I borrowed some of the figures and equations in this lecture from Yohanes E. Riyanto, an associate professor at Nanyang Technological University in Singagpore

Addresses the nonexistence of Hotelling equilibrium Major changes to the model a. Market space is a circle, not a line (Salop says an infinite line yields the same results). Circle is of unit mass. One imagery is a tropical island with a mountain in the middle b. Firms choose to enter, or not, at a specific location. These are the differentiated goods c. Salop has a second, undifferentiated, competitively supplied good that a consumer can buy instead of the differentiated good Allows us to look at optimal and equilibrium product diversity

Firms Firms are located around the circle market, equidistance from each other. Subscript i indicates a specific firm at location i. There are N firms. There is a fixed cost and constant marginal cost. Firms choose output and price to maximize profit given by

Consumers Consumers are located uniformly around the circle. A consumer’s location represents her most preferred brand. Each consumer purchases one or no units of the differentiated good (excess income is spent on the homogenous good). Transportation costs per unit of distance is t. There are no transportation costs for the homogenous good The consumer derive utility from consuming her one unit of the good Salop has L consumers. I normalize L  1

5 x Salop’s Circle Model (example: N=6) Firm 1 Firm 2 Firm 3 Firm 4 Firm 5 Firm 6 1/6 Firm 1 Firm 2Firm 6 p1p1 pp x 1/6 Yohanes E. Riyanto

Entry and Pricing Two stage game 1.Firms choose whether to enter and where to locate. Assume the principle of maximum differentiation – if firms enter they try to be as far as possible from the closest competitors, to increase market power. If N firms enter, they locate equidistance around the circle, so there is 1/ N distances between them 2.Firms set price to maximize profit, given the number of other firms (ie, given the distance to their closest competitors) Assume a symmetric equilibrium, so p 1 =p 2 =…=p N =p Firm has only two competitors, the firms located immediately to its right or left. Why?

Consumer choice and firm demand Given price p charged by the adjacent firms (left and right) and price p 1 charge by firm 1 the indifferent consumer is at distance so and this give firm 1’s market share (demand) as

Firm’s profit Profit of firm 1 is Remember p is the price of the adjacent firm. All firms are the same, hence p=p 1 and so Like Hotelling, price and profit margin increase with transportation cost. Moreover, they decrease with the number of firms in the market

Local monopolies So far assumed firms are close enough that the compete for the same consumers. However, if firms are far apart, some consumers may choose to buy none of the differentiated good. This occurs when So that price plus transportation cost exceeds the value of the good

Yohanes E. Riyanto10 Firm 1 Firm 2 p1p1 p 1/N xm1xm1 xm1xm1 xm2xm2 xm2xm2 these consumers do not buy since price is higher than the value obtained (p>V) Indifferent consumer gets 0 surplus value from the differentiated good, so The demand for firms 1 and 2 is given by because they have monopoly over consumers on either side

Yohanes E. Riyanto11 Price Quantity monopoly region competitive region Gives a kinked demand curve is the price given that consumers located at the locations on the previous slide are indifferent between buying the good or not. As any lower price the firm is competing with adjacent firms for those consumers and all consumers. xmxm

Where is the kink? Demand can never exceed monopoly demand, so the kink must be on the monopoly demand curve. As N increases, the kink moves to the left off the monopoly demand curve

Symmetric Zero Profit Equilibrium (SZPE) SZPE is a price, p, and number of firms (brands), N, such that every equally spaced Nash price setters’ maximum profit price earns zero profit. In equilibrium, a firm’s demand curve and average cost curve will be tangent (assures zero profit is maximum profit). Three equilibria are possible

Monopoly equilibrium, some consumers do not buy the differentiated good. Markets of neighboring firms do not overlap, each firm acts like a monopolist. At a kinked equilibrium markets just touch (there is a clear marginal consumer). The monopoly demand lies above the AC curve so what would be the monopoly price (shown by p m ) is below the kinked-equilibrium price (p k ) Competitive equilibrium all markets overlap, not really concerned with it here

SZPE SZPE satisfies two conditions: 1.MR  MC 2.P=AC From symmetry if the equilibrium has no gaps q=1/N (remember we normalized L =1) Point G is dominated by F so the equilibrium is at the kink unless AC is exceedingly flat – giving the monopoly equilibrium, or steep, giving the competitive equilibrium (2 slides above)

Number of firms: Free entry Entry takes place until profit is fully dissipated. Since Solve for N gives Price exceeds MC, but profit=0

Equilibrium with sufficient firms for competition An increase in fixed cost causes a decrease in the equilibrium number of firms ( N c ) and an increase in each firms’ profit margin ( p-c ). When FC  0, N c  An increase in transportation cost ( t ) causes an increase in the equilibrium number of firms ( N c ) and an increase in each firms’ profit margin ( p-c).

Social optimum Choose N to minimize total production and transportation costs So Profits are positive and equal 3 F Competitive market has too much entry (too much differentiation) compared to social optimum. Total transportation costs = which decrease in N. Since N s < N c, too little is spent on transportation (too much is spent on differentiation) if there is free entry. Too much of societal resources is spent on fixed costs

What is important in the model Which of the model innovations were most important? The second good and the circle (or infinite line) were tools to remove the discontinuities in the profit function that plagued the Hotelling model. They were innovations, but not the focus of the paper Notice how little Salop talks about the outside good. It just enabled demand for the differentiated good to be elastic (buy 1 or 0, depending on price) Equivalent, in a way, to the congestion costs of Ahlin and Ahlin Focus is on product differentiation and competition. That is the research issue of this paper

Most important conclusions/contributions 1.Competition results in too much differentiation 2.Explains where a kinked-demand curve comes from 3.In equilibrium, P>MC but profit still equal 0 4.Monopoly demand is more elastic than competitive demand How important are these conclusions/contributions? Evaluation is not just stating something, it is telling us whether it is good or bad, and why. For example, how valuable is it that we understand where kinked- demand curves come from? Why? Evaluation means assessing what it adds to our knowledge, whether that is valuable, and maybe, as a weakness, where it misleads us