ECON 4100 Industrial Organization Lecture 7 Product variety

ECON 4100 Industrial Organization Lecture 7 Product variety, price discrimination and spatial models 1

Introduction • • • introduction to multiproduct firms product homogeneity and product variety net prices, screening and consumer identification vertical versus horizontal price differentiation spatial model of price differentiation (Hotelling) monopoly pricing in the spatial model without price discrimination 2 4 -1

Introduction • A monopolist can offer goods of different varieties – multiproduct firms • The “big” issues: – pricing – product variety: how many? – product bundling: • how to bundle • how to price • whether to tie the sales of one product to sales of another • Price discrimination 3 4 -1

Price Discrimination • This is a natural phenomenon with multiproduct firms – restaurant meals: you can eat the menu of the day or à la carte – different varieties of the same car (now you can build and customize your own car, we will se more about flexible technologies) – airline travel • “goods” of different quality are offered at very different prices • Note the constraints – arbitrage • ensuring that consumers buy the “appropriate” good – identification • How to price goods of different quality? 4

Price discrimination and quality • Extract all consumer surplus from the low quality good • Use screening devices – Set the prices of higher quality goods • to meet incentive compatibility constraint • to meet the constraint that higher price is justified by higher quality 5

Price discrimination and quality • One interesting type of screening: crimping the product – In May 1990 IBM introduced the Laser. Printer E, an inexpensive alternative to its very popular and successful Laser. Printer. The Laser. Printer E was virtually identical to the original Laser. Printer, except that the E model printed text at 5 pages per minute (ppm), while the Laser. Printer could reach 10 ppm. The slower performance of the Laser. Printer E was accomplished by adding five chips to the E model. 6

Price discrimination and quality • One interesting type of screening: crimping the product – offer a product of reasonably high quality – produce lower quality by damaging the higher quality good • • student version of Mathematica, different versions of Vensim etc the “slow” 486 SX produced by damaging the higher speed 486 DX Is the post office deliberately slow with the regular mail? Third-class coaches used to be made uncomfortable on purpose!!! – why? • for cost reasons: it must be cheaper to keep one line of production for the high-quality good and then crimp the low-price good 7

Price discrimination and quality In addition to providing a justification for the price differential, crimping also prevents arbitrage that might erode the gains from price discrimination in the first place. 8

A Spatial Approach to Product Variety • Approach to product quality in Chapter 3 is an example of vertical product differentiation – products differ in quality – consumers have similar attitudes to quality: value high quality – But they might have different willingness to pay for the extra quality • An alternative approach – consumers differ in their tastes – firm has to decide how best to serve different types of consumer – offer products with different characteristics but similar qualities • This is horizontal product differentiation 9

A Spatial Approach to Product Variety (cont. ) • The spatial model (Hotelling) is useful to consider – pricing – design – variety • Has a much richer application as a model of product differentiation – location can be thought of in • space (geography) • time (departure times of planes, buses, trains) • product characteristics (design and variety) 10

A Spatial Approach to Product Variety (cont. ) • Assume N consumers living equally spaced along Main Street – 1 mile long. • Monopolist must decide how best to supply these consumers • Consumers buy exactly one unit provided that price plus transport costs (full price) is less than V (reservation price) • Consumers incur there-and-back transport costs of $t per unit • If the monopolist operates one shop – reasonable to expect that this is located at the center of Main Street, why? (relate to TV programming or radio content) 11

The spatial model Price Suppose that the monopolist Price p sets a price of p 1 + t. x 1 p 1 + t. x V V All consumers within distance x 1 to the left and right of the shop will by the product x=0 t x 1 t p 1 1/2 What determines x 1? x 1 x=1 Shop 1 + t. x 1 = V, so x 1 = (V – p 1)/t 12

The spatial model Price p 1 + t. x Suppose the firm reduces the price to p 2? V Then all consumers within distance x 2 of the shop will buy from the firm x=0 Price V p 1 p 2 x 1 1/2 x 1 x 2 x=1 Shop 1 13

The spatial model • Suppose that all consumers are to be served at the same price p – The highest price is that price charged to the consumers at the ends of the market – Their transport costs are t/2 : since they travel ½ mile to the shop – So they pay p + t/2 which must be no greater than V – So p = V – t/2. • Suppose that marginal costs are c per unit. • Suppose also that a shop has set-up costs of F. • Then profit is p(N, 1) = N(V – t/2 – c) – F. 14

Monopoly Pricing in the Spatial Model • What if there are two shops? • The monopolist will coordinate prices at the two shops • With identical costs and symmetric locations, these prices will be equal: p 1 = p 2 = p – Where should they be located? – What is the optimal price p*? 15

Location with Two Shops Suppose that the entire market is Price If there are two shops they will be located V symmetrically a distance d from the The maximum price p(d) end-points of the firm can charge market is determined by the Now raise the price consumers at the at each shop Start with market center of the a low price at each shop Suppose that d < 1/4 x=0 Delivered price to consumers at to be served the market center equals their reservation price Price V p(d) What determines p(d)? d Shop 1 1/2 1 -d Shop 2 x=1 The shops should be moved inwards 16

Delivered Shops Location with Twoprice to consumers at the end-points equals their reservation price The maximum price the firm can charge is now determined by the consumers at the end-points of the market Price V V p(d) Now raise the price at each shop Start with a low price at each shop Now what determines p(d)? x=0 Now suppose that d > 1/4 d Shop 1 1/2 1 -d Shop 2 x=1 The shops should be moved outwards 17

It follows that shop 1 should be located at 1/4 and shop 2 at 3/4 Location with Two Shops Price at each shop is then p* = V - t/4 Price V V V - t/4 Profit at each shop is given by the shaded area c c x=0 1/4 Shop 1 1/2 3/4 Shop 2 x=1 Profit is now p(N, 2) = N(V - t/4 - c) – 2 F 18

Three Shops What if there are three shops? Price at each shop is now V - t/6 By the same argument they should be located at 1/6, 1/2 and 5/6 Price V V V - t/6 x=0 V - t/6 1/6 Shop 1 1/2 Shop 2 5/6 x=1 Shop 3 Profit is now p(N, 3) = N(V - t/6 - c) – 3 F 19

Optimal Number of Shops • A consistent pattern is emerging. Assume that there are n shops. They will be symmetrically located distance 1/n apart. We have already considered n = 2 and n = 3. How many shops should When n = 2 we have p(N, 2) = V - t/4 there be? When n = 3 we have p(N, 3) = V - t/6 It follows that p(N, n) = V - t/2 n Aggregate profit is then p(N, n) = N(V - t/2 n - c) – n. F 20

Optimal number of shops (cont. ) Profit from n shops is: and the profit from having n + 1 shops is: Adding the (n +1)th shop is profitable if p(N, n+1) - p(N, n) > 0 This requires which requires that n(n + 1) < t. N/2 F 21

An example Suppose that F = $50, 000 , N = 5 million and t = $1 Then t. N/2 F = 50 So we need n(n + 1) < 50. This gives n = 6 There should be no more than seven shops in this case: if n = 6 then adding one more shop is profitable. But if n = 7 then adding another shop is unprofitable. 22

Some Intuition • What does the condition on n tell us? • Simply, we should expect to find greater product variety when: • there are many consumers • set-up costs of increasing product variety are low • consumers have strong preferences over product characteristics and differ in these. 23

Some Intuition • there are many consumers (there should be more cinemas restaurants shops etc in Toronto than in Carbonnear). Shopping is cooler there too. In Carbonnear there is just not enough choice (variety) • set-up costs of increasing product variety are low (there are 3 Tim Hortons here, only one Raymond’s). • consumers have strong preferences over product characteristics and differ in these. (Again people drive more often to buy donuts, while they need only one jewelry in town; you will see varieties of food for diabetics, for people on a diet, etc, they face a high t, a high transportation cost to the desired variety) 24

Do we want to serve the whole market? ? ? • Or is this assumption too strong? 25

How Much of the Market to Supply • Should the whole market be served? – Suppose not… Then each shop has a local monopoly – Each shop sells to consumers within distance r – How is r determined? • it must be that p + tr = V so r = (V – p)/t • We supply a fraction r of the whole 2 N consumers (2 left and right and N consumers evenly distributed along the street) • so total demand is 2 N(V – p)/t • profit to each shop is then p = 2 N(p – c)(V – p)/t – F • differentiate with respect to p and set to zero: • dp/dp = 2 N(V – 2 p + c)/t = 0 – So the optimal price at each shop is p* = (V + c)/2 – If all consumers are to be served then price is p(N, n) = V – t/2 n 26

Partial Market Supply • Only part of the market should be served if p(N, n) > p* • This implies that V > c + t/n. • If c + t/n > V supply only part of the market and set price p* = (V + c)/2 • If c + t/n < V supply the whole market and set price p(N, n) = V – t/2 n • Supply only part of the market: – if the consumer reservation price $V is low relative to marginal production costs and transport costs – if there are very few outlets – But if the consumer’s $V is high relative to transportation costs and production costs and it is cheap to open many stores (the optimal number of n is high) then you probably want to serve the entire market 27

Are there too many shops or What number of shops maximizes total surplus? too few? Social Optimum Total surplus is consumer surplus profit Consumer surplus is total willingness to pay minus total revenue Profit is total revenue minus total cost Total surplus is then total willingness to pay minus total costs Total willingness to pay by consumers is N. V if the whole market is served. That will be NV regardless of number of shops. Total variable cost is given too, regardless of the number of shops. Total surplus is therefore N. V - Total Cost So what is Total Cost? 28

Social Optimum Are there too many shops or too few? Total willingness to pay by consumers is N. V if the whole market is served. That will be NV regardless of number of shops. Total variable cost is given too, regardless of the number of shops. Total surplus is therefore N. V - Total Cost So what is Total Cost? The number of shops changes the total transportation costs and the total setup costs The question is then: will the monopolist minimize the sum of set up and transportation costs or not? 29

Assume that there are n shops Social optimum (cont. ) Price V Consider shop i Total cost is total transport cost plus set-up costs t/2 n x=0 t/2 n 1/2 n Shop i V Transport cost for each shop is the area of these two triangles multiplied by consumer density x=1 This area is t/4 n 2 30

Social optimum (cont. ) Total cost with n shops is, therefore: C(N, n) = n(t/4 n 2)N + n. F = t. N/4 n + n. F If t = $1, F = $50, 000, Total cost with n + 1 shops is: C(N, n+1) = t. N/4(n+1)+fivethis. F There 5 should be (n+1) N = million then shops: with. C(N, n adding C(N, n) n = 4 + 1) < another Adding another shop is socially efficient ifcondition tells us shop is efficient that n(n+1) < 25 This requires that t. N/4 n - t. N/4(n+1) > F which implies that n(n + 1) < t. N/4 F The monopolist operates too many shops and, more generally, provides too much product variety 31

Social optimum (cont. ) The monopolist will try to convince you that you really need to choose the type of organic experience that is right for you, I mean… It is no longer good enough to buy old boring “shampoo”! You need to define who you are and what your objective in life is by… Choosing the right variety of toothpaste for example The monopolist will try to increase t for consumers!!! Make the street more difficult to walk They will persuade you that the standard Grand Cherokee is the most uncool you can buy!!! You really have to customize yours! 32

Social optimum (cont. ) We will use these insights again when we consider the case of oligopolies later in the course But now we will look at the case when the multiproduct monopolist will discriminate by means other than having different customers pay different full (including transport costs) prices 33

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Product variety (cont. ) d < 1/4 We know that p(d) satisfies the following constraint: p(d) + t(1/2 - d) = V This gives: p(d) = V - t/2 + t d Aggregate profit is then: p(d) = (p(d) - c)N = (V - t/2 + t. d - c)N This is increasing in d so if d < 1/4 then d should be increased. 35

Product variety (cont. ) d > 1/4 We now know that p(d) satisfies the following constraint: p(d) + td = V This gives: p(d) = V - td Aggregate profit is then: p(d) = [p(d) – c] N = (V - t. d - c)N This is decreasing in d so if d > 1/4 then d should be decreased. 36