Techniques and Isoquants
© 1998 by Peter Berck
Definitions
 Output Q; specific amount Q*
 Inputs x= (x1…xn)
 If using inputs x results in output Q*, then x
is a technique to make Q*.

1 brisket, 1 pan, 3 hours of oven services at
375, 1 large sheet foil, 4 coarsely sliced onions,
salt, pepper, paprika are a technique for
making pot roast. (Esther Lipow’s (z’’l) recipe.)
Efficient
 If x is less than or equal to y in every
dimension and x and y both produce Q*,
then y is not efficient.

xi  yi for every i
y
input 2
x
input 1
Isoquant
 Let Q* be some specific output like 4 units
 All efficient input combinations that
produce Q* are the Q*th isoquant
Corn Yield in lbs.
Lbs P2O5
40
80
120
160
Lbs N
80
82.3
95.9
102.4
105.4
120
86.7
102.1
110.1
114.2
160
88.5
105.4
114.5
119.6
200
88.6
106.8
116.9
122.9
Rice Milling
 Why mill rice at all?
 What is wrong with white rice from a
nutritional point of view?
Techniques for Milling Rice
Technique Hand
Pound
Investment 0
Laborers
45.83
Technique Large
Mill
Investment 29,675
Laborers
5.25
Notes:
Small
Mill
9,359
13.95
Small
Bulk
44,335
2.64
Large
Bulk
77,835
1.17
Source P. Timmer Choice of Technique in Rice Milling in Java. Techniques
to produce Rp 10 Million in Value added . Investment in USD.
Milling
 Why is this in value added rather than tons?

VA = Revenue – Cost of materials
 How do you convert capital costs into a
yearly equivalent?


interest
depreciation
Investment Costs
Isoquant for Rice Milling
90000
80000
70000
60000
50000
40000
30000
20000
10000
0
0
10
20
30
Laborers
40
50
What Technique Minimizes Cost
 Need prices for labor and investment
 Price of investment is 1. Plant is assumed
to last 50 years with no maintenance (urrg.)
 Price of 50 years worth of labor is
calculated as the size of bank account (with
24% interest) that would pay a laborer $200
per year for 50 years. It is $833 per laborer
Interest Rates
 Is 24% per year a high interest rate for a
developing country?
 Are there investment clubs in the US that
charge their members 2.5% per month?
Outlay or Isocost Line
 All input combinations of K, investment,
and L, laborers, that cost amount E, an
unknown, are given by
 E = K + $833 L
 More generally:
 E = Pk K + PL L
About equi-cost or outlay lines
 E = Pk K + PL L
 K = E/Pk - L PL/PK



So varying E (which is not known) gives a
family of parallel equi-outlay lines
The cost of every input bundle on the line is
the vertical intercept times PK.
When PK conveniently equals one, the vertical
intercept is the cost of every bundle on the line
Which line?
 The least cost way of producing output Q*
is found by finding the equi-cost line
tangent to the Q*th isoquant.
 C(Q*) is the cost of any input bundle on
that line
 The input bundle (or technique) at the
tangency is the least cost way to produce
Q*
Investment Costs
Small Rice Mill Costs Least
90000
80000
70000
60000
50000
40000
30000
20000
10000
0
Small Mill
Hand
0
10
20
30
Laborers
40
50
Story:




Widows used to hand pound rice.
Now SRM’s are used instead.
How is this bad?
How is this good?
Technology Transfer
 In US, build small dam with tractors,
backhoes, dump trucks, very few workers
 In India, the same dam would be built by
using many many laborers and hand tools.


These are two efficient techniques for building
a dam.
Why would we say that the US technique, if
used in India was inappropriate tech. transfer?