Costs and Cost Minimization

1
Chapter 7

• Costs and Cost Minimization

2
Introduction

• The last chapter considered how to represent
  production in economic theory
• This chapter presents cost concepts, and links
  the analysis of cost to the theory of production

3
Cost Concepts

• Some Terminology
• Opportunity Cost
• Implicit and Explicit Costs
• Sunk and Non-sunk Costs
• Fixed Costs and Variable Costs
• Long-run and Short-run Costs

4
Opportunity Cost

• Opportunity Cost The cost of using a resource is
  the value that resource would have produced in
  its best alternative activity.
• Opportunity cost is always the relevant concept
  for use in economic decision-making.
• Opportunity cost includes implicit and explicit
  costs.
• Explicit costs involve direct flows of money in a
  transaction, implicit costs do not.

5
Sunk Costs

• Sunk cost If a cost has already been incurred
  and is irretrievable or irreversible, it is sunk.
  
• Sunk costs are irrelevant for current economic
  decisions.
• Whether a cost is sunk or not depends on the
  timing
• Before you build a factory, your investment is
  not sunk.
• However, after a factory is built, and if the
  factory has no alternative uses or resale value,
  then the investment expenditure is sunk.

6
Fixed Costs and Variable Costs

• A fixed cost is one that does not vary with
  output produced within a period
• Variable costs do vary with output produced in a
  period

7
Fixed Costs and Sunk Costs

• Fixed costs are not always sunk
• Example You need a plane to run an air shuttle
  service between two towns.
• Costs associated with the plane may be fixed, but
  if the plane can be sold these costs are not sunk.

8
Long-run and Short-run

• The long run is a time period in which all of a
  firms inputs can be varied
• The short run is a time period in which the
  quantity of at least one input is considered fixed

9
Cost Minimization

• We will assume that firms maximize profits, which
  will require that they minimize the cost of
  production of their chosen output
• We examine cost minimization in the long run and
  in the short run

10
Cost Minimization Long Run

• Consider a firm that uses only two inputs, L and
  K, to produce output in a period.
• Prices of the services of capital and labor for a
  period are w and r.
• If the firm uses quantities L and K to produce
  output, its total costs are given by

11
Isocost Lines

• Consider plotting combinations of inputs that are
  equally costly
• For example, let w 5 and r 10.
• What are all the bundles that would cost 100?
  150? 200?
• The resulting lines are isocost lines (these are
  very similar in construction to consumer budget
  lines)
• What is the slope of an isocost line?
• Plot L on the horizontal axis and K on the
  vertical axis.
• Answer is w/r

12
A Diagram

• Consider a diagram this problem for a firm
• Minimize the cost of producing a given output,
  say Q 20, using quantities of inputs, L and K,
  which have prices w and r.
• Plot the isoquant for Q 20 plot a family of
  isocost curves.

13
A Diagram
K
Find a point on the Q 20 isoquant with the
lowest production cost (on the isocost line with
lowest cost).
Q 20
L
14
Question

• Does the preceding diagram illustrate the
  solution to a long-run or a short-run cost
  minimization problem?
• A Short-run
• B Long-run

15
Question

• Does the preceding diagram illustrate the
  solution to a long-run or a short-run cost
  minimization problem?
• A Short-run
• B Long-run

16
The Tangency Condition

• The solution to the cost minimization problem
  occurs at a point of tangency
• This implies that the slope of the isoquant is
  equal to the slope of an isocost line

17
Question

• Suppose
• MPL 5
• MPK 8
• w 10
• r 12
• True or False? The firm should use more capital
  and less labor.
• A True
• B False

18
Question

• Suppose
• MPL 5
• MPK 8
• w 10
• r 12
• True or False? The firm should use more capital
  and less labor.
• A True
• B False

19
Derive the Long-run Total Cost Curve

• Use the isoquant/isocost diagram
• For each possible output, find the cost
  minimizing input combination, and the resulting
  level of total cost
• Then plot Q versus TC using the data generated
  from the isoquant-isocost diagram.
• This is a long-run total cost curve.

20
A Diagram
K
Find a point on the Q 20 isoquant with the
lowest production cost (on the isocost line with
lowest cost).
Q 30
Q 20
Q 10
C 100
C 300
C 170
L
21
Long-Run Total Cost Curve
C
300
200
100
Q
10
20
30
22
Long-Run Total Cost Curve
C
300
200
100
Q
10
20
30
23
Input Substitutability

• Suppose that labor becomes more expensive. What
  happens to the cost-minimizing combination of
  inputs to produce a given output?
• If the wage rate rises, the capital/labor ratio
  rises.
• Show this in a diagram!
• Recall the elasticity of substitution
• What does this say about how changes in input
  prices affect input combinations?

24
Cost Minimization Short Run

• In the short-run, at least one input quantity is
  fixed
• For example, over a short time horizon the size
  of a factory may be fixed, but labor employed
  could vary.
• If capital is fixed, then the costs associated
  with capital will also be fixed.
• For any positive output we must pay the fixed
  cost associated with the capital input.
• If output is zero, this cost is avoidable if the
  cost is not sunk.

25
Short-run Cost Minimization Diagram
K
With capital fixed, find the amount of labor
needed to produce a given output, then find the
isocost through that point.
K1
Q 30
Q 20
Q 10
L
26
Short-Run Total Cost Curve
C
300
200
100
Q
10
20
30
27
I-clicker Question

• Which statement correctly describes the
  relationship between long-run and short-run total
  costs?
• A The long-run total cost of producing an given
  output (for example, Q 100) is always less than
  the short-run cost of producing the same output.
• B The long-run total cost of producing an given
  output (for example, Q 100) is always less than
  or equal to the short-run cost of producing the
  same output.
• C The short-run total cost of producing an given
  output (for example, Q 100) is always less than
  the long-run cost of producing the same output.
• D The short-run total cost of producing an given
  output (for example, Q 100) is always less than
  or equal to the long-run cost of producing the
  same output.

28
I-clicker Question

• Which statement correctly describes the
  relationship between long-run and short-run total
  costs?
• A The long-run total cost of producing an given
  output (for example, Q 100) is always less than
  the short-run cost of producing the same output.
• B The long-run total cost of producing an given
  output (for example, Q 100) is always less than
  or equal to the short-run cost of producing the
  same output.
• C The short-run total cost of producing an given
  output (for example, Q 100) is always less than
  the long-run cost of producing the same output.
• D The short-run total cost of producing an given
  output (for example, Q 100) is always less than
  or equal to the long-run cost of producing the
  same output.

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The End