ECON 641 Homework #3

1双面市场
1.考虑具有两种类型的买方和两种类型的同类产品市场

vH> vL的估值vL。卖方H的机会成本为cH，卖方L的机会成本为cH

（a）确定每项的预期分配和预期盈余

（b）分配效率最高吗？说明。
（c）中介人进入市场并主动提出交易要约

（d）在具有中介的模型中，您能说出均衡的效率特性吗？
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
where ui
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
e
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
e
.
(b) Express the willingness to pay for the nth unit of the good when n
e
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
equilibrium condition.