Lecture # 11aLecture # 11a

Inputs and Production Inputs and Production FunctionsFunctions

(conclusion)(conclusion)

Lecturer: Martin ParedesLecturer: Martin Paredes

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1. Returns to Scale2. Technological Progress

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Definition: Returns to scale is the concept that tells us the percentage increase in output when all inputs are increased by a given percentage.

Returns to scale = % Output .% ALL Inputs

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Suppose we increase ALL inputs by a factor

Suppose that, as a result, output increases by a factor .

Then:1. If > ==>Increasing returns to

scale2. If = ==>Constant returns to

scale3. If < ==>Decreasing returns to

scale.

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Example: Returns to Scale

L

K

Q0

0 L0

K0 •

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Example: Returns to Scale

L

K

Q0

0 L0 L0

K0

K0 •

•

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Example: Returns to Scale

L

K

Q0

Q0

0 L0 L0

K0

K0 •

•

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Example: Returns to Scale

L

K

Q0

Q0

0 L0 L0

K0

K0 •

•

If > , then we have Increasing returns to scale

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Example: Returns to Scale

L

K

Q0

Q0

0 L0 L0

K0

K0 •

•

If = , then we have Constant returns to scale

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Example: Returns to Scale

L

K

Q0

Q0

0 L0 L0

K0

K0 •

•

If < , then we have Decreasing returns to scale

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Notes: When a production process exhibits

increasing returns to scale, there are costs advantages from large-scale operation.

Returns to scale need not be the same at different levels of production

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Note: Substantial difference between returns to

scale and marginal product: Returns to scale: All inputs increase in

same proportion Marginal product: Only one input

increases, while the others remain constant

Therefore, it is possible to have diminishing marginal returns and increasing/constant returns to scale.

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Example: Returns to scale

Suppose a Cobb-Douglas utility function: Q1 = AL1

K1

==> Q2 = A(L1)(K1) = + AL1

K1

= +Q1

Hence, returns to scale depends on the value of + .

If + = 1 ==> Constant returns to scale (CRS)If + < 1 ==> Decreasing returns to scale (DRS)If + > 1 ==> Increasing returns to scale (IRS)

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Definition: Technological progress shifts the production function by allowing the firm to:

1. Produce more output from a given combination of inputs, or

2. Produce the same output with fewer inputs.

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Three categories:1. Neutral technological progress2. Labor-saving technological progress 3. Capital-saving technological progress

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Definition: Neutral technological progress shifts the isoquant inwards, but leaves the MRTSL,K unchanged along any ray from the origin

In other words, for any given capital-labor ratio, the MRTSL,K remains unaffected.

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K/L

Q = 100 before

Example: Neutral technological progressK

L

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K/L

Q = 100 before

Q = 100 after

Example: Neutral technological progressK

L

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K/LMRTS remains same

Q = 100 before

Q = 100 after

Example: Neutral technological progressK

L

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Definition: Labor-saving technological progress results in a decrease in the MRTSL,K along any ray from the origin

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Example: Labor Saving Technological Progress

K/L

Q = 100 before

K

L

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Example: Labor Saving Technological Progress

K/L

Q = 100 before

Q = 100 after

K

L

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Example: Labor Saving Technological Progress

K/LMRTS gets smaller

Q = 100 before

Q = 100 after

K

L

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Definition: Capital-saving technological progress results in an increase in the MRTSL,K along any ray from the origin

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K/L

Example: Capital-saving technological progressK

L

Q = 100 before

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K/L

Example: Capital-saving technological progressK

L

Q = 100 before

Q = 100 after

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K/L

MRTS gets larger

Q = 100 before

Q = 100 after

Example: Capital-saving technological progressK

L

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Example: Technological Progress

Before: Q = 500 (L + 3K)

MRTSL,K = MPL = 500 = 1 MPK 15003

After: Q = 1000 (0.5L + 3K)

MRTSL,K = MPL = 500 = 1 MPK 30006

Since MRTSL,K has decreased, technological progress is labor-saving

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1. Production function is analogous to utility function and is analyzed by many of the same tools.

2. One of the main differences is that the production function is much easier to infer/measure than the utility function. Both engineering and econometric techniques can be used to do so.

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3. Technological progress shifts the production function by allowing the firm to achieve more output from a given combination of inputs (or the same output with fewer inputs).

4. Returns to scale is a long run concept: It refers to the percentage change in output when all inputs are increased a given percentage.

5. The production function is cardinal, not ordinal