Homework #4
(Econ 411)
F. Gahvari
Spring 2017
1. Prove that if preferences are Leontie, excess burden is zero.
2. Discuss what dierence it may make to workers and their employers if the
50-50 division of social security contributions in the U.S. is change
the game, which describe what actions the parties can undertake,
and what outcomes these actions would be obtained. In most cases
the rules of the game are designed by someone: in chess, basketball,
etc. The rules are designed to achieve better outcomes.
= xie h + i(h), i = 1, 2 (11.36) where i(h) = e h bi(h)dh. (11.37)
Ui(xi , h) is then clearly not quasi-linear in xi . It is further assumed
that for all h (0, ], b1(h) > , b2(h) < 0, b i (h) < 0 (i = 1, 2), b1(0) +
b2(0) , and b1() + b2() . We then have
consequently it is a function, denoted by g(h), of h only: U1 h /U1
x1 + U2 h /U2 x2 = g(h) = 0. (11.39) Let Fi(xi , h) = Ui h / Ui
xi (i = 1, 2), which can be generally expressed as Fi(xi , h) = xii(h) +
fi(xi , h) + bi(h), where fi(xi , h) are nonsepara
cheat. That is, when the consumers are asked to report their utility
functions or MRSs, they will have incentives to report a smaller MRS
so that they can pay less, and consume the public good (free riders).
This causes the major difficulty in the public
assesses that as long as property rights are clearly assigned, the two
parties will negotiate in such a way that the optimal level of the
externality-producing activity is implemented. As a policy implication,
a government should simply rearrange property
variable is the subset of 401 types, which are induced to produce a
positive amount. Reducing the subset of producing agents obviously
reduces the rent of the most efficient type. 13.8 The Theory of the
Firm Under Asymmetric Information When the delegatio
interaction of a single incentive constraint with a single participation
constraint. Here we would mention some possible extensions. One
can consider a straightforward three-type extension of the standard
model. One can also deal with a bidimensional adve
there exists a legal framework for this contractual relationship. The
contract can be enforced by a benevolent court of law, the agent is
bounded by the terms of the contract. The main objective of this
chapter is to characterize the optimal rent extracti
with this solution is that it requires that the taxing authority knows
the externality cost e(x). But, how does the authority know the
externality and how do they estimate the value of externality in real
world? If the authority knows this information, it
respect to t and t yields, respectively, the following first-order
conditions: 1 + 1u (t ) = 0, (14.6) (1 1) + (1 1)u (t
) = 0, (14.7) 432 where t and t are the first-best transfers.
From (14.6) and (14.7) we immediately derive that = 1 u(t ) = 1 u
(t) >
informational problems prevent society from achieving the first-best
allocation of resources that could be possible in a world where all
information would be common knowledge. The additional costs that
must be incurred because of the strategic behavior of
for a fixed up-front payment T . The agent benefits from the 409
full value of the good and trades off the value of any production
against its cost just as if he was an efficiency maximizer. We will say
that the agent is residual claimant for the firms pr
even if the agent is risk-neutral. Indeed, when he wants to induce a
high effort, the principals program is written as max cfw_(t,t ) 1(S
t) + (1 1)(S t) (14.19) subject to (14.15) to (14.18). Then, we
have the following proposition. 435 Proposition 14.4
this case, consumer 2s problem is: max h1,T1 2(h1) T1 s.t : 1(h1)
+ T1 = 1(h ) Again, we know that the constraint will bind, and so
consumer 2 chooses h1 and T1 in order to maximize max 1(h1) +
2(h1) 1(h ) which is also maximized at h1 = h , since the
fir
the risk-averse agent bear some risk. To guarantee the participation
of the risk-averse agent, the principal must now pay a risk premium.
Reducing this premium calls for a downward reduction in the
inefficient types output so that the risk borne by the ag
ones. i.e., the binding ones at the optimum or the principals problem.
397 Let us first consider contracts without shutdown, i.e., such that
q > 0. This is true when the so-called Inada condition S (0) = + is
satisfied and limq0S (q)q = 0. Note that the -
revelation by the efficient type is no longer obtained in equilibrium.
There is a fundamental trade-off between raising efficiency ex post
and hardening ex ante incentives when renegotiation is an issue.
13.13.2 Reneging on a Contract A second source of i
Mechanism The Pigovian taxes were not adequate in general to solve
externalities due to the information problem: the tax authority
cannot know the cost imposed by the externality. How can one solve
this incomplete information problem? Varian (AER 1994) pr
is: i(g ) gi 5 0 with equality if gi > 0 for all i = 1, . . . , n. (12.30)
Thus, we have i gi = ui xi (1) + ui y f (g i + n jj=i gj ) 5 0
with equality if gi > 0. So, at an interior solution g , we have ui y
ui xi = 1 f (g i + jj=i gj ) , 379 and thus MRS
type with the design of his contract. We will briefly present the
contract theory in four chapters. Chapters 13 and 14 consider the
principal-agent model where the principal delegates an action to a
single agent with private information. This private info
incentive to match the announcement of firm 2. But consider firm 2s
incentive. If firm 2 thinks that firm 1 will propose a large
compensation rate t1 for him, he wants firm 1 to be taxed as little as
possible so that firm 1 will produce as much as possibl
= U SB() + qSB() (13.127) becomes T(q) = t SB( SB(q) = (q)
q SB( )d + (q)q. (13.128) To the optimal truthful direct revelation
mechanism we have associated a nonlinear transfer T(q). We can
check that the agent confronted with this nonlinear transfer choo
2 (h2) = 0. But, this is the same conditon that defnes the socially
optmal level of h2. Thus consumer 2 chooses h2 = h , and, using
the constraint, T2 = 1(h ) 1(0). And, the offer (h2, T2) is
accepted by consumer 1. Thus this bargaining process implement
theorem is that, costs of negotiation and organization, in general, are
not negligible, and the income effect may not be zero. Thus, a
privatization is optimal only in case of zero transaction cost, no
income effect, and perfect economic environments. Tia
agent residual claimant for the hierarchys profit, also provides full
insurance to the principal. By making the risk-neutral agent the
residual claimant for the value of trade, ex ante contracting allows
the risk-averse principal to get full insurance and
U1/h > 0 but U2/h < 0 for (xi , h) (0, ) (0, ), i = 1, 2. Then,
the level of pollution is independent of the assignments of property
rights if and only if the utility functions Ui(x, y), up to a monotonic
transformation, have a functional form given by Ui
the optimal linear rule inducing effort must solve max (1 )(1q+
(1 1)q) (14.58) subject to (1q+ (1 1)q) = (0q+ (1
0)q), (14.59) (1q+ (1 1)q) = 0 (14.60) Obviously, only
(14.59) is binding at the optimum. One finds the optimal linear
sharing rule to be SB
Let q = n i=1 qi : the market price vector of y. Let p RL + be the
price vector of private goods. The profit is defined as = qy pv with
y = f(v). Definition 12.4.1 (Lindahl Equilibrium) An allocation (x , y
) R nL+K + is a Lindahl equilibrium allocation i
those transfers such that (q q) t t (q q). (13.16)
Remark 13.4.1 In this two-type model, the conditions for
implementability take a simple form. With more than two types (or
with a continuum), the characterization of these conditions might get
harder. The