# 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
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+...
SOLUTION.PDF