We find that the increased loss to consumers from consuming a low-quality product may negatively benefit low-quality firms. For high-value markets, equilibrium prices, quantities, and profits for both types of firms increase in the proportion of high-quality firms; this parameter does not affect the equilibrium game in the monopoly signaling model or in the full information model. Finally, an increase in the loss borne by consumers from a low-quality product may (for parts of the parameter space) perversely increase the price, quantity, and profit of the low-quality firm; this effect also does not appear in the monopoly signaling model or the full information model.
In the next period, each firm has private information about its own quality, which sets up a signaling game in which a firm's price can reveal the quality of its product. In the imperfect information model, firms do not observe the types of other firms, and consumers do not directly observe the types of any firm. In a model with perfect information, firms and consumers observe all types in the second period before firms choose prices.
In high-value markets, an increase in 8 results in an increase in the quantity of type H, QH, and profits, AH. Since the equilibrium involves the H-type firm posting a higher price than the L-type firm, an increase in the proportion of firms that are likely to be H-types shifts the incentive compatibility constraints. Moreover, since firms' prices are strategic complements (( > 0), the best response functions are upward sloping, so an increase in the expected price of a firm's competitors encourages each firm to raise its price. her.
Let PF(2i, 2-i) denote the full information price for firm i if its true quality is 2i and the vector of its rivals' true qualities is 2-i; the formula for the price function with full information is given in the Appendix. Proposition 5 (Effects of product value, product substitutability and number of firms). i) An increase in the consumer's willingness to pay (") gives an increase in L-type and H-type equilibrium prices, quantities and profits, and an increase in the difference in equilibrium prices and the difference in equilibrium quantities In markets high-value, an increase in the degree of substitutability of the product () leads to a decrease in L- and H-type equilibrium prices, quantities, and profits, and a decrease in the differences in both equilibrium prices and equilibrium quantities , namely iii).
In high-value markets, an increase in the number of firms (n) leads to a decrease in both L-type and H-type equilibrium prices, quantities, and profits, and a decrease in the differences in both equilibrium prices and the equilibrium quantities. ; that is,. The following statement characterizes the results of an exogenous increase in the consumer loss parameter. Statement 6 (Effects of Low Quality Loss). i) The price difference always increases due to the loss associated with low quality.
For high value markets, the difference in quantities always increases in the loss associated with low quality, *; that is, *8Y QL - QH8. ii). As the proportion of H-types becomes arbitrarily small, an increase in the loss * leads to a decrease in the L-type's price, quantity and profits. iii). The above statement paints a surprising picture: for an industry consisting of a sufficiently large proportion of H-type firms, an increase in the loss can actually make the L-type.
In the next section we discuss the implications of this finding in a number of contexts.
Applications to Tort Reform, Innovation, and Licensing Requirements
The first section of the bill, section 101, sets limits on the recovery of non-economic damages in medical malpractice suits. While medical malpractice technically falls under the negligence regime, this distinction is not particularly relevant hereafter, as a low-quality manufacturer is negligent by presumption, while a high-quality manufacturer is never negligent. An example of the former is medical expenses for "economic losses" (such as hospitalization costs), and the latter may be "non-economic losses" (such as emotional distress resulting from the harm suffered), so limiting recovery to non-economic damages would mean that * U > 0.
Such caps are in place at the state level and are currently being debated in the U.S. Congress.18 Damages that are reimbursed must be paid by the company, so this means that the company's per-unit cost of production of low quality is now positive. : cL = *C. As in the previous section, one can show that (for the adjusted model) for high value markets the L-type price, quantity and profit increase in *U for sufficiently high 8.
Thus, the effect of a cap on non-economic damages resulting from torts arising from products offered in high-value markets, where there is a sufficiently high percentage of high-quality producers, is to improve the prospects of companies of low quality. This decision, which allowed for lawsuits from customers alleging a manufacturer's negligence even if they were not direct purchasers, is widely seen as the turning point in the development of modern product liability law; by 1946 this statement had become permanent law (see Keeton, et. al., 1989, pp.16, 52). 21 See http://www.mutualwheel.com/history.html for the history of a company that was once active in the wooden wheel business.
In the first quarter of the twentieth century, cars rode on wooden wheels with metal rims, no doubt as the transmission of horse-drawn carriages. If the wooden spokes are not made of sufficient quality wood (eg high quality hickory), the wooden spokes can break, causing serious personal injury. 22 We are aware of the possibility that safer wheels on cars would cause drivers to drive at higher speeds (if the car could do it), which could lead to more accidents. improvements in the production of special metal parts for various products) have led to a reduction in harm to consumers, including those caused by special products such as vehicle wheels.22.
There is certainly reason to expect this link between general innovation and specific product quality improvements to operate in many aspects of economic activity. The model from the previous section suggests that when conditions are such that MPL/M* > 0, the incentives for low-quality producers (whose products are the source of the loss) to make or adopt such product-specific innovations will be lower than might otherwise have occurred. In our model, the effect of a license requirement that lowers *, leaving marginal costs unchanged, can have a dual benefit for consumers in high-value markets with a sufficiently high proportion of H-type.
Conclusions
Our method for deriving the separation of equilibrium prices is to first derive a best response function for firm i that reflects the signaling need of its type. No firm is willing to distort its price away from its best response (if its type were known) in order to be perceived as type L (because that is the worst type we can perceive). Thus, if an L firm is perceived as such, its best response is DLL, which yields a profit of b(dL - cL)2/4.
If a firm of type H is perceived as being of type L, its best response is DHL, which makes a profit of b(dL - cH)2/4. However, any firm would be willing to distort its price away from its best response (if its type known) in order to be perceived as type H. Thus, a candidate for a revealing equilibrium must involve a best response for type H that satisfies two conditions .
First of all, it must prevent imitation of the L-company type (which therefore returns to DLL); and secondly, it must be worthwhile for the Type H company to use this price instead of being considered a Type L company (and thus returning to DHL). The first inequality implies that the type L firm prefers to price at DLL (and be seen as type L) than to price at p (and be seen as type H). The second inequality means that the type H company prefers to price at p (and be seen as type H) than to price at DHL (and be seen as type L).
23 The H-type firm can also deter imitation by the L-type firm by using a downward-distorting price, but H-type will prefer to give up and be taken as an L-type firm rather than using a low price to differentiate itself. This whole interval involves prices of more than DHH = (dH + cH)/2; so the type H firm distorts its price upward from the best response function it would follow if it were known to be of type H.23 Refinement of Best Response Functions. The intuitive criterion states that consumers type H should infer firm i's price p as long as type H would be willing to charge p, yet imitation by type L would be deterred even under this most favorable inference.
Thus, an H-type firm distorts its best response to the smallest extent necessary to deter mimicry with its alter ego (L-type). Each type of firm i has the best response to a common competitor separation strategy (summarized for the purposes of firm i by expected value). Then, by construction, an L-type firm i would be unwilling to charge a price at or above PH (which is equal to DH(X*)) in order to be taken as an H-type.
On the other hand, the type H firm i would be willing to charge a price at or slightly above PH (which is equal to DH(X*)) to be hired for type H, but of these it prefers the lowest price. ; that is, PH. We don't need to actually construct a pooling equilibrium, because we only need to show that if it exists, there is a price to which the H-type firm could profitably switch (which would be unprofitable for an L- type of company) as consumers would. update their beliefs and conclude that the signal came from an H-type company.
