14.01 Spring2013 Exam1 Solutions
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7/21/2019 14.01 Spring2013 Exam1 Solutions
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L S U(L, S) =
2L + S
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7/21/2019 14.01 Spring2013 Exam1 Solutions
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U(x) =(x3)2 + 9
x > 3 dUdx
Qs = 2p2 Qd= 7p
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7/21/2019 14.01 Spring2013 Exam1 Solutions
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C
B
U(C, B) = max{C, B} M
M/3
C B
Qd = 100 P2 P = 10
QdP PQ
23
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(2p)p100p2 2/3 p= 5
B A U(B, A) = 12
B+ 2A
3B
dUdB =
6B
dUdA = 2
3B
= 1 B
B = 9
M M dAdM = 1
M >9
F C P U(F, C) = F
(C)
P= $8
F2C.
14 C= 2F
8F+ 4F= 48 F = 4 C= 8
P
F = 2C 4C+2C= 48 C= 8 F = 16
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321/3 8 4
F2C 1 =1
U(4, 8) = 4
8 F2C =1,F = 2C 4
8 = 2C
C
2
8 = C3/2, C = 321/3
C 321/3
8
P = 2 (2)(4) + (2)(8) = $24 P= 2 4C+ 2C = 24 C= 4 F = 8 48
=4
M A G
U(A, G) = ln(A) + 2ln(G) ln PA
PG
PAA + PGG= M
G2A
dUdA =
1A
dUdG =
2G
M3PA
G2A =
PAPG
G = 2APAPG
2PAA + PAA= M A= M3PA
G = 2M3PG G
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M >0 PA PG
G= 0 G A= 0
A G
C T Uj(Cj , Tj) = Cj + Tj Um(Cm, Tm) = 2Cm+ Tm pC
pT = 1
pC
pC= $1.50
203
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101.50 =
203
pC = $1.50 pC = $0.50
1103
1010 = 0 (2)(203 )(1.50)(203 ) = 103 ) 20 (0.50)(20)+(2)(20)
(0.50)(20) =40 40 103 = 1103
U(W) = W
d2UdW2
