这个作业是完成同类产品买方、卖方市场的需求供给研究

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
卖方的类型,其中每个卖方可以出售一个单位,并且每个买方都有
单位需求。买方H对产品的估值为vH,买方L为产品
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
具有cH> cL的cL。每个买家和每个卖家都有一个单位质量
类型。考虑参数限制vH> cH> vL> cL。假设
买卖双方随机匹配一次。进一步假设
买卖双方有效地讨价还价,
比赛均分。如果买方-卖方内部的联合盈余为负
两者之间没有交易发生。
(a)确定每项的预期分配和预期盈余
买卖双方。写一两个句子描述结果。
(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
平台。每当中间人向卖方收取费用P> 0
发生交易。如果至少一名卖方和至少一名买方加入
中介,它们是随机匹配的。买卖双方
决定是否保留在非中介匹配市场中
或转向中间市场。随机配对
将净盈余从贸易中平均分配。是否存在交易
费用P> 0,以便在中间平台上进行交易,并且
中介人因此赚取严格的正利润?可以交易
一个单元通过中介得到平衡支撑吗?是个
在平衡中活跃的非中介匹配市场(即
交易是在中介平台上还是在外部平台上进行?
(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.


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