Chapter 18
TECHNOLOGY
18.1 Inputs and Outputs

Factors of production: inputs to production.
 Capital
goods: inputs that are themselves
produced goods.
 Financial capital: the money used to start up or
maintain a business.
 Physical capital: produced factors of production.
18.2 Describing Technological
Constraints

Production set
 The

set of all feasible combinations of inputs and outputs.
Production function
A
function that associates given inputs with the maximum
possible output.
 Gives the boundary of the production set.

Isoquant
 The
set of all possible combinations of inputs that are just
sufficient to produce a given amount of output.
18.2 Describing Technological
Constraints
18.2 Describing Technological
Constraints
18.3 Examples of Technology

Fixed Proportions: f(x1,x2)=min{x1,x2}
18.3 Examples of Technology

Perfect Substitutes: f(x1,x2) =x1+x2
18.3 Examples of Technology

Cobb-Douglas
f(x1,x2) = Ax1ax2b
18.4 Properties of Technology

Monotonicity (free disposal)
 Increase
the amount of at least one of the inputs
and output will increase.

Convexity
 Two
ways to produce y units of output: (x1, x2) and
(z1, z2),
 their weighted average will produce at least y units
of output.
18.4 Properties of Technology
18.5 The Marginal Product

Marginal product of factor 1:
f ( x1  x1 , x2 )  f ( x1 , x2 )
y
MP1  lim
 lim
x1  0 x
x1  0
x1
1
f ( x1 , x2 )

x1

Similar to the concept of marginal utility.
18.6 The Technical Rate of Substitution

Technical rate of substitution
 The
rate at which the firm has to substitute one
input for another in order to keep output constant.
f
f
dy 
dx1 
dx2
x1
x2
dx2
f
TRS12 

x1
dx1
 Similar
MP1
f

x2
MP2
to the concept of marginal rate of
substitution.
18.7 Diminishing Marginal Product

Law of diminishing marginal product
 The
marginal product of a factor will diminish as
we get more and more of that factor.
 The law of diminishing marginal product applies
only when all other inputs are being held fixed.
18.8 Diminishing Technical Rate of
Substitution

Diminishing Technical Rate of Substitution
 As
we increase the amount of factor 1, and adjust
factor 2 so as to stay on the same isoquant, the
technical rate of substitution declines.
 Diminishing marginal product implies diminishing
technical rate of substitution.
 Diminishing technical rate of substitution does not
necessarily imply diminishing marginal product.
18.9 The Long Run and the Short Run


In the short run, there
will be some factors of
production that are fixed
at predetermined levels.
In the long run, all the
factors of production
can be varied.
18.10 Return to Scale

Constant returns to scale
tf(x1, x2) =f(tx1, tx2)

Increasing returns to scale
tf(x1, x2) < f(tx1, tx2) for all t>1

Decreasing returns to scale
tf(x1, x2) > f(tx1, tx2) for all t>1