# Презентация на тему Lecture # 09. Inputs and Production Functions

Презентация на тему Презентация на тему Lecture # 09. Inputs and Production Functions, предмет презентации: Экономика. Этот материал содержит 42 слайдов. Красочные слайды и илюстрации помогут Вам заинтересовать свою аудиторию. Для просмотра воспользуйтесь проигрывателем, если материал оказался полезным для Вас - поделитесь им с друзьями с помощью социальных кнопок и добавьте наш сайт презентаций ThePresentation.ru в закладки!

## Слайды и текст этой презентации

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Lecture # 09

Inputs and Production Functions

Lecturer: Martin Paredes

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Outline

The Production Function
Marginal and Average Products
Isoquants
Marginal Rate of Technical Substitution
Returns to Scale
Some Special Functional Forms
Technological Progress

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Definitions

Inputs or factors of production are productive resources that firms use to manufacture goods and services.
Example: labor, land, capital equipment…
The firm’s output is the amount of goods and services produced by the firm.

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Definitions

Production transforms a set of inputs into a set of outputs
Technology determines the quantity of output that is feasible to attain for a given set of inputs.

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Definitions

The production function tells us the maximum possible output that can be attained by the firm for any given quantity of inputs.

Q = F(L,K,T,M,…)

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Definitions

A technically efficient firm is attaining the maximum possible output from its inputs (using whatever technology is appropriate)
The firm’s production set is the set of all feasible points, including:
The production function (efficient point)
The inefficient points below the production function

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Example: The Production Function and Technical Efficiency

L

Q

C

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Example: The Production Function and Technical Efficiency

L

Q

C

D

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Example: The Production Function and Technical Efficiency

Q = f(L)

L

Q

C

D

Production Function

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Example: The Production Function and Technical Efficiency

Q = f(L)

L

Q

C

D

A

B

Production Function

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Example: The Production Function and Technical Efficiency

Q = f(L)

L

Q

C

D

A

B

Production Set

Production Function

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Notes:
The variables in the production function are flows (amount of input per unit of time), not stocks (the absolute quantity of the input).
Capital refers to physical capital (goods that are themselves produced goods) and not financial capital (money required to start or maintain production).

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Comparison between production function and utility function

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Comparison between production function and utility function

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Marginal Product

Definition: The marginal product of an input is the change in output that results from a small change in an input

E.g.: MPL = ∂Q MPK = ∂Q
∂L ∂K

It assumes the levels of all other inputs are held constant.

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Example: Suppose Q = K0.5L0.5

Then: MPL = ∂Q = 0.5 K0.5
∂L L0.5

MPK = ∂Q = 0.5 L0.5
∂K K0.5

Marginal Product

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Average Product

Definition: The average product of an input is equal to the total output to be produced divided by the quantity of the input that is used in its production

E.g.: APL = Q APK = Q
L K

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Example: Suppose Q = K0.5L0.5

Then: APL = Q = K0.5L0.5 = K0.5
L L L0.5

APK = Q = K0.5L0.5 = L0.5
K K K0.5

Average Product

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Law of Diminishing Marginal Returns

Definition: The law of diminishing marginal returns states that the marginal product (eventually) declines as the quantity used of a single input increases.

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Q

L

Q= F(L,K0)

Example: Total and Marginal Product

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Q

L

MPL maximized

Q= F(L,K0)

Example: Total and Marginal Product

Increasing marginal returns

Diminishing marginal returns

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Q

L

MPL = 0 when
TP maximized

Q= F(L,K0)

Example: Total and Marginal Product

Diminishing total returns

Increasing total returns

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Example: Total and Marginal Product

L

MPL

Q

L

MPL maximized

TPL maximized where
MPL is zero. TPL falls
where MPL is negative;
TPL rises where MPL is
positive.

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Marginal and Average Products

There is a systematic relationship between average product and marginal product.
This relationship holds for any comparison between any marginal magnitude with the average magnitude.

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Marginal and Average Products

When marginal product is greater than average product, average product is increasing.
E.g., if MPL > APL , APL increases in L.
When marginal product is less than average product, average product is decreasing.
E.g., if MPL < APL, APL decreases in L.

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Example: Average and Marginal Products

L

APL
MPL

MPL maximized

APL maximized

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Example: Total, Average and Marginal Products

L

APL
MPL

Q

L

MPL maximized

APL maximized

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Isoquants

Definition: An isoquant is a representation of all the combinations of inputs (labor and capital) that allow that firm to produce a given quantity of output.

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Example: Isoquants

L

K

Q = 10

0

Slope=dK/dL

L

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L

Q = 10

Q = 20

All combinations of (L,K) along the
isoquant produce 20 units of output.

0

Slope=dK/dL

K

Example: Isoquants

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Isoquants

Example: Suppose Q = K0.5L0.5

For Q = 20 => 20 = K0.5L0.5
=> 400 = KL
=> K = 400/L

For Q = Q0 => K = (Q0)2 /L

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Definition: The marginal rate of technical substitution measures the rate at which the firm can substitute a little more of an input for a little less of another input, in order to produce the same output as before.

Marginal Rate Of Technical Substitution

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Marginal Rate Of Technical Substitution

Alternative Definition : It is the negative of the slope of the isoquant:
MRTSL,K = — dK (for a constant level of
dL output)

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Marginal Product and the Marginal Rate of Technical Substitution

We can express the MRTS as a ratio of the marginal products of the inputs in that basket
Using differentials, along a particular isoquant:
MPL . dL + MPK . dK = dQ = 0
Solving:
MPL = _ dK = MRTSL,K
MPK dL

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Marginal Product and the Marginal Rate of Technical Substitution

Notes:
If we have diminishing marginal returns, we also have a diminishing marginal rate of technical substitution.
In other words, the marginal rate of technical substitution of labour for capital diminishes as the quantity of labour increases along an isoquant.

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Marginal Product and the Marginal Rate of Technical Substitution

Notes:
If both marginal products are positive, the slope of the isoquant is negative
For many production functions, marginal products eventually become negative. Then:
MRTS < 0
We reach an uneconomic region of production

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Example: The Economic and the Uneconomic Regions of Production

L

K

Q = 10

Q = 20

0

Isoquants

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Example: The Economic and the Uneconomic Regions of Production

L

K

Q = 10

Q = 20

0

B

A

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Example: The Economic and the Uneconomic Regions of Production

L

K

Q = 10

Q = 20

0

MPL < 0

B

A

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Example: The Economic and the Uneconomic Regions of Production

L

K

Q = 10

Q = 20

0

MPK < 0

MPL < 0

B

A

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Example: The Economic and the Uneconomic Regions of Production

L

K

Q = 10

Q = 20

0

MPK < 0

MPL < 0

B

A

Uneconomic Region

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Example: The Economic and the Uneconomic Regions of Production

L

K

Q = 10

Q = 20

0

MPK < 0

MPL < 0

B

A

Uneconomic Region

Economic Region

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