Econ 145b. Problem Set 2 (Spring 2009) (with solutions)
Please type your solutions or write legibly. Always provide arguments. Each question
1, 2(a), 2(b), 3(a), 3(b) is worth 20 points (100 points total)
A monopolistic seller with zero cost of producing a good maximizes expected profits.
Given a pricing schedule
T
that determines the transfer to the seller as the function of
quantity bought, a buyer buys quantity
q
≥
0
that maximizes the net utility equal to
gross utility
U
(
q
)
minus transfer
T
(
q
)
. The buyer’s gross utility from buying quantity
q
is
U
(
q
) =
θ
(1

exp (

q
))
where
θ
equals
θ
L
with probability
λ
and
θ
H
with probability
1

λ
.
Assume that
θ
H
>
θ
L
>
0
and that the seller needs to o
ff
er the same pricing scheme to both buyer
types. The buyers are not coerced to buy; they will buy only if their net utility from
buying is nonnegative. We will allow the seller to produce and sell an infinite quantity
of good to any buyer
θ
; in line with the above formulas, the buyer’s gross utility from
buying an infinite quantity is
θ
.
(1) Assuming the seller is constrained to uniform pricing,
T
(
q
) =
pq
, compute the
profit maximizing price
p
m
.
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 Winter '10
 Obara
 Derivative, Equals sign, p1, low type

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