and suppose that consumers differ in their valuation of both the stand-alone and the network benefits (it can indeed be argued that it is more plausible that a user who has a higher value for the stand-alone component of a
Consider the market for a single network good and suppose that
consumers differ in their valuation of both the stand-alone and the
network benefits (it can indeed be argued that it is more plausible
that a user who has a higher value for the stand-alone component of a
technology also assigns more importance to the size of its network.) To
capture this idea, write the consumer’s utility function for joining the
network as U(θ) = θ(a + νne), where a is the stand-alone benefit, ν > 0
measures the network effect, ne
is the expected number of users joining
the network, and is uniformly distributed on the unit interval.
a. What happens if p > a + νne? (Hint: Identify all consumer who buy
the good for at price p and a given expected network size ne).
b. What is the consumer’s
good when ne units are expected to be sold? Is the demand downward
sloping? Does the demand increase with the expected network size?
c. Express the fulfilled-expectations demand curve and draw it. In
particular, show that for ν ≤ a, the fulfilled-expectations demand is decreasing everywhere and there is a single equilibrium for all p ≤ a. On
the other hand, for ν > a, show that the fulfilled-expectations demand
has both an increasing and a decreasing portion; characterizes the
range of prices for which two levels of demand satisfy the equilibrium
condition.
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