Product differentiation and mergers ECON 4100: Industrial Organization Lecture 15 add-on Product differentiation and mergers

Introduction Product differentiation and mergers The spatial model…again Add price discrimination

Product Differentiation and Merger The discussion so far has assumed that products are identical It can be extended to differentiated products: suppose demand is of the form: q1 = A - Bp1 + C(p2 + p3 +…+ pn) and similarly for the other products Now a merger allows coordination of the outputs of the different products but the merger does not lead to one of the products being eliminated

An Example of Product Differentiation QC = 63.42 - 3.98PC + 2.25PP MCC = $4.96 QP = 49.52 - 5.48PP + 1.40PC MCP = $3.96 This example can be generalized to more than two products

Product differentiation Take a different approach spatial model of product differentiation The idea is simple suppose firms are offering different varieties of a product the analogy is that these products have different “locations” then merger between some of these firms avoids some of the problems of the merger paradox don’t have to close down particular locations but can coordinate prices and, perhaps, locations Many mergers “look like” this join product lines that compete but do not perfectly overlap

The Spatial Model The model is as follows a market called Main Circle of length L consumers uniformly distributed over this market supplied by firms located along the street the firms are competitors: fixed costs F, zero marginal cost each consumer buys exactly one unit of the good provided that its full price is less than V consumers incur transport costs of t per unit distance in travelling to a firm a consumer buys from the firm offering the lowest full price What prices will the firms charge? To see what is happening consider two representative firms

The spatial model illustrated Assume that firm 1 sets price p1 and firm 2 sets price p2 What if firm 1 raises its price? Price Price p’1 p2 p1 xm x’m Firm 1 All consumers to the left of xm buy from firm 1 xm moves to the left: some consumers switch to firm 2 Firm 2 And all consumers to the right buy from firm 2

The Spatial Model Suppose that there are five firms evenly distributed 1  these firms will split the market r12 r51  we can then calculate the Nash equilibrium prices each firm will charge 2 5  each firm will charge a price of p* = tL/5 r45 r23  profit of each firm is then tL2/25 - F 4 3 r34

Merger of Differentiated Products A merger of firms 2 and 4 does nothing  now consider a merger between some of these firms A merger of firms 2 and 3 does something Price  a merger of non-neighboring firms has no effect  but a merger of neighboring firms changes the equilibrium r51 1 r12 2 r23 3 r34 4 r45 5 r51 Main Circle (flattened)

Merger of Differentiated Products  merger of 2 and 3 induces them to raise their prices Price  so the other firms also increase their prices  the merged firms lose some market share, but less when the surrounding firms increase their prices  what happens to profits? r51 1 r12 2 r23 3 r34 4 r45 5 r51 Main Circle (flattened)

Spatial Merger (cont.)  The impact of the merger on prices and profits is as follows Pre-Merger Post-Merger Price Profit Price Profit tL/5 tL2/25 1 1 14tL/60 49tL2/900 2 tL/5 tL2/25 2 19tL/60 361tL2/7200 3 tL/5 tL2/25 3 19tL/60 361tL2/7200 4 tL/5 tL2/25 4 14tL/60 49tL2/900 5 tL/5 tL2/25 5 13tL/60 169tL2/3600

Spatial Merger (cont.) This merger is profitable for the merged firms And it is not the best that they can do change the locations of the merged firms expect them to move “outwards”, retaining captive consumers perhaps change the number of firms: or products on offer expect some increase in variety

Spatial Merger (cont.) But consumers lose out from this type of merger all prices have increased For consumers to derive any benefits either increased product variety so that consumers are “closer” there are cost synergies not available to the non-merged firms e.g. if there are economies of scope Profitability comes from credible commitment

Spatial Merger (cont.) Profitability comes from credible commitment In the case with no product differentiation, we had to think of commitment in terms of output levels Now we only need to commit to a certain range of locations or varieties It is easier now to establish a credible commitment!!! Commitment in terms of output levels is less credible (unless we go back to ideas of capacity), because producing that high level of output is not the best Cournot response to an output decision by the other firms

Price Discrimination  What happens if the firms can price discriminate?  This leads to a dramatic change in the price equilibrium Price p1i  take two neighboring firms p1i+1  consider a consumer located at s p2i  suppose firm i sets price p1i p*i(s)  i+1 can undercut with price p1i+1  i can undercut with price p2i  and so on  i wins this competition by “just” undercutting i+1’s cost of supplying s t t  the same thing happens at every consumer location i s i+1 Firm i supplies these consumers and firm i+1 these consumers  equilibrium prices are illustrated by the bold lines

Merger with price discrimination This is much better for consumers than no price discrimination Merger with price discrimination Price equilibrium pre-merger is given by the bold lines Profit for each firm is given by the shaded areas  Start with a no-merger equilibrium 1 2 3 4

Interestingly, the highest pre-delivery price that the consumers pay now is the lowest price they paid with no price-discrimination (tL/5) Price-discrimination benefits consumers. Why? With no price-discrimination, if you reduce the price for one consumer you have to reduce it for all With price-discrimination you can reduce the price in one location (shop, or variety) without reducing it in others This will make it less credible for you to commit to high prices Therefore price competition between firms will be fiercer And consumers benefit 

Merger with price discrimination This is beneficial for (only ) the merged firms but harms consumers Merger with price discrimination  Now suppose that firms 2 and 3 merge Prices to the captive consumers between 2 and 3 increase  They no longer compete in prices so the price equilibrium changes Profits to the merged firms increase 1 2 3 4

Next  Vertical and Complementary Mergers