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Production Theory 1

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# Production Theory 1 - PowerPoint PPT Presentation

Production Theory 1. Short-Run v. Long-Run. Fixed input/factor of production: quantity of input is fixed regardless of required output level, e.g. capital or specialized labour Variable input/factor of production: quantity of input used depends on the level of output

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Short-Run v. Long-Run
• Fixed input/factor of production: quantity of input is fixed regardless of required output level, e.g. capital or specialized labour
• Variable input/factor of production: quantity of input used depends on the level of output
• Short run: at least one input/factor is fixed
• Long run: all inputs/factors are variable
Production Function
• A technology is a process by which inputs (e.g. labour and capital) are converted into output.
• The output level is denoted by y.
• The technology’s production function states the maximum amount of output possible from an input bundle.
Production Function

One input

Output Level

y = f(x) is the

production

function

y’

y’ = f(x’) is the maximum output level obtainable from x’ input units.

x’

x

Input Level

Technology Set
• The collection of all feasible production plans is the technology set.
Technology Set

One input

Output Level

y = f(x) is the

production

function.

y’

y”

y” = f(x’) is an output level that is feasible from x’ input units.

x’

x

Input Level

Technology Set

One input

Output Level

y’

The technologyset

y”

x’

x

Input Level

Technology Set

One input

Output Level

Technicallyefficient plans

y’

The technologyset

Technicallyinefficientplans

y”

x’

x

Input Level

Technology: Multiple Inputs
• What does a technology look like when there is more than one input?
• The two input case: Input levels are x1 and x2. Output level is y.
• Example of production function is
PREVIEW: ISOQUANT
• An isoquant is the set of all combinations of inputs 1 and 2 that are just sufficient to produce a given amount of output.
• The slope of the isoquant = the marginal rate of technical substitution (MRTS) = the technical rate of substitution (TRS)
• MRTS (TRS): The number of units of K that we can dispose of if one more unit of L becomes available while remaining on the original isoquant.
Technologies with Multiple Inputs
• The complete collection of isoquants is the isoquant map.
• The isoquant map is equivalent to the production function.
• Example
Isoquants with Two Inputs
• Properties

Y/K>0, Y/L>0

2Y/K2<0, 2Y/L2<0

Diminishing marginal product

(Diminishing marginal utility)

Cobb-Douglas Technology

x2

All isoquants are hyperbolic,asymptoting to, but nevertouching any axis.

x1

Marginal (Physical) Product
• The marginal product of input i is the rate-of-change of the output level as the level of input i changes, holding all other input levels fixed.
Marginal (Physical) Product

then the marginal product of input 1 is

Marginal (Physical) Product

then the marginal product of input 1 is

Marginal (Physical) Product

then the marginal product of input 1 is

and the marginal product of input 2 is

Marginal (Physical) Product

then the marginal product of input 1 is

and the marginal product of input 2 is

Marginal (Physical) Product
• The marginal product of input i is diminishing if it becomes smaller as the level of input i increases. That is, if
Technical Rate-of-Substitution

The slope is the rate at which input 2 must be given up as input 1’s level is increased so as not to change the output level. The slope of an isoquant is its technical rate-of-substitution.

x2

yº100

x1

Technical Rate-of-Substitution
• How is a technical rate-of-substitution computed?
Technical Rate-of-Substitution
• How is a technical rate-of-substitution computed?
• The production function is
• A small change (dx1, dx2) in the input bundle causes a change to the output level of
Technical Rate-of-Substitution

Along an individual isoquant, dy = 0, therefore the changes dx1 and dx2 must satisfy the following,

Technical Rate-of-Substitution

which rearranges to

or

Technical Rate-of-Substitution

is the rate at which input 2 must be givenup as input 1 increases so as to keepthe output level constant. It is the slopeof the isoquant = MRTS = TRS.