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.
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References
Zusammenfassung
Der Arzneimittelsektor der Gesetzlichen Krankenversicherung stand wiederholt im Fokus zahlreicher Gesundheitsreformen. Dennoch ist es bislang nicht gelungen, den Trend steigender Ausgaben nachhaltig zu bremsen. Die vorliegende Untersuchung leistet einen Beitrag dazu, die Ursachen dieser Entwicklung zu erklären und Lösungsansätze aufzuzeigen. Mittels Hauptkomponenten- und Cluster-Analyse wurden Gruppen von Arzneimitteln mit vergleichbaren Konsumeigenschaften gebildet. Jede Gruppe wurde auf den Einfluss der Altersabhängigkeit und des technologischen Fortschritts hin analysiert. Aufbauend auf diesen Ergebnissen wurde eine Prognose der zukünftigen Ausgabenentwicklung bis zum Jahr 2050 erstellt. Obwohl die Hauptkostenfaktoren exogen sind, steht der Gesetzgeber dem vorhergesagten ansteigenden Kostenpfad nicht hilflos gegenüber. Im Gegenteil: Anhand ökonometrischer Tests wird gezeigt, dass die Gesundheitspolitik in der Vergangenheit durch wahl- und klientelorientierte Interessendurchsetzung geprägt war. Mehr Effizienz in der Arzneimittelversorgung könnte durch die Einführung individueller Gesundheitssparkonten erzielt werden. Dies bestätigen die Resultate eines vertikal differenzierten Wettbewerbsmodells.