ECO 3104

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ECO 3104

• Lecture 16

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Introduction

• So far, we have been concerned with the choices
  consumers make in deciding what products to buy
• demand side
• We shall now focus on the production decisions of
  firms
• supply side

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Introduction

• Firms must decide
• how much to produce
• given a certain output, how to produce the
  desired quantity
• will first look at how inputs are transformed
  into final product

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The Technology of Production

• Production Function
• function showing the relationship between the
  quantities of inputs used and the output produced
• indicates the highest output that a firm can
  produce for every specified combination of
  inputs, given the state of technology
• shows what is technically feasible when the firm
  makes the best possible use of its inputs
• assumes firm operates efficiently

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The Technology of Production

• General production function

• Q F(K,L,M)
• Q Output, K Capital, L Labor,
• M raw materials

• The production function for two inputs
• Q F(K,L)

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The Technology of Production
The Short Run versus the Long Run

• Short-run
• period of time in which quantities of one or more
  production factors cannot be changed
• these inputs are called fixed inputs

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The Technology of Production
The Short Run versus the Long Run

• Long-run
• Amount of time needed to make all production
  inputs variable
• actual amount of time will be different for
  different businesses

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Short-Run Production with One Variable Input
(Labor)
Amount Amount Total of Labor (L) of Capital
(K) Output (Q)

• 0 10 0
• 1 10 10
• 2 10 30
• 3 10 60
• 4 10 80
• 5 10 95
• 6 10 108
• 7 10 112
• 8 10 112
• 9 10 108
• 10 10 100

Observation with additional workers, output (Q)
increases, reaches a maximum, and then decreases
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Short-Run Production withOne Variable Input
(Labor)

• Measuring the impact of inputs on quantity
  produced
• The average product of labor (AP)

• The marginal product of labor (MP)

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Short-Run Production with One Variable Input
(Labor)
Amount Amount Total
Average Marginal of Labor (L) of Capital
(K) Output (Q) Product Product

• 0 10 0
  --- ---
• 1 10 10
  10 10
• 2 10 30
  15 20
• 3 10 60
  20 30
• 4 10 80
  20 20
• 5 10 95
  19 15
• 6 10 108
  18 13
• 7 10 112
  16 4
• 8 10 112
  14 0
• 9 10 108
  12 -4
• 10 10 100
  10 -8

Observation the marginal product of labor (MP)
increases rapidly initially and then decreases
and becomes negative
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Short-Run Production withOne Variable Input
(Labor)
The Law of Diminishing Marginal Returns

• As the use of an input increases in equal
  increments, a point will be reached at which the
  resulting additions to output decreases (i.e. MP
  declines).
• Less of fixed input per unit of variable input
• Explains a declining MP, not necessarily a
  negative one

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Short-Run Production withOne Variable Input
(Labor)

• Questions
• If there were increasing marginal returns for an
  input, what would that imply about use of the
  input?
• Would a firm want to use an input that had a
  negative marginal product?

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Long-Run Production withTwo Variable Inputs

• In long-run both K L are variable
• want to consider the tradeoffs between the use of
  inputs

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Long-Run Production with Two Variable Inputs
(Labor and Capital)
Amount Amount Total of Labor (L) of Capital
(K) Output (Q)

• 0 3 0
• 1 3 55
• 2 3 75
• 3 3 90
• 3 0 0
• 3 1 55
• 3 2 75
• 3 3 90
• 2 5 90

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Long-Run Production withTwo Variable Inputs
Diminishing Marginal Rate of Substitution

• Assume capital is 3 and labor increases from 0 to
  1 to 2 to 3.
• Notice output increases at a decreasing rate (55,
  20, 15) illustrating diminishing returns from
  labor in the short-run and long-run.

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Long-Run Production withTwo Variable Inputs
Diminishing Marginal Rate of Substitution

• Assume labor is 3 and capital increases from 0 to
  1 to 2 to 3.
• Output also increases at a decreasing rate (55,
  20, 15) due to diminishing returns from capital.

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Long-Run Production withTwo Variable Inputs

• Substituting Among Inputs
• The marginal rate of technical substitution
  (MRTS) equals

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Long-Run Production withTwo Variable Inputs

• Observations
• increasing labor from 2 to 3 results in a
  decreasing MRTS from 2 to 1
• diminishing MRTS occurs because of diminishing
  returns

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Long-Run Production withTwo Variable Inputs

• Observations
• MRTS and Marginal Productivity
• The change in output from a change in labor
  equals

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Long-Run Production withTwo Variable Inputs

• Observations
• MRTS and Marginal Productivity
• The change in output from a change in capital
  equals

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Long-Run Production withTwo Variable Inputs

• Observations
• MRTS and Marginal Productivity
• If output is constant and labor is increased,
  then

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Long-Run Production withTwo Variable Inputs
Perfect Substitutes

• Observations when inputs are perfectly
  substitutable
• the MRTS is constant
• rate at which you can trade off want input for
  another (and keep output constant) is the same no
  matter what the level of inputs

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Long-Run Production withTwo Variable Inputs
Fixed-Proportions Production Function

• Observations when inputs must be in a
  fixed-proportion
• no substitution is possible
• each output requires a specific amount of each
  input
• to increase output requires more labor and capital

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Long-Run Production withTwo Variable Inputs

• Questions
• Give an example of a fixed proportions
  production process. What is the MRTS for such a
  production technology?
• If workers receive training that makes them more
  productive, what happens to the MRTS?

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Returns to Scale

• Constant Returns to Scale
• If all inputs are doubled, output will double
• average cost is constant with increases in output

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Returns to Scale

• Increasing Returns to Scale
• If all inputs are doubled, output will more than
  double
• average cost decreases with increases in output
• Also called economies of scale

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Returns to Scale

• Decreasing Returns to Scale
• If input is doubled, the increase in output is
  less than twice as large
• average cost increases with output
• Also called diseconomies of scale

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Economies of Scope

• Economies of scope exist when the joint output of
  a single firm is greater than the output that
  could be achieved by two different firms each
  producing a single output.

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Economies of Scope

• Examples
• Dunkin Donuts and Baskin-Robbins combination
  stores
• Automobile company--cars and trucks

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Economies of Scope

• What are the advantages of joint production?
• Consider an automobile company producing cars and
  tractors
• both use capital and labor
• the firms share management resources
• both use the same labor skills and type of
  machinery.

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Economies of Scope

• Observations
• There is no direct relationship between economies
  of scope and economies of scale.
• May experience economies of scope and
  diseconomies of scale
• May have economies of scale and not have
  economies of scope

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End of Lecture 16