HW XXXXXXXXXXPolitical Pressure XXXXXXXXXXAbe has 1 unit of wealth and Beatrice has 0, but a policy maker is considering a transfer ?? of wealth from Abe to Beatrice. The size of the transfer ?? =...

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HW XXXXXXXXXXPolitical Pressure

XXXXXXXXXXAbe has 1 unit of wealth and Beatrice has 0, but a policy maker is
considering a transfer ?? of wealth from Abe to Beatrice. The size of the transfer
?? = ????
????+????
will depend on the pressure ???? and ???? that Abe and Beatrice
generate. Objective functions for Abe and Beatrice can therefore be written as
follows,
???? = √1 − ?? − ????
???? = √?? − ????
where the square root reflects a decreasing marginal benefit of wealth, and the
negative terms −???? and −???? reflect the cost of pressuring the policy maker.
a. (+4) Derive the first-order condition for the level of pressure that Abe
will optimally exert on the policy maker, taking Beatrice’s pressure as
given, as well as the first-order condition for the level of pressure that
Beatrice will optimally exert on the policy maker, taking Abe’s pressure as
given.
. (+4) The symmetry of the first-order conditions is such that any pair
(????,????) of pressure levels that satisfies both first-order conditions must
also satisfy ????∗ = ????∗ = ??∗. Use this fact to determine the level of
pressure that both individuals exert in equili
ium. Also, determine the
size ??(????∗ ,????∗ ) of the resulting transfer.
c. (+4) Now suppose that the policy maker ignores pressure from Abe
and Beatrice and chooses the level of transfers ?? to maximize utilitarian
social welfare ?? = ???? + ????. What transfer policy is implemented in that
case? How much pressure do Abe and Beatrice then exert?
d. (+4) Use your answers above to discuss the welfare implications of
setting policy in response to political pressure.
    HW XXXXXXXXXXPolitical Pressure
Answered Same DayApr 12, 2022

Solution

Komalavalli answered on Apr 13 2022
14 Votes
Given objective function
uA = -pA
uB = –pB
a)
First order condition
MuA=∂ uA/∂ pA = -1
MuB=∂ uB/∂ pB = -1
MuA / M uB = -1/-1 = 1
)
M uA / M uB = pA/ pB
M uA / M uB = -1/-1 = 1
pA/ pB = 1
At equili
ium the pressures p*A= p*B =p* = 1
Resulting transfer t = p*B/ p*A+ p*B
t* = 1/1+1 = 1/2 =0.5
t* =0.5
c)Social welfare W = uA+ uB
W = -pA+–pB
WA=∂WA/∂ pA = -1
WB=∂WB/∂ pB = -1
WA / WB = -1/-1 = 1 = pA = pB
At equili
ium the pressures p*A= p*B =p* = 1
Resulting transfer t = p*B/ p*A+...
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