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Unformatted text preview: . Name l% ISyE 4803A Supply Chain Economics
Exam 1 — Spring 2007 By signing this you agree that all work on this exam is your own: you satisfy all
conditions of the honor code, and that you did not use any additional materials/notes and
or your calculator for anything other than for calculations. In addition, you agree that if
you break any of the above conditions, your exam score will be changed to a 0. Signature (note: exams not signed will not be graded) Instructions: Please put all answers to your solutions in the space provided below.
Partial credit (for all non true/false questions) will be based on work shown on the space
given on the rest of the exam. No credit will be giVen if no answer below.. “/2. (i 00 1150? » 7/; (bee PM no — 27A 2A; True/False Questions (5 points each) Name 1. For the price response function d(p)=100p, the elastic region is where p<50.
unkﬁ’ {\bS‘FIC {5 (um (t‘ ’> =' go
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2. There are three fare classes with booking limits (from class 1 to 3) of 100, 70, 20'.
The corresponding protection levels are 30, 80, 0. 7/ Use the following data for problems 3 and 4. Suppose we have two buyers (B1 and
B2) and two items (11 and 12). The willingness to pay for each buyer/item is as follows (assume the incremental cost is $0, and that each buyer would by at most one
of each item): ‘ 
$300 $500
$300 3. If we price each item individually, the most proﬁt we can make is $900. . I z 2 S $1: 0 ‘
' 4. We would make less money by bundling the products compared to selling each
1nd1v1dually. (94 r M t Z L s; ,1 005 < 4'9 0'0 5. For the price response function given in problem 1, if the incremental cost is $5,
then the marginal revenue is 1002p and the marginal cost is 10. MC = CAT?) : toGZ) =io 6. If the incremental cost for an item is $0, then for the basic price optimization
problem, it is optimal to price the good so that the elasticity is greater than 1. \s‘l‘ €(‘)) 2 .791"? S: F 7. (10 points) Suppose the priceresponse function for an individual is: d(p) =100—2p In addition, we desire to use a 2part tariff. If the incremental cost is $25, how many
additional dollars will we make using the optimal price/tariff compared to pricing at
$10 and using the optimal tariff at that price? 8. (10 points) Suppose we have two fare classes with the price of full fare equal to
$500 and the price of discount fare equal to $200. If demand for the full fare is
uniformly distributed on the interval [30, 70], what should the booking limit be
for the discount fare? ' Cafe“ T") : \00
“93.2 FBI»): \’ goo : ‘° 3»  zoetbﬂ19’3°\: 5'4 L}: \901' ‘;\l 7' ”\b 9. (15 points) Suppose there are two price response functions, one for students and
one for the general pUblic for a Georgia Tech basketball game: ds(ps) =8000—110px
dg (pg) =11000—120pg There are 5000 tickets available and different prices can be charged to students and the general population. What would the optimal total margin be in this case? (assume
the incremental cost of a ticket is $0) ZCV$€>1 w WM an g, 9“ +0 M144
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.. ‘4000 ' . 0A a) ‘5‘) S\W)1uf\’€0 ”:7 V9: 695% fs’ >L.§2— n 59.3»(“09’ 9g M7” ) 3*000 gAﬁo F67 . t. I." it .1 gay/5,4,) ' Mr o—LSB (uooo ’ WARN$8) : 304 33‘0‘5 0 10. (5 points) Consider the data from problem 9. Suppose students can sell their
tickets to the general population at a cost to the student of $6 per ticket (consider this
the cost of scalping; this would be in addition to the student purchase price). Write
the complete formulation for this problem. 7% 9 a $0\ vb 9;) [>090 11.‘ (10 points) For the formulation given in 10, use the KT conditions and solve for
prices assuming that the only binding constraint is the one where students sell
their tickets to the general population (Don’t worry about determining if the
values are feasible). \L'r melaﬁgi, 0/6 (vastN/t) (v’)¢c:7") army/Yum) ‘ \ a my:
§\/) Ll nOAb‘n‘),/‘,\7) . ____7 3 7 73 ”J’s
$000  12:2 Vs — ,\(—)\ = 0 L\\.
Han ' 140 F5 ~>\(\\ :o C13
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Ma‘ﬂmj RN’fo Q3 "ﬁdai lgoOo  2319(i7$+ (a) —>\ '—__ O (”W
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”00373;,” ‘Honsf' “N0 :o ’3 Vs: €2.17.. )3? MAW. o/ 12. (10 points) For the following price response function: d(p)=abp2 a. Find the unit elastic price.
b. Find the willingness to pay at that price (Note: for both a. and b., make sure both answer are written in terms of the parameters a
and b.) . ji szz
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Mia‘3'; q .1 "a‘ E; 13. (10 points) For the following two price response functions: d1(P1) = 100 — P1
d2(P2) =120 — 2P2 If 2 tariffs and prices are being offered (p1, A1 and p2, A2). Write the constraints that
will ensure participation of both individuals. Do not use any simpliﬁcations in the
constraints, that is, write them out explicitly. gm") St (r1) 2 A! 82 (P2) 7‘ A z. , .7 2
)i( ‘00???) ZA\ ré(bo—F;K\2v~zﬁﬁ Z A; ...
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