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Production Theory 1

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Production Theory 1

- 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

- 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.

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

- The collection of all feasible production plans is the 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

One input

Output Level

y’

The technologyset

y”

x’

x

Input Level

One input

Output Level

Technicallyefficient plans

y’

The technologyset

Technicallyinefficientplans

y”

x’

x

Input Level

- 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

- 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.

- The complete collection of isoquants is the isoquant map.
- The isoquant map is equivalent to the production function.
- Example

K

Y=40

Y=20

L

- Properties
Y/K>0, Y/L>0

2Y/K2<0,2Y/L2<0

Diminishing marginal product

(Diminishing marginal utility)

x2

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

x1

- 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.

then the marginal product of input 1 is

then the marginal product of input 1 is

then the marginal product of input 1 is

and the marginal product of input 2 is

then the marginal product of input 1 is

and the marginal product of input 2 is

- The marginal product of input i is diminishing if it becomes smaller as the level of input i increases. That is, if

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

- How is a technical rate-of-substitution computed?

- 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

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

which rearranges to

or

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.