ECON 641 Homework #3
类型。考虑参数限制vH> cH> vL> cL。假设
2. Consider a monopoly platform serving two distinct groups of users. Each
group i = a, b comprises a unit mass of users who interact on the platform.
The platform charges (possibly different) membership fees for the two
groups, Ma and Mb. The constant marginal cost of attracting users on
the platform is normalized to zero. A user of group i enjoys the following
net utility when interacting on the platform with users of the other group
Ui = ui + γinj − Mi
is the intrinsic value of being on the platform, γi measures the
indirect network effect provided by an additional member of side j on each
member of side i, nj is the number of members of side j on the platform.
We assume that ui
is drawn from a uniform distribution on [0, vi
]. As for
indirect network effects, we assume that they are positive on both sides
(γa, γb > 0).
2 Network Goods
1. 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 + vne
where a is the stand-alone benefit, v > 0 measures the network effect, n
is the expected number of users joining the network, and θ is uniformly
distributed on the unit interval.
(a) Identify the indifferent consumer for a given price p and a given
expected network size n
(b) Express the willingness to pay for the nth unit of the good when n
units are expected to be sold.
(c) Express the fulilled-expectations demand curve and draw it. In particular, show that for v ≤ a, the fulfilled-expectations demand is
decreasing everywhere and there is a single equilibrium for all p ≤ a.
On the other hand, for v > a, show that the fulfilled-expectations
demand has both an increasing and a decreasing portion. Characterize the range of prices for which two levels of demand satisfy the
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