3. Ignoring the nonnegativity constraints, we can solve the system of two equations
given by the two optimal response functions and obtain an interior solution as we
did in class. Doing that we obtain:
g
h
=

25
g
p
=
125
2
Note that this cannot be an equilibrium since Hannah’s donations are negative
which violates the nonnegativity constraint.
Hence the equilibrium can only be one of the two special cases considered in problem
b).
First, consider the corner solution when
g
h
= 0 and
g
p
= 50. Note that
g
h
(50) =

50
3
<
0
Hence Hannah has no incentives to deviate from donating nothing. So this is an
equilibrium.
Finally consider the corner solution when
g
p
= 0 and
g
h
= 50
/
3. Note that
g
p
(50
/
3) =
1
2
(100

50
/
3)
>
0
Philip has an incentive to deviate. Hence this not an equilibrium.
In summary, there is a unique equilibrium of the model where Hannah donates
nothing and Philip donates 50.
3
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4. The equilibrium is not efficient. This is obvious because only person is donating in
equilibrium. By assumption, Philip ignores the benefits that Hannah reaps from his
generosity. Hence the equilibrium cannot satisfy the Samuelson condition. Hannah
is freeriding on Philip’s generosity.
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 Fall '12
 Sieg
 Economics, Fiscal Policy, Opportunity Cost, Democracy, Englishlanguage films

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