Download Intermediate Microeconomics March 24, 2004

Intermediate Microeconomics
Due:
March 24, 2004
March 31, 2004
Prof. Li-Chen Hsu
Answer Key to Problem Set #6
1.
(a) False.  
dq p
p
 3mp 2 
 1 which is a constant. As the result, absolute
dp q
3m / p
value of the price elasticity of demand is unchanged as price increases.
1
1
(b) False. q  20  2 p  p  10  q  R  pq  10q  q 2
2
2
 MR  10  q  10  20  2 p  10  2 p  MR / p 
10
 2 . As the result, the
p
ratio of marginal revenue to price increases as price increases.
(c) False. consumer 1: 11  20  3x  x1  3
consumer 2: 11  16  x  x2  5 . The total quantity demanded by the two
consumers is 8 when the price is 11.
(d) False. If a good has an elasticity of demand greater than 1 in absolute value we say
that it has an elastic demand. We cannot know the elasticity of demand according to
the questions, so we cannot conclude that the demand for cucumbers is elastic.
(e) True. The weighted average of the income elasticities must be 1, so if one good has a
negative income elasticity, the other good must have an elasticity greater than 1 to
get the average to be 1.
2.
(a) q( p)  130  p / 5  p / 5  130  q  p(q)  650  5q .
(b) R(q)  pq  650q  5q 2
dR(q)
max R 
 0  650  10q  0  q*  65  p*  650  5  65  325 .
dq
(c)  
3.
dq p
1 325

 1 .
dp q
5 65
Q  Qs  Qa  Qh  (520  230  200)  (13  1  5) P  950  19P

.
dq p
P
 19
 1  38P  950  P  25 .
dp q
950  19 P
4.
(a) 48  518  5q  q  94   
dq p
1 48
48
.


dp q
5 94
470
20036sol-1
.
5.
(b)  
dq p
p
 2.5 1000 p 3.5 m2
 2.5(m  60, p  45) .
dp q
1000 p 2.5 m2
(c)  
dq p
p
2 p
38
 2( p  1)3


 1.9 .
2
dp q
( p  1)
( p  1) 20
(d)  
dq p
20
 1000  (undefined ) .
dp q
0
Q  2500  400 p 
R  pQ  2.5Q 
 MR  2.5 
m
m
15000
1
 400 p  2500   Q  2500 
 Q  p  2.5 
Q
10
10
10
400
1 2
1
15000
Q  MR  2.5 
Q and Q  2500  400(1.5) 
 400
400
200
10
1
400  0.5 .
200
6.
(a) PD (qt* )  t  PS (qt* )  305  5qt*  54  8  4qt*  qt*  27 .
(b) PD (q* )  PS (q* )  305  5q*  8  4q*  q*  33 , PDt  305  5  qt*  305  135  170
PSt  8  4qt*  8  108  116 , DWL 
(170  116)  (33  27)
 162 .
2
7.
qD  960  7  40  680, qS  160  3  40  280  excess demand  680  280  400 .
8.
qD  200  140  60, qS  50  0.5 140  120  excess supply  120  60  60 , so the
government costs 60  $140  $8400 to buy the corn.
20036sol-2