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# Product Differentiation

Product Differentiation. Horizontal product differentiation: Consumers have different preferences along one dimension of a good. Example: some consumers prefer hot salsa, some prefer mild.

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## Product Differentiation

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1. Product Differentiation • Horizontal product differentiation: Consumers have different preferences along one dimension of a good. • Example: some consumers prefer hot salsa, some prefer mild. • Vertical product differentiation: Consumers have the same ordinal preferences, but not the same cardinal preferences. • Example: all consumers prefer better fuel efficiency, but their willingness to pay will differ.

2. Product Differentiation as a Competitive Strategy • Firms seek to be unique along some dimension that is valued by consumers. • Differentiation can be based on the product itself, the delivery system, or the marketing approach. • If the firm/product is unique in some respect, the firm can command a price greater than cost.

3. Price Competition and Product Differentiation • Model of Bertrand competition combined with “location” choice • Firms choose “location” along a spectrum • Can think of this as the same product in different location, or • Can think of this as different products

4. Chili Peppers -- Hotness measured in Scoville Units* Habanero = 100K Sweet Italian = 0 Cayenne = 30K Jalapeno = 2.5K Thai = 50K *Source: http://www.cybersauce.com/knowldge.htm#scoville

5. Firm A at location 0 Firm B at location 1 0 1 • Assumptions on firms in the model • Both firms have the same marginal cost, c • Each firm located at a specific point of the spectrum • Firms set prices pA and pB

6. Firm A at location 0 Firm B at location 1 0 X 1 • Assumptions on consumers in the model • Each consumer has a gross value for the good, V • Consumers buy from firm that provides highest net value • Each consumer located at certain point on the spectrum • Consumer must transport the good from firm • Net value = V - p - t*(distance between firm & consumer) • Will not purchase if net value < 0

7. Firm A at location 0 Firm B at location 1 0 X 1 • Example • Consumer at X compares net value from each firm • If [V - pA - tX] > [V - pB - t(1-X) ], buy from firm A • Rearrange to get: pB - t(2X-1) > pA • So, if X  .5, pA must be less than pB • If X < .5, pA can be higher than pB

8. Z Firm A at location 0 Firm B at location 1 0 X 1 • Nash Equilibrium • Look for NE where all consumers buy (requires a high V) • Step 1: Figure out each firm’s profit • First, need to get a handle on demand • If person at X buys from A, so will everyone to his left • Find consumer, Z, who is indifferent between A and B • Then demand for A = ZN and for B = (1-Z)N • (N = size of market)

9. Z Firm A at location 0 Firm B at location 1 0 1 • Nash Equilibrium, con’t • Find Z so that: [V - pA - tZ] = [V - pB - t(1-Z)] • This simplifies to: pA + tZ = pB + t(1-Z) • Or: Z = (pB - pA + t)/2t • Then demand of firm A = ZN = N(pB - pA + t)/2t • And profit of A = (pA- c)*N(pB - pA + t)/2t • By symmetry, profit of B = (pB- c)*N(pA - pB + t)/2t)

10. Z Firm A at location 0 Firm B at location 1 0 1 • Nash Equilibrium, con’t • Next step: Derive Best Response • Take derivative of profit w.r.t. Price • Profit of A = (pA- c)*N(pB - pA + t)/2t • Or: N/2t*(pApB - pA2 + pAt - c pB + c pA - ct ) • So derivative = N/2t*(pB - 2pA + t + c) • Set = 0: N/2t*(pB - 2pA + t + c) = 0 • Solve: pA = (pB + t + c)/2

11. Z Firm A at location 0 Firm B at location 1 0 1 • Nash Equilibrium, con’t • Final step: Use BR’s to find NE • BR for firm A: pA = (pB + t + c)/2 • By symmetry, BR for firm B: pB = (pA + t + c)/2 • Substitute BR for firm B into BR for firm A: • pA = (pB+t+c)/2 = [(pA+t+c)/2+t+ c]/2 = pA/4+3t/4+3c/4 • 3/4 pA = 3/4[t + c] • So, pA* = t + c, and by symmetry pB* = t + c,

12. So..... • With differentiated products, Bertrand competition does not collapse to zero profits • Firms price above marginal cost and make profit • Note that the higher t is, the higher are prices and the more profit the firms make • t is a measure of the degree of product differentiation • Why? • Demand for each firm’s product is downward sloping: qA = a - bpA + dpb

13. Product Positioning • How do firms choose where to “position” their products? • Previous model explains competition once position determined, but position is not exogenous. • Two stage game: Position selected first, then price.

14. Product Positioning, con’t • The closer your product is to your competitor’s, for a given set of prices, the higher your demand will be, “the direct effect”. • The closer your product is to your competitor’s, the more intense will be price competition and thus the lower your demand will be, “the strategic effect”.

15. Firm A’s new location Firm A at location 0 Firm B at location 1 0 0.5 0.66 0.33 1 • The “Direct Effect” • Assume both firms set the same price • If located at either end of the spectrum, they split demand. • If firm A moves closer to Firm B, Firm A’s demand (and thus profit) will increase, assuming no change in price.

16. But if Firm A moves to 0.33, Firm B will also want to relocate to get closer to Firm A. • How do you find a NE in locations? It becomes very complicated. • If both locate in the same place, products are identical and competition drives price to MC so firms have an incentive to differentiate. • However both firms want to maximize demand and thus are driven towards the middle. • The end result depends on consumer’s value for the product, the “transportation costs” and the firms’ costs.

17. Search Costs • Consumers often lack information about a product’s characteristics or price related to the characteristics or price of other goods. • To gain information, the consumer must “search” i.e. incur a cost of acquiring the information. • Consumers should search as long as the benefit from search (increase in consumer surplus either because higher value product or lower price) is greater than the cost of search. • Firms can take advantage of the fact that consumers limit search and price above cost.

18. Switching Costs • Consumers often must incur a cost to switch from one product to another. • For example, changing word processing software or finding a new insurance company. • Consumers will only switch when the benefit (increase in CS from higher value product or lower price) is greater than the cost of switching. • Since consumers don’t switch instantaneously, firms may be able to price above cost. • Firms may lower switching costs to compete: • Example: Sprint will switch you for free.

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