**
3.3.2 Changes in the Number of Varieties as a Result of Compatibility
Decisions**

Economides (1991b) considers the interplay of compatibility and the number of varieties
of complementary goods. There are two types of goods, *A* and *B*, consumed in 1:1 ratio.
There are two brands of good *A*, *A _{1}* and

__Figure 9__

__Figure 10__

Under incompatibility, each *B*-type firm incurs higher fixed costs; it follows that
ceteris paribus the number of *B*-type brands will be smaller under incompatibility.
An *A*-type firm prefers incompatibility or compatibility according to the equilibrium profits it
realizes in each regime. These profits, and the decision on compatibility, depends on the
specifics of the utility function of consumers, and in particular on the impact of an increase of
the number of varieties on utility. If industry demand is not sensitive to increases in the number
of varieties of composite goods n (and does not increase much as *n* increases), then
equilibrium profits of an *A*-type firm decrease in the number of firms; therefore profits of an
*A*-type firm are higher at the smaller number of firms implied by incompatibility,
and an *A*-type firm prefers incompatibility. Conversely, when consumers have a strong
preference for variety and demand for composite goods increases significantly in *n*, equilibrium
profits of an *A*-type firm increase in the number of firms; therefore its profits are higher at the
larger number of firms implied by compatibility, and an *A*-type firm prefers compatibility.

Church and Gandal (1992b) and Chou and Shy (1990a,b,c) also examine the impact of the number of varieties of complementary (B-type) goods on the decisions of consumers to buy one of the A-type goods under conditions of incompatibility.