Production

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Production

• Outline
• Introduction to the production function
• A production function for auto parts
• Optimal input use
• Economies of scale
• Least-cost production

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The production function

• Production is the process of transforming inputs
  into semi-finished articles (e.g., camshafts and
  windshields) and finished goods (e.g., sedans and
  passenger trucks).
• The production function indicates that maximum
  level of output the firm can produce for any
  combination of inputs.

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General description of a production function
Let Q F (M, L, K)
6.1 Where Q is the quantity of output produced
per unit of time (measured in units, tons,
bushels, square yards, etc.), M is quantity of
materials used in production, L is the quantity
of labor employed, and K is the quantity of
capital employed in production.
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Technical efficiency
The production function indicates the maximum
output that can be obtained from a given
combination of inputsthat is, we assume the firm
is technically efficient.
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A production function for auto parts
Consider a multi-product firm that supplies parts
to major U.S. auto manufacturers. Its production
function is given by Let Q F(L, K) Where Q is
the quantity of specialty parts produced per day,
L is the number of workers employed per day, and
K is plant size (measured in thousands of square
feet).
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This table 6.1 shows the quantity of output
that can be obtained from various combinations of
plant size and labor
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The short run
The short run refers to the period of time in
which one or more of the firms inputs is
fixedthat is, cannot be varied

• Inputs that cannot be varied in the short run are
  called fixed inputs.
• Inputs that can vary are called (not
  surprisingly) variable inputs

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The long run
The long run is the period of time sufficiently
long to allow the firm to vary all inputse.g.,
plant size, number of trucks, or number of apple
trees.
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Marginal product

• Marginal product is the additional (or extra)
  output resulting from the employment of one more
  unit of a variable input , holding all other
  inputs constant.
• In our example, the marginal product of labor
  (MPL) is the extra output of auto parts realized
  by employing one additional worker, holding plant
  size constant

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Production of specialty parts, assuming a plant
size of 10,000 square feet
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Law of diminishing returns
As units of a variable input are added (with
all other inputs held constant), a point is
reached where additional units will add
successively decreasing increments to total
outputthat is, marginal product will begin to
decline.
Notice that, after 40 workers are employed,
marginal product begins to decline
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The total product of labor
500
400
300
200
100
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
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The marginal product of labor when plant size is
10,000 square feet
Marginal Product
5.0
4.0
3.0
2.0
1.0
0
10
20
30
40
50
60
70
80
90
100
110
130
140
120
1.0
2.0
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Optimal use of an input
By hiring an additional unit of labor, the firm
is adding to its costsbut it is also adding to
its output and thus revenues.
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Marginal revenue product of labor (MRPL)
The marginal revenue product of labor (MRPL) is
given by MRPL (MR)(MPL)
6.2 Where MR marginal revenuethat is, the
additional (extra) revenue realized by selling
one more unit. Example If MPL is 5 units, and
the firm can sell additional units for 6 each,
then MRPL (MR)(MPL) (5)(6) 30
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Marginal cost of labor (MCL)
What additional cost does the firm incur (wages,
benefits, payroll taxes, etc.) by hiring one more
worker?
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?-maximizing rule of thumb
The firm should employ additional units of the
variable input (labor) up to the point where MRPL
MCL1
1In terms of calculus, we have MRPL
(MR)(MPL) (dR/dQ)(dQ/dL) and MCL dC/dL
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Example

• Example
• The firm has estimated that the cost of hiring
  an additional worker is equal to 160 per day,
  that is, MCL PL 160.
• Assume the firm can sell all the parts it wants
  at a price of 40. Hence, MR 40
• Thus the MRPL (MR)(MPL) (40)(MPL)

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Problem
Let the production function be given by Q 120L
L2 The cost function is given by C 58
30L The firm can sell an unlimited amount of
output at a price equal to 3.75 per unit

1. How many workers should the firm hire?
2. How many units should the firm produce?

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Production in the long run

• The scale of a firms operation denotes the
  levels of all the firms inputs.
• A change in scale refers to a given percentage
  change in all the firms inputse.g., labor,
  materials, and capital.
• If we say the scale of production has increased
  by 15 percent, we mean the firm has increased
  its employment of all inputs by 15 percent.

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Returns to scale
Returns to scale measure the percentage change in
output resulting from a given percentage change
in inputs (or scale)
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3 cases

1. Constant returns to scale 10 percent increase in
   all inputs results in a 10 percent increase in
   output.
2. Increasing returns to scale 10 percent increase
   in all inputs results in a more than 10 percent
   increase in output.
3. Decreasing returns to scale 10 percent increase
   in all inputs results in a less than 10 percent
   increase in output.

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Sources of increasing returns

1. Specialization of plant and equipmentExampleLarg
   e scale production in furniture manufacturing
   allows for application of specialized equipment
   in metal fabrication, painting, upholstery, and
   materials handling.
2. Economies of increased dimensionsExample
   Doubling the circumference of pipeline results in
   a fourfold increase in cross sectional area, and
   hence more than doubling of capacity, measured in
   gallons per day.
3. Economies of massed reserves.Example A factory
   with one stamping machine needs to have spare 100
   parts in inventory to be prepared for
   breakdowndoes a factory with 20 machines need to
   have 2,000 spare parts on hand?