There are two central issues when analysing product differentiation. The first is that the customer is always right. If goods are identical but customers believe them to be different, e.g. brand names and supermarket's own products then the products are differentiated. Also if the products are different and customers believe them to be the same then they are homogenous. Secondly the closer the substitutes the greater the constraint that it exerts on another through change of price. Essentially an industry is differentiated if customers care about which brands they buy, and this will be determined by a number of different reasons. In an industry with differentiated products the residual demand facing a product is determined by the supply of each of it's individual competitors. The residual demand that they are facing is given by:
Pi = D(q1, q2)
So the price charged by firm I is depends on the quantity it sells and the quantity sold by it's competitors. If products are differentiated then the above applies, if the products are perceived to be perfect substitutes then it can be simplified. This simple model all firms charge the same price as the consumer does not tolerate higher prices for one product and therefore the determining factor in price is total market output. So the demand curve for this is just:
Pi = P = D(q1 + q2) = D(Q)
If these two products are viewed as identical then the demand curve can be seen as:
P = a - bQ = a - b(q1 +q2) = a - bq1 - bq2
a and b are positive constraints. If products are viewed as imperfect substitutes then the firms demand curve will be:
P1 = a - b1q1 + b2q2
Where a > 0 and b1 - b2 > 0.
This means that an increase in firm 1's output has a greater effect on its price than firm 2's out put. The greater a firm succeeds in differentiating its product the less sensitive it becomes to the actions of other firms in the industry. A good example of this is a change in the quantity sold or price of Ford Escorts has little or no effect on the price or demand of a Ferrari. In perfectly competitive markets, there cannot be differentiated goods. A good example of this is the Credit Card industry that on the surface seems to be perfectly competitive, but subtle differences in the credit cards and the services offered mean that there are differentiated and the industry is far from perfectly competitive. Differentiated products can be in oligopolistic or monopolistic markets and if a firm produces such a product, it faces a downward sloping demand function. When considering a firm's price taking behaviour this is inconsistent, in fact the more differentiated a product becomes, the less close substitutes it has and therefore it gets closer to being a monopoly and therefore the greater the downward slope of the demand curve.
In general, brands with close substitutes compete more energetically than those with fewer substitutes or those that are more differentiated. Certain brands have certain characteristics that others do not e.g. free travel insurance on a credit card that American Express may have and a Visa card may not. Therefore, all credit cards that have this free travel insurance "characteristic" are a similar brand. It is possible, as a result, to "locate" each brand at a point in product characteristic space. You can also classify brands by location. Some people may have a credit card from the only bank that is located in their town. Further from this, if there are two banks then the two cards offered by them will be closer substitutes b nature of their location. Therefore, a firm can be located at a Particular point in product location space. These location models by their nature mean that it costs customers more to shop at stores further away from home or they derive less pleasure from products that deviate from their ideal. Each firm in these models have some market power as they only compete with firms that are "close" to them.
In 1929, Hotelling developed a model to explain the location and pricing behaviour of firms in geographic space. Hotelling's Linear City Model simplifies things by varying products in one dimension, this can be interpreted as geographical and firms are placed at an address on the line or it can be their location in characteristic space. In Hotelling's model, the locations of firms are represented on a line from 0 to 1 and two similar firms, a and b, are located on this line at set points. Consumers are uniformly located on this line. If each consumer buys one unit the good at price, P, then each consumer suffers a transportation cost of t, by unit of distance to get to one of the two shops.
Market for a Market for b
0 a b 1
If a is located a miles from the end of the line and b is located b miles from the other end of the line. If goods are homogenous then customers will buy the good from the closest store to them. Consumers will incur a transport cost of, t, per mile they have to travel. Therefore, consumers will buy from the cheapest store. There does exist a consumer Xm who is indifferent to either store.
U(Xm,a) = u(Xm,b) and
Xm = (a + b) / 2 + (Pb - Pa) / [2t(b - a)]
All other customers will pick the store closest to them. If prices are set then a game will be played about location. If store b is set in it's location then store a will locate just to the left of store b to capture the largest market possible.
Market for a Market for b
0 a b 1
If firm b could then relocate it would then relocate to the left of a, this process would then carry on until both firms were located in the centre of the line and shared the customers. There is a propensity for firms to locate close to each other, e.g. cash machines near an office building or in a shopping mall. The demands for the game are as follows:
Da(Pa,Pb) = 1 if (Pa,Pb) s.t. Xm > 1
= (a + b) / 2 + (Pb - Pa) / [2t (b - a)] if (Pa,Pb) s.t. Xm ? [0,1]
= 0 if (Pa,Pb) s.t. Xm < 0
Db(Pa,Pb) = 1 if (Pa,Pb) s.t. Xm > 1
= 1 - (a + b) / 2 + (Pb - Pa) / [2t (b - a)] if (Pa,Pb) s.t. Xm ? [0,1]
= 0 if (Pa,Pb) s.t. Xm < 0
With a given price, location is determinable and it is seen that, as shown below, the solution is a pure Nash equilibrium i.e. when equilibrium is set firms will not move. In addition, if location is set then firms will not vary their prices. This is similar to Bertrand equilibrium and Hotelling shows that Bertrand only holds when goods are homogenous. The general solution for the game is as follows:
The best result for firm a is: 0.5t (a + b) (b - a) + 0.5Pb
The best result for firm a is: 0.5t (2 - a - b) (b - a) + 0.5Pa
Therefore the Nash equilibrium: Pa = t (2 + a + b) (b - a) / 3
Pb = t (4 - a - b) (b - a) / 3
?a = t (b - a) (2 + a + b)2 / 18
?b = t (b - a) (4 - a - b) / 18
If the two firms are located a distance apart, then store a could charge less than b and b still could maintain a number of customers. This is because store b is so close for a number of customers that they can charge them more for the convenience and the customers will be willing to Pay. Bertrand equilibrium where P = MC only if products are located in the same place, in terms of location or characteristics. More generally, firms with Bertrand expectations can charge different prices (all satisfying P > MC) and still earn positive profits. Differentiation by location or characteristics gives firms market power. This is with the assumption that there are relocation costs that will be incurred, if it is costless it can be seen that firms may constantly change location and price and therefore never find equilibrium.
In 1978, Richard Schmalensee produced a Paper on the ready to eat breakfast cereal industry. It was well documented that consumers preferences for breakfast cereal are based on their characteristics e.g. taste, consistency, sugar on top etc. In 1972, the United States Federal Trade Commission (FTC) investigated the four largest cereal manufacturers for differentiating similar products and through brand proliferation barring entry to the industry. Each of these firms was located in their characteristic space and therefore must compete with rivals in that space. The company of that brand can, if it so desires, surround itself with other similar brands of it's own not its rivals. This forces one firm's brands to compete with each other. These other brands can be called defensive brands and these can bar entry to other firms into this space. In addition, it is possible for a number of brands to collude to create a number of brands that may not be profit maximising n a given space to again bar entry to other firms. The FTC eventually lost its case but it highlighted that the firms under investigation had managed to obtain 95% of the market share and shared approximately 80 similar brands. The FTC lost the case due to the entry of more 'healthy' cereal brands that gained 10% of the market share. This was because the previous monopoly where not located in this product space and therefore there were little or no barriers to entry into the industry through this location.
Product differentiation creates more market power for firms. A higher price can be charged if the perceived difference between two imperfect substitutes is greater. If free entry is allowed, then firms enter and price is driven down to marginal costs and therefore profits are zero. A monopolistic equilibrium is one where zero profits are earned and firms face a down ward sloping residual demand curve. Hotelling's model shows us that consumers inherently like the products close to them and even though there are many brands the firms are essentially oligopolistic, since small changes in price or geographical or characteristic location will have only an impact on a small number of local brands. This means that firms maintain some local market power. Pricing of other brands has little or no impact if consumers do not like those brands for location or characteristic reasons. New entry into the market only lowers price if a firm chooses to locate close to another firm that consumers like. If the new product is dissimilar to the old product then price is unaffected. This leads to the same conclusion that Salop's 1979 Circle Model came to. There are too many products in the industry. In the industry when there is competition, when fixed costs rise there are less firms and brands and therefore prices rise. As marginal costs rise, when there is competition, all the increase is pushed onto the consumer and therefore prices rise by an equal amount, but equilibrium variety stays the same. At the price where the industry or the demand curve changes to competitive from monopolistic, an increase in marginal costs or fixed costs reduces the variety or number of firms but also lowers price! Schmalensee, when talking about the breakfast cereal industry, echoes this. There are too many brands but they are not sufficiently differentiated to give the consumer the best choice. This brand proliferation led to barriers of entry to the industry in this case. So firms are proposing too little variety in their brands if the are seeking to maintain market share. If there are no barriers to entry then Hotelling and Salop show that there are too many brands if the products are sufficiently differentiated.