An extension to Salop’s model Focused on variety differentiation: consumers differ on the most preferred variety Expands it to include quality differentiation: all consumers prefer more quality to less, but differ in their willingness to pay for quality The model here, each differentiated product is defined by one feature of variety, and one feature of quality. 1.Allows exploration of substitution of variety for quality; if the overabundance of variety from the Salop model persists 2.How firms strategic interaction define the variety-quality mix in the market Products are differentiated in each dimension, so within a variety, consumers compare quality. Across varieties, they compare variety-quality combinations (eg, computer type – Apple or IBM – and cpu speed)

Basic assumptions Quality is independent of MC of production. Quality comes from better design, not variable production costs. Makes quality a fixed cost issue. Why is this important in the Salop model? Consumers have preferences for specific variety At the same price, all consumers prefer higher quality to lower quality. They differ on their willingness to pay for higher quality

Where does quality choice fit in decisions? Traditional Salop model has three stages of firm decision making before consumers make their choice of whom to patronize 1.Firms decide to enter or not (long run)fore con 2.If a firm enters, it chooses location (medium run) 3.Firms in the market choose price (short run) Adding quality gives three choices on how firms choose it 1.Quality and price are chosen simultaneously in stage 3, after location (3- stage game) 2.Quality choice precedes the price stage, so is precommitted (4-stage game) 3.Quality and location are chosen simultaneously in stage 2, which is equivalent to no precommitment in location, and has the same equilibrium as the 4-stage game because there is no strategic value to location

Precommitment In short run, when quality choice precedes price choice, the equilibrium quality choice depends on the price response of neighboring firms Gives quality a greater strategic variable for securing revenue -- it is more useful than when chosen simultaneously with price Since the strategic value is larger, less much be used to achieve strategic goals Result is firms use lower levels of quality when it is chosen first than when chosen simultaneously with price – precommitment to quality lowers quality In medium run, with fixed number of firms, precommitment brings higher prices and profits, so there is more entry, hence more variety Both games over-provide variety and under-provide quality, but quality precommitment has the bigger distortion from optimum

Policy implications of the results A key result is the inverse relationship between variety and quality in equilibrium This means raising quality above its equilibrium value reduces variety Since in equilibrium variety is over-provided and quality is under-provided, minimum quality standards can be efficiency improving

The model set-up Product is defined by a pair (x j,a j ) denoting its variety and quality Variety characteristics lie on the unit circle with circumference denoted by C Quality is chosen from the interval so the product space is a cylinder of size An alternative numeraire good is also available to all consumers Consumers are defined by two parameters (z,  ) z indicates her preferred variety, and lies on C  denotes her relative preference for quality with CDF G(  ) Preferences are defined on

Conceptualization of Salop circle with quality We have a cylinder. The edge of the cylinder defines the variety, while the distance along the tube defines quality. Variety 1 Variety 2 Variety 3  quality 

Consumer problem The value of one unit of product (x j,a j ) sold at p j to consumer (z,  ) is Utility is separable in quality and variety There is a linear penalty for variety deviating from consumer optimum (symmetric in direction) and utility increases with quality, independent of variety Marginal consumer z j indifferent between (x j,a j ) and (x j+1,a j+1 ) has Similarly marginal consumer z j-1 is between (x j,a j ) and (x j-1,a j-1 )

Location of the marginal consumers Opening the cylinder and rotating 90 o to the left shows the market area for firm j z j-1 (  ) zj()zj() The shaded area represents all consumers who prefer to buy (x j,a j ) given current prices. Hence, the demand for product j is Where is the expectation of , ie, the average intensity of quality preference. As this increases, the influence of quality on demand goes up too

The profit function for firm j With n firms and assuming zero MC of production, cost of quality is give by C(a)=ca 2 /2 and fixed costs of F, firm j has a profit function where are the n-tuples of strategies for prices, quality and variety

Entry  location  (quality and price): stage 3 Assume no price undercutting because it drives demand to zero Firms choos price and quality. Thesubgame is to maximize profits wrt p j and a j since the locations, vector x, are already made He uses some fancy matrix algebra to show that profits for firm j are where p* and a* and are the vectors of equilibrium qualities and prices. We use this for the location decision

Entry  location  (quality and price): stage 2 At stage 2, firm j chooses location to maximize so and he shows which is a result of the linear model with inelastic demand. A shift of location to the left results in as many lost sales to the right. Equilibrium values for price and qualities are thus Price and quality both increase in the distance between firms, given by. As the number of firms increases, the strategic value of high quality falls because the potential market gain falls. The level of quality and the number of varieties are inversely related.

Entry  location  (quality and price): stage 1 Firms enter as long as profits will be positive. Hence we need to solve for n when which gives the solution the integer part of Letting the superscript 3s* indicate the equilibrium from the 3-stage game, we have Since an increase in the average intensity of preference for quality gives higher quality and lower profit when the number of firms is fixed, in the long run, increases in the preference for quality results in fewer firms (less variety) and more quality in long run equilibrium

Note on symmetry Results are for a symmetric equilibrium. Prices are proportional to quality levels, so symmetry implies equal prices, quality and profit. If locations are asymmetric some firms have larger markets, which also implies higher prices, quality and profits. In such a case, entry occurs until the marginal firm makes zero profit. All other firms will have larger market shares, meaning somewhat fewer firms, no less variety and higher average quality, along with some firms making profits

Entry  location  quality  price game Now quality is announced before price is set; it is a commitment that allows firms to reveal how aggressively they will behave in setting price. Because it is communicated earlier, it is a more potent signal about strategy, so firms can use “less of it” to achieve the same result. Hence, we expect lower quality in this game than when price and quality are a combined decision. Working backwards, starting with price we again have and

Price, quality and profit in the 4-stage game Working through the stages now, like we did in the 3-stage game gives where we know from footnote 13 that 1>b 1 -b 2 >0. Compare these to the results from the 3-stage game for the same number of firms: So for the same number of firms, price is the same, quality is lower, and since quality is costly, profits are higher than in the 3-stage game

Entry and firms in the 4-stage game Again looking for zero profit we find in long-run equilibrium Since 1>b 1 -b 2 >0 we know that n 4s* > n 3s* so there is more variety in the four-stage game, indicating also that price and quality are also lower Precommitment to quality reduces quality and increases the number of brands

The optimal number of firms For n equally space firms all selling at the same quality and price we can find the total society value by integrating its demand. As shown in equation (21) this generates a total surplus value of. Taking Substituting this into S(n,a) and optimizing wrt n gives

Both games give too many varieties Comparing the optimum to the results of the two games shows and The surplus with precommitted quality is lower than when price and quality are chosen simultaneously

Policy implication Quality and variety are substitutes in the market. Salop has shown that in horizontal differentiation we get too much variety. Adding quality exacerbates the problem. Higher quality attracts new consumers to a market by expanding the number of firms needed to get profit to zero. Reducing the number of firms will improve welfare If entry prohibition is infeasible, setting a minimum quality standard can increase welfare by reducing the number of firms (through the inverse relationship of quality and variety)

Surplus values with fixed and variable quality standards

Minimum quality standards There is always an opportunity to improve welfare by setting minimum quality standards. Let In the three stage game, any minimum quality within this range will improve social welfare. Likewise in the four stage game, any minimum quality within will improve social welfare.