chapter 18 technology. 18.1 inputs and outputs factors of production: inputs to production. capital...

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