chapter 18 technology. 18.1 inputs and outputs factors of production: inputs to production. capital...
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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 s
ufficient to produce a given amount of output.
18.2 Describing Technological Constraints
input
output
Production set
y=f(x)
18.2 Describing Technological Constraints
18.3 Examples of Technology
Fixed Proportionsf(x1,x2)=min{x1,x2}
x1
x2
isoquants
18.3 Examples of Technology
Perfect Substitutes f(x1,x2) =x1+x2
x1
x2
isoquants
18.3 Examples of Technology
Cobb-Douglas
f(x1,x2) = Ax1ax2
b
18.4 Properties of Technology
Monotonicity (free disposal)Increase the amount of at least one of the inputs an
d 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
x1
x2
isoquant
18.5 The Marginal Product
Marginal product of factor 1:
1 1
1 1 2 1 21
0 01 1
1 2
1
( , ) ( , )lim lim
( , )
x x
f x x x f x xyMP
x x
f x x
x
Similar to the concept of marginal utility.
18.6 The Technical Rate of Substitution
Technical rate of substitutionThe rate at which the firm has to substitute one
input for another in order to keep output constant.
1 21 2
f fdy dx dx
x x
2 112
1 21 2
dx MPf fTRS
x xdx MP
Similar to the concept of marginal rate of substitution.
18.7 Diminishing Marginal Product
Law of diminishing marginal productThe 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.
x1
yY=f(x1, x2’)
18.10 Return to Scale
Constant returns to scaletf(x1, x2) =f(tx1, tx2)
Increasing returns to scaletf(x1, x2) < f(tx1, tx2) for all t>1
Decreasing returns to scaletf(x1, x2) > f(tx1, tx2) for all t>1