Question I
a
8C 20115 r 75
zor 8C 375
b.cn
5 slope 告 ⼆ ⼀ 梁⼆ ⼀三5
i
ii
I5 ⼦
c maxrist208⼗8C 375
⼟ rc2 ⼊1375 2or 8C
Fae C2 20⼊ 0 2rc 8⼊ ⼆ 0
We have Tangency Condition Éc ⼆号 c 5r
Combine with 375 20r 18C
We have 375 2or 4or 6or r
5
6.25
The labor hours are 15⼀ 平 云5 8.75
do
labor 0
When leisure is r 15 C 85
1 8C2 ⼊ 15w 75 wr 8C
FO.C c2⼀⼊w 0 zrc 8⼊ 0 C ⼆ 华⼦
put r 15 and c 85 in 85 5w w 5
answer w E LO Ʃ5
Intuition
When O labor is supplied the consumer picks 15셈 85
It must be true that the highest IC is at 115셈 85
The Slope of IC should be more in value than the
slope f BC
__ ˋ
___
ii
i
In this case 告 É w 三
Otherwise the solution envol.es less than 15 hours leisure
Q2
. f(x , 4) =xxi We = 4 Wa = 1 p = 100
a
.
Fix 22 =1 f(xe , 1) =x
.
5
i) it = Pf(r+2) = Wix-wats
= 100 .xie?
"
- 4x1-1 .i &
= 100x5 - 4x1 = 1
ii) mac 100x5 -421-1
x1
Fod : 100 . 0
.
5450
.5-4 = 0 or ④
VMPs=
x* = 156 . 25
b) To find the firm's return to scale we need to compute
flure , Krez) = Ikx1)0
* Ikezion
0 . 5 t 0 . 1 0 . 5 0 . 1
= K x - x2 ⑥
= k00 f(x , 22)
Since if K31 , then K**K we have that
flksen , Kx2) which implies that the firm has decreasing return to scale.
2) mas 100 x2" - 401-x2
21 , 42
FOC : 100 0
.540
.5 - 4 = 0 ⑧
100 · 8 .1xx. -1 = 0
=> 100 · 0 .52
0
.50 .
1
x2 = 4
0
.
5
- 0
. 9
100 · 8 . 12142
0.5
-
t
x2= x
Plugging this into the second FOC
10x(01 =>r4.(0:
x: (0 = 10 = n = (10 = 522 . 45
*
x1 = 522 . 45
AlsoOK to use the alternative method given in
the
appendixe to the profit maximization chapter
.
x = 5
. 522 . 45 = 417
. %6




Question 5
r
Qs
40
es
QD
管 is
16 72
Since theworld price is 4 the firm cannot sell in a
rice that is higher than 4
At p 4 QD 80 2P 72
Qs 4p 16
so 16unitsareproduced and 56 units are imported
CS 72X36X'Ʃ ⼆ 1296
ps 4x16x'Ʃ 32
b After policy change price increase to 6
Qp 80 2p 18
Qs 4p 24 Import I Qp Qs 44
T Ixt 2 44 88
c r
i谱 iii
16 24
DWL 8 2XÍ 4ㄨ2ㄨƩ 12
New SS 1296 32 12 1316

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