SubstitutesL = - E-1 1 yields L 𝟏 =− 𝟏 𝒆 𝟏𝟏 𝟏− 𝒆 𝟏𝟐 𝒆 𝟐𝟐 𝟏− 𝒆 𝟏𝟐 𝒆 𝟐𝟏 𝒆 𝟐𝟐 𝒆 𝟏𝟏 Is positive for substitutes Markup rises because firm “is competing with itself”, lowering the incentive to drop prices. Effect is larger when cross price elasticities are larger and own price elasticity of the “good 2” is smaller. Intuition: when own price elasticity of good 2 is relatively small (close to 1), I have lots of pricing power on that good. If the cross price elasticity is relatively high, then lowering the price of good 1 cannibalizes lots of sales that would have been high profit.

49 Two Good Formula for ComplementsIs negative for complements, so markup goes down L = - E-1 1 yields L 𝟏 =− 𝟏 𝒆 𝟏𝟏 𝟏− 𝒆 𝟏𝟐 − 𝟎−𝟏 Markup goes down because products “help each other”. Effect is larger when cross price elasticities (can give more help) are larger and own price elasticity of the “good 2” is smaller (meaning dropping the other price is a relatively efficient way to help). Intuition: when own price elasticity of good 2 is relatively small (close to 1), I have lots of pricing power on that good. If I can drop price of good 1 to help that good, I get lots of benefit from doing so due the high margins on good 2.

50 Two Good Formula ReviewL = - E-1 1 yields =− 𝟏 𝒆 𝟏𝟏 𝟏− 𝒆 𝟏𝟐 𝒆 𝟐𝟐 𝟏− 𝒆 𝟏𝟐 𝒆 𝟐𝟏 𝒆 𝟐𝟐 𝒆 𝟏𝟏 𝒆 𝟏𝟐 >𝟎, goods are substitutes. A price decrease on product 2 decreases sales on product 1 (go in same direction) 𝒆 𝟏𝟐 <𝟎, goods are complements. A price decrease on product 2 increases sales on product 1 (go in opposite directions) 𝒆 𝟏𝟏 & 𝒆 𝟐𝟐 will be negative due to law of demand (note before we “embedded the negative sign)

51 Bundling Pure bundling: only sell the bundleCars & tires Cable TV Cars + feature “models” Mixed bundling: sell separately with a discount for bundle Video games w/ console Sports passes (clubs, ski resorts)

52 Enormous Bundle

53 Utilities with Independent ValuesAction Utility Buy Nothing Buy Good 1 v1 – p1 Buy Good 2 v2 – p2 Buy Both v1+v2 – pB

54 Buy Good 2 Buy Both Buy Nothing Buy Good 1pB p2 p1 v1 v2 Buy Both Buy Good 1 Buy Good 2 Buy Nothing Buy neither, but would buy a bundle. Starting from the top right of the square, there is always some bundle I want to offer

55 Buy Good 2 Buy Both Buy Nothing Buy Good 1v2 If p2 optimal, this price reduction doesn’t affect profits – sales gains just balance price cut pB Buy Good 2 Buy Both p2 Buy Nothing Buy Good 1 v1 p1

56 Buy Good 2 Buy Both Buy Nothing Buy Good 1v2 pB Buy Good 2 If p1 optimal, this price reduction doesn’t affect profits – sales gains just balance price cut Buy Both p2 Buy Nothing Buy Good 1 v1 p1

57 Buy Good 2 Buy Both Buy Nothing Buy Good 1v2 pB Buy Good 2 Reducing bundle price gives the additional sales of both goods with a single price cut Buy Both p2 Buy Nothing Buy Good 1 v1 p1

58 Conceptualizing bundlesA bundle can be thought of as a “conditional discount”. E.g. If you buy good 1, I’ll give you a discount on good 2. This lets me give “targeted offers” Especially powerful when my valuation of good 2 is much lower if I already have good 1. E.g. gym memberships bundle many partner locations for a small increase in price because otherwise people would rarely buy more than 1.

59 Bundling as a part of corporate strategyRethink Product Jack Walsh noticed GE made more profit on engine service than aircraft engines Redefined product: sell engines in order to sell service Rather than selling service to make engines more attractive Very profitable IBM pivoted from providing software and services to sell hardware IBM Global Services Hardware margins typically low except Apple

60 Bundling Insights Mixed bundling is always more profitable than no bundling With independent or negatively correlated goods Better for consumers as well! Often a “grand bundle” does well for firms, but can be bad for consumers Skims out the most willing-to-pay with a “super good” Bundles can be used to help customers