82 The ? rst summand represents the quantity which is consumed by people who are still inside their accounts, the second summand stands for people who are already outside their accounts. We obtain the same reaction function as in the coinsurance case: . (4.9) Consequently, ? rm B’s maximization problem is: . (4.34) The results for B are: (4.35) and . (4.36) For ? rm G we get: (4.37) and . (4.38) 4.6. Economic Analysis II: Quality Equilibrium 4.6.1. Coinsurance Firms choose their products’ quality based on the price equilibrium conditions we found in section 4.5. Since the results for an additional quality sub-game are complex and not informative, we will solve the model parametrically. In doing so, we assume ?B = 1. This assumption should be adequate for generic competition, at least in the short run: in the strict sense, the brand-name drug and its generic copy are qualitatively identical, but the manufacturers have the possibility of boosting the perceived quality of their product e.g. by means of advertising. We presume that the brand-name drug had been highly pushed during its period of patent protection. Thus even after patent expiry it is well-known by physicians as well as consumers and possesses high valuation due to positive experiences and brand awareness. The perceived quality of 83 the branded drug is the benchmark for the generic competitor so the latter must decide how to position its product relative to the brand. Figure 4.4 plots ? rms’ prices for the case of ?B = 1 as a function of G’s quality in the case of proportional coinsurance of 10 % (k = 0.1; model 1). Figure 4.4: PB and PG as a Function of G’s Quality, ?G. 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 0 0,2 0,4 0,6 0,8 1 Price s G's quality, ?G Prices B Prices G Notes: ?B = 1. While ?G = 0 ? rm B possesses a monopoly and thus sets the monopoly price, PB = 5. But when ?G increases, competition becomes stronger (the ratio of equilibrium prices declines) and PB falls. G’s optimal price increases with ?G as long as PB is suf? ciently high. As soon as quality levels of the drugs get close together, the optimal prices for both B and G fall.76 Solving ? rm G’s maximization problem (4.39) reveals that it chooses . (4.40) Therefore, equilibrium prices, quantities and ? rms’ pro? ts are: PB = t.w, PG = wx , QB = st , QG = u8 and ?B + ?G = s.w8. 76 See Metrick and Zeckhauser (1996) for the case of no insurance, pp. 6 - 7. 84 4.6.2. Reference Pricing Considering RP (model 2) no single solution can be obtained because the results depend on ?, i.e. the weight of PRPG for determining the reference price. G’s maximization problem is: . (4.41) Hence, for each apportionment between = and >, ? rm G chooses a speci? c quality level ?RPG (table 4.1). Table 4.1: G’s Quality Dependent on Reference Price Setting Scheme. = > ?RPG = > ?RPG 0 1 0.67 0.6 0.4 0.41 0.1 0.9 0.58 0.7 0.3 0.39 0.2 0.8 0.52 0.8 0.2 0.38 0.3 0.7 0.48 0.9 0.1 0.37 0.4 0.6 0.45 1 0 0.35 0.5 0.5 0.43 As we can see, quality of the generic drug decreases when = increases. Thus, the more the reference price depends on PRPG , the more it is optimal for ? rm G to pursue a lowquality strategy and to compete via the price component. Diminishing quality of the generic drug would suggest increasing prices for the branded drug as well as decreasing prices for the generic version. However, ? gure 4.5 does not support this supposition. In fact, both PRPB and PRPG show a u-shaped development. Figure 4.5: PRPB and PRPG as a Function of ? and ? (from left to right the weight of ? increases and consequently, as we have just seen, ?RPG decreases). 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 0 /1 0, 1/ 0, 9 0, 2 /0 ,8 0, 3/ 0, 7 0, 4/ 0, 6 0, 5/ 0, 5 0, 6 /0 ,4 0, 7/ 0, 3 0, 8/ 0, 2 0, 9/ 0, 1 1/ 0 Pr ic e s ? / ? Price B, RPS Price G, RPS Notes: ?RPB = 1.