Chapter 5: Production and Cost

1
Chapter 5 Production and Cost

• Brickley, Smith, and Zimmerman, Managerial
  Economics and Organizational Architecture, 4th
  ed.

2
Chapter Objectives

• Describe production function and distinguish
  between returns to scale and returns to a factor
• Use isocosts and isoquants to illustrate
  production trade-offs
• Employ short and long run cost curves to describe
  firm characteristics
• Productions functions, choice of inputs, costs,
  profit maximization, cost estimation, and factor
  demand curves

3
Production Functions

• A production function is a descriptive relation
  that links inputs with output.
• It specifies the maximum feasible output that can
  be produced for given amounts of inputs.
• Production functions are determined by the
  available technology

4
Production functions

• A production function specifies maximum output
  from given inputs for instance, given current
  technology, an automobile supplier is able to
  transform inputs like steel, aluminum, plastics,
  and labor into finished auto parts.
• In its most general form, the production function
  is expressed as
• Where Q is the quantity produced and x1, x2, .xn
  are various inputs used in the production process

5
Production functions

• To simplify the exposition, suppose that the auto
  part in this example is produced from just two
  inputs steel and aluminum.
• An example of a specific production function in
  this context is QS1/2A1/2
• Where S is pounds of steel, A is pounds of
  aluminum, Q is the number of auto parts produced

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Production functions

• With this production, 100 pounds of steel and 100
  pounds of aluminum will produce 100 auto parts
• And 400 pounds of steel and 100 pounds of
  aluminum will produce 200 auto parts, and so on
  Please see page 131 for complete details and
  calculations
• 1001/2 X 1001/2 10 X 10 100
• 4001/2 X 1001/2 20 X 10 200

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Returns to scale

• Defined The relation between output and a
  proportional variation of all inputs together
• With a constant returns to scale used in our
  previous example, a 1 percent change in all
  inputs results in a 1 percent change in output.
  If the firm increases both inputs from 100 to
  101, it produces 101 auto parts instead of 100
• Increasing returns to scale QSA
• Decreasing returns to scale QS1/3A1/3
• Constant returns to scale QS1/2A1/2

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Returns to scale

• Increasing returns to scale QSA a 1 percent
  change in all inputs results in a greater than 1
  percent change in output
• Decreasing returns to scale QS1/3A1/3 a 1
  percent change in all inputs results in a less
  than 1 percent change in output
• Constant returns to scale QS1/2A a 1 percent
  increase in inputs results in 1 percent change in
  output
• Next slide shows this relationship between costs
  and returns to scale

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Long-Run Production Costs
Alternative Long-Run ATC Shapes
Economies Of Scale
Constant Returns To Scale
Diseconomies Of Scale
Average Total Costs
Long-Run ATC
q1
q2
Output
Long-Run ATC Curve Where Economies Of Scale Exist
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Returns to a Factor

• Refers to the relationship between output and the
  variation in a single input, holding other inputs
  fixed.
• Returns to a factor can be expressed as total,
  marginal or average quantities
• The total product of an input is the schedule of
  output obtained as that input increases, holding
  other inputs fixed
• The marginal product of an input is the change in
  total output associated with a one-unit change in
  the input, holding other inputs fixed
• The average product is the total product divided
  by the number of units of the inputs employed

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Returns to a factor page 132, Table 5.1

• Production function QS1/2A1/2

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Law of Diminishing Marginal Product

• The law of diminishing marginal returns explains
  this relationship between total, marginal and
  average product,
• Which states that the marginal product of a
  variable factor eventually will decline as its
  use is increased holding other factors fixed,
  page 133
• Next slide shows this relationship through cost
  curves

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Returns to a factora common case Figure 5.1,
page 134
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Short-Run Production Relationships

• Total Product (TP)
• Marginal Product (MP)
• Average Product (AP)

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Law of Diminishing Returns

• Rationale
• Tabular Example

0 10 25 45 60 70 75 75 70
- 10.00 12.50 15.00 15.00 14.00 12.50 10.71 8.75
0 1 2 3 4 5 6 7 8
10 15 20 15 10 5 0 -5
Increasing Marginal Returns
Diminishing Marginal Returns
Negative Marginal Returns
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Law of Diminishing Returns

• Graphical Portrayal

TP
Increasing Marginal Returns
Diminishing Marginal Returns
Negative Marginal Returns
AP
MP
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Choice of Inputs - Production isoquants

• Most production function allow some substitution
  among inputs different combinations of inputs
  that can be used to produce the same output
• Isoquants portray technical combination of inputs
  to produce a given level of output
• Shape of isoquants indicates substitutability
  between input

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Isoquants Curve

• Iso, meaning the same, and quant from quantity
• An isoquant show all input combinations that
  produce the same quantity of output assuming
  efficient production efficiency allows you to
  produce maximum quantity (on the curve) with
  given inputs. Any points inside or outside the
  curve may be attainable but are inefficient
• There is a different isoquant curve for each
  possible level of production. Figure 5.2, page
  135 shows the isoquants for 100, 200 and 300 auto
  parts for the production function QS1/2A1/2

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Optimal input combinationisoquants Figure 5.2,
page 135
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Differing input substitutabilityisoquants -
Figure 5.3, page 136
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Differing input substitutabilityisoquants -
Figure 5.3, page 136

• Production functions vary in terms of how easily
  inputs can be substituted for one another.
• Right Angle (fixed proportions, no substitutes)
  inputs may be used in fixed proportions and no
  substitute is possible
• Straight Lines (perfect substitutes) at the other
  extreme are perfect substitutes, where inputs can
  be freely substituted for one another. Here,
  isoquants are straight lines.
• Normal Case (Convex to the origin, curvature line
  but are not right angles) Most production
  functions have isoquants that are between the two
  extremes. The isoquants in the normal cases.
  Convexity implies that the substitutability of
  one input for another declines as less of the
  first is used

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Isocost Lines

• Given that there are many ways to produce a given
  level of output, how does a manager choose the
  most efficient input mix?
• The answer depends on the costs of the inputs TC
  Ps S Pa A Total Cost price of steel times
  quantity of steel price of aluminum times
  quantity of aluminum (5.5, page 136)

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Isocost lines - Figure 5.4, page 137

• Isocosts portray combinations of inputs that
  entail the same cost iso same, cost of
  different combinations of inputs
• Isocost lines for different expenditure levels
  are parallel (holding the price of inputs
  constant)
• In this example Price of steel is 0.50 per pound
  and Price of aluminum is 1 per pound. The
  figure shows isocost lines for 100 and 200 of
  expenditures. The slope of the line is -1 times
  the ratio of the input prices in this example,
  -0.5.
• The farther away the line from the origin, the
  higher the total cost
• Isocosts change as input prices change

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Isocost lines holding the prices of inputs
constant, p137
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Isocost lineschanges in input prices (TC 100)
- Figure 5.5, page 138
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Optimal input mix - 5.8, page 139

• Where MPi is the marginal product of input i and
  Pi is the price of input i.
• This means that last dollar spent on each input
  bring the same amount of output. Ratio is equal.
  Any other combination will not minimize costs
• Where MRP MRC (marginal resource product and
  costs are equal

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Cost minimization - Figure 5.6, page 138
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Cost Minimization Figure 5.6, page 138

• The input that minimizes the cost of producing
  any given output Q, occurs where an isocost line
  is tangent to the relevant isoquant
• In this example, the tangency occurs at (S, A).
  This is where combination of inputs can be
  achieved at lowest cost.
• The firm would prefer to be on an isocost line
  closer to the origin because of lower costs
  closer to origin.
• However, the firm would not have sufficient
  resources to produce Q.
• The firm could produce Q using other input
  mixes, such as (S, A). However, the cost of
  production would increase.

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Optimal input mixinput price changes - Figure
5.7, page 140
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Optimal input mixinput price changes - Figure
5.7, page 140

• This figure illustrates how the optimal input mix
  for producing a given output, Q, changes as the
  price of an input increases and the firm uses
  less steel and more aluminum to produce the
  output.
• This effect is called substitution effect
• The strength of the substitution effect depends
  on the curvature
• the greater the curvature, the less the firm will
  substitute between two inputs because
• It will resemble right angle isoquant in which
  substitution is not possible

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Costs

• We have analyzed how firms should choose their
  input mix to minimize costs of production
• We now extend this analysis to focus more
  specifically on costs of producing different
  levels of output
• Analysis of these costs plays an important role
  in output and pricing decisions

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Cost concepts

• Total cost
• relation between total cost and output
• Marginal cost
• change in total cost when output rises one unit
• Average cost
• total cost divided by total output
• Opportunity cost
• value of best alternative resource use

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Cost curves - Figure 5.8, page 141
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Short run versus long run

• Short run
• at least one input is fixed
• cost curves are operating curves
• Long run
• all inputs are variable
• cost curves are planning curves
• Fixed costs--incurred even if firm produces
  nothing
• Variable costs--change with the level of output

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Short-run cost curves - Figure 5.9, p144
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Long-run average costenvelope of short-run
average cost curves page 145
37
Long-run average and marginal cost curves Figure
5.11, page 146
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Additional cost concepts

• Minimum efficient scale
• plant size at which long-run average cost first
  reaches its minimum point (Q)
• Economies of scope
• cost of producing a joint set of products is less
  than cost of producing separately in separate
  firms
• Learning curves
• costs decline with production experience

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Learning Curves

• For some firms, the long-run average cost of
  producing a given level of output declines as the
  firm gains production experience due to improved
  production processes, proficiency of workers and
  experience on the job
• A learning curve displays the relation between
  average cost for a given period, Q, and
  cumulative past production volume
• Figure 5.12, page 148 presents an example where
  there are significant learning effects in the
  early stages of production. Eventually however,
  these effects frequently become minimal as the
  firm continues to produce the product

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Learning curve
41
Economies of Scale Versus Learning Effects Figure
5.13, page 148

• Economies of scale imply reductions in average
  cost as the quantity being produced within the
  production period increase
• Learning Effects imply a shift in the entire
  average cost curve down The average cost for
  producing a given quantity in a production period
  decreases with cumulative volume

42
Economies of scale versus learning effects
43
Economies of scale versus learning effects

• Example Please read Economies of Scale and
  Learning Effects in the Chemical Processing
  Industry top pink box, page 149

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Economies of Scope

• Thus far we have focused on the production of a
  single product. Most firms, however, produce
  multiple products.
• Economies of scope exist when the cost of
  producing a set of products jointly within one
  firm is less than the cost of producing the
  products separately across independent firms

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Economies of Scope

• Economies of scope help explain why firms produce
  multiple products.
• For instance, PepsiCO is a major producer of soft
  drinks yet it also produces a wide range of
  snack foods (for example, corn chips, and
  cookies).
• These multiple products allow PepsiCo to leverage
  its product development, distribution, and
  marketing systems.

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Economies of Scope versus Economies of Scale

• Are different concepts. Economies of scope
  involves cost savings that result from joint
  production
• Whereas economies of scale involve efficiencies
  from producing higher volumes of a given products
• It is possible to have economies of scope without
  having economies of scale and vice versa
• Please read two examples Apartment Management
  p149 and DSP production, p 150

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Profit maximization

• Thus far, we have focused on the costs of
  producing different levels of output
• However, what level of output should a manager
  choose to maximize firm profits?
• To answer this question, we return to the concept
  of marginal analysis initially introduced in
  chapter 2

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Profit maximization

• A firm should increase output as long as marginal
  revenue exceeds marginal cost
• A firm should not increase output if marginal
  cost exceeds marginal revenue, instead it should
  cut back the production
• At the profit-maximizing level of output,
• MRMC

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Optimal output and changes in marginal cost -
Figure 5.14, page 151
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Optimal output and changes in marginal cost -
Figure 5.14, page 151

• This figure illustrates that a decrease in
  marginal cost (from MC0 to MC1) raises the
  optimal level of output of the firm (from Q0 to
  Q1)
• Opposite would be true if MC would have shifted
  upward
• At the profit-maximizing level of output,
• MRMC

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Factor demand curve - Figure 5.15, p 152
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Factor demand curve - Figure 5.15, p 152

• The demand curve for a factor of production is
  the marginal revenue product curve (MRP) for the
  input
• The MRP (marginal revenue product) is defined as
  MP (marginal product) of the inputs times the MR
  (marginal revenue)
• It represents the additional revenue that comes
  from using one more unit of input.
• The firm maximizes profits where it purchases
  inputs up to the point where the price of the
  input (MC) equals its MRP (MR)

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Optimal Combination of Resources

• Two questions are considered
• The Least-Cost Combination Rule (1)
• The cost of any output is minimized when the
  ratios of marginal product to price of the last
  units of resources used are the same for each
  resources

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Least cost rule

• The cost of producing any specific output can be
  reduced as long as equation 1 does not hold.
• Any firm that combines resources in violation of
  the least-cost rule would have a higher-than
  necessary average total cost (ATC) at each level
  of output. (X-inefficiency)

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Profit Maximization Rule (2)

• MRP (Resource) MRC (Price of Resource)
• Minimizing cost is not sufficient for maximizing
  profit. A firm can produce any level of output in
  the least costly way by applying earlier equation
  1.
• But the profit maximizing position in equation 2
  includes the cost-minimizing condition of 1 and
  not the other way around

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Profit Maximization Rule (2)

• Note that in equation 2 that it is not sufficient
  that MRPs of the two resources be proportionate
  to their prices(MRC)
• MRPs must also be equal to 1
• Example 15/5 9/3 ratios are equal but profits
  are not maximized. Resources are underemployed.
  MRP MRC
• 5/5 3/3 1 where profits are maximized

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Profit Maximizing

• The profit maximizing position in equation 2
  includes the cost-minimizing condition of
  equation 1
• That is, if a firm is maximizing profit according
  to equation 2, then it must be using the
  least-cost combination of inputs to do so.
• A firm operating at the least cost according to
  equation 1 may not be operating at the output
  level that maximizes its profits

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Cost Estimation

• Our discussion indicates that a detailed
  knowledge of costs is important for managerial
  decision making
• Short term costs play an extremely important role
  in operating decisions
• For instance, when the MR MC, profits increase
  by expanding production
• Alternatively, if MR increases profits

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Cost Estimation

• Long-run costs, in turn, provide important
  information for decisions on optimal plant size
  and location.
• For instance, if economies of scale are
  important, one large plant is more likely optimal
  with the product transported to regional markets.
  
• Alternatively, if scale economies are small,
  smaller regional plants, which reduce
  transportation costs, are more likely optimal
• If managers are to incorporate costs in their
  analysis in this manner, they must have accurate
  estimates of how short-run and long-run costs are
  related to various factors both within and beyond
  the control of the firm.

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Cost Estimation

• Managers often use estimates of cost curves in
  decision making.
• A common statistical tool for estimating these
  curves is regression analysis.
• A regression estimates the relation between costs
  and output
• One common problem in statistical estimation is
  the difficulty of obtaining good information on
  the opportunity costs of resources.
• Another problem with estimating cost curves
  involves allocating fixed costs in a multiproduct
  plant.
• Cost accountants track the costs and estimate
  product costs.

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The End

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