1. A new type of technology has been invented that allows the widget factory to
ID: 1131858 • Letter: 1
Question
1. A new type of technology has been invented that allows the widget factory to produce widgets using capital instead of labor. The daily production choices faced by the firm are now:
Workers
Output
MPL
Capital (units)
Output
MPK
0
0
-
0
0
-
1
100
a
1
50
f
2
150
b
2
95
g
3
190
c
3
135
h
4
225
d
4
170
i
5
250
e
5
200
j
A). Fill in a-j.
B). If the daily wage is $100 per worker and the cost of a unit of capital per day is $60, how many workers and how many units of capital should the firm utilize in order to minimize the cost of producing 350 widgets?
Workers
Output
MPL
Capital (units)
Output
MPK
0
0
-
0
0
-
1
100
a
1
50
f
2
150
b
2
95
g
3
190
c
3
135
h
4
225
d
4
170
i
5
250
e
5
200
j
Explanation / Answer
Answer
MPL = Change in Output per unit change in labor and MPK = Change in Output per unit change in capital.
B)
Think like that cost minimizes, w/MPL = r/MPK. When w/MPL is lesser than r/MPK we use L i.e. worker otherwise Capital. Here w = 100 and r = 60.
When worker = 1 then 100/MPL = 100/100 = 1. and when Capital = 1 then 60/50 = 1.2. Hence we will use Worker. Next If worker = 2 them w/MPL = 100/50 = 2(> 1.2) hence we will use 1 unit of Capital.Till now wehave employed 1 unit of labor and 1 unit of capital and output produced = 150 If Capital = 2 then 60/45 (<2) hence we again use 1 unit of capital. So we have used 2 unit of capital and 1 unit of labor and output produced = 195. If capital = 3 then 60/40(1.5) Now again we use one more unit of capital. continiung like that when we use 5units of capital r/MPK = 2(=100/MPL when L =2). So if we employ 5 units of Capital and 2 units of labor. Total Output produces = 200+150 = 350.
Hence r/MPK = w/MPL when K = 5 and L = 2 and output produced = 200 + 150 = 350
Hence to minimize 350 widgets, we require 5 units of capital and 2 units of labor.
So, L = 2 and K = 5.
Workers Output MPL Capital Output MPK 0 0 - 0 0 - 1 100 100 1 50 50 2 150 50 2 95 45 3 190 40 3 135 40 4 225 35 4 170 35 5 250 25 5 200 30Related Questions
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