Cost Concepts and Curves in Microeconomics

Walter Nicholson
1
Amherst College
Christopher Snyder
Dartmouth College
PowerPoint Slide Presentation | Philip Heap, James Madison University
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

CHAPTER
2
7
Costs

• Last chapter we saw how a firm’s output changes as it uses more
inputs.
• In this chapter we will focus on two issues:
1. How the firm chooses the inputs it uses to produce a given
output at the lowest possible cost.
2. How the firm’s production costs change as it changes the
number and mix of its inputs.
Ch. 7 • 3
Chapter Preview

Basic Cost Concepts
Ch. 7 • 4
• Opportunity cost:
– The cost of a good measured by the alternative uses that are
foregone by producing the good.
• Accounting cost:
– The actual cost paid for inputs.
• Economic cost:
– The amount required to keep an input in its present use or the
amount that input would be worth in its next best alternative
use.

Basic Cost Concepts
Ch. 7 • 5
• Labor costs:
– Wage payments are an explicit costs
– Wage rate is the amount a worker would earn in her next best
alternative employment.
• Capital costs:
– An accountant uses the historical cost of capital and some
depreciation rule.
– An economist treats the cost of capital as a sunk cost, which is
an expenditure that once made can’t be recovered.
– The implicit cost of capital is equal to its rental rate.

Basic Cost Concepts
Ch. 7 • 6
• Entrepreneurial costs:
– Owners of the firm are entitled to the difference between
revenue and costs: accounting profit
– Entrepreneurial cost is the salary an owner of the firm could
earn at his or her next best alternative employment.
• Economic profit:
– Accounting profit minus the entrepreneurial cost.
– Revenue minus total costs, which include both explicit and
implicit costs.

Economic Profits and Cost Minimization
Ch. 7 • 7
• Assumptions:
– Two inputs: labor (L) and capital (K).
– Inputs are hired in a perfectly competitive market.
• Total costs: TC = wL + vK
• Economic profit = π = Total Revenues – Total Costs
– π = Pq – wL – vK
– π = Pf(K,L) – wL – vK
• Note that a firm’s economic profit depend only on the amount of
labor and capital it hires.

Cost Minimizing Input Choice
Ch. 7 • 8
• How does a firm produce a given output at the lowest possible
cost?
• We’ll look a this three ways:
1. RTS = w/v
2. Graphically this is the point where the isoquant is tangent to
the total cost line.
3. MPL/w = MPK/v
• Parallel between the consumer’s utility maximizing choice and
firm’s cost minimizing choice.

Cost Minimizing Input Choice: RTS= w/v
Ch. 7 • 9
• Assume the firm makes q units of output with 10 K and 10 L. The
RTS = 2, w = $1 and v = $1
• What’s wrong?
– Total costs = $20 = 10 x $1 + 10 x $1
– But RTS = 2 ≠ w/v = 1
– Since the RTS = 2, the firm could replace two units of capital
with one worker
– This would allow the firm to reduce costs by $1.
• Therefore, as long as RTS ≠ w/v the firm can substitute one input
for the other and reduce its costs.

Capital
per
week
K
*
Labor
per
week
L*
TC1
q
TC3
TC2
Cost Minimizing Input Choice: Graphical
Approach
At this point the RTS > w/v.
Ch. 7 • 10
So the firm should use less labor, and more capital.
It continues to do this until RTS = w/v.

Cost Minimizing Input Choice: MPL/w =
MPK/v
Ch. 7 • 11
• Last chapter we showed that: RTS = MP /MP
L K
• We also know to minimize costs: RTS = w/v
• Therefore:
L K
– MP /MP = w/v
L K
– MP /w = MP /v
• To minimize costs the firm should hire inputs so that the output
per dollar spent on the last unit of labor is equal to the output per
dollar spent on the last unit of capital.

Cost Minimizing Input Choice: MPL/w =
MPK/v
Ch. 7 • 12
L K
• Suppose that at its current input mix, the MP /w > MP /v. Should
the firm hire more labor or more capital?
L K
– Since MP /w > MP /v, the firm could spend $1 more (less) on
labor (capital), and increase total output.
L K
– As the firm hires more labor (less capital) the MP (MP ) falls
(rises).
– Therefore, MP /w falls, and MP /v rises.
L K
– . . . MP /w > MP /v.
L K

Capital
per
week
K
1
q1
Labor
per
week
L1
Expansion path. The set of
cost-minimizing input combinations a
firm will use to produce different levels
of output.
q2
q3
The Firm’sExpansion Path
Ch. 7 • 13

Cost Curves
Ch. 7 • 14
• What is the relationship between output and total costs?
• Depends on the nature of production: constant, decreasing,
increasing returns to scale.
• Returns to scale and the relationship between input and output.
• Now look at the relationship between output and costs.

Cost Curves: Constant Returns to Scale
Total
Cost
Ch. 7 • 15
Quantity
per week
TC
As output expands, costs expand proportionally.

Cost Curves: Decreasing Returns to Scale
Total
Cost
Quantity
per week
TC
Costs expand more rapidly than output.
Ch. 7 • 16

Cost Curves: Increasing Returns to Scale
Total
Cost
Quantity
per week
TC
Costs expand less rapidly than output.
Ch. 7 • 17

Cost Curves: Optimal Scale
Total
Cost
Quantity
per week
TC
Over lower levels of
output there are
increasing returns As output expands
decreasing returns
kicks in
Ch. 7 • 18

Average and Marginal Costs
• Average Cost is total cost divided by output.
• Marginal Cost is the additional cost of producing one more unit of
output.
Ch. 7 • 19

Average and Marginal Cost
Curves: Constant Returns
AC, MC
Ch. 7 • 20
Quantity
per week
As output expands, MC and AC remain the same.
AC, MC

Curves: Decreasing
Returns
Quantity
per week
AC, MC
MC AC
As output expands, both MC and AC increase.
Ch. 7 • 21

Curves: Increasing Returns
AC, MC
Quantity
per week
As output expands, both MC and AC decrease
MC
AC
Ch. 7 • 22

Curves: Optimal Scale
AC, MC
Quantity
per week
MC
AC
q*
Ch. 7 • 23

The Short Run and the Long Run
Ch. 7 • 24
• Short run – the period of time in which a firm must consider
some inputs to be fixed.
• Long run – the period of time in which a firm may consider all of
its inputs to be variable.
• Fixed Costs – costs associated with inputs that are fixed in the
short run.
• Variable Costs – costs associated with inputs that can be varied in
the short run.

Input Inflexibility and Cost Minimization
Ch. 7 • 25
• Will a firm always be able to use the cost minimizing combination
of inputs in the short run?
• No. Capital is fixed in the short run so the firm may have to use
non-optimal amounts of labor to produce some given output.
• What about the long run?

Capital
per
week
K
1
Labor
per
week
L0
STC0
q0
Suppose the amount of capital is fixed at K1, and
the firm produces q0 units.
To produce q0 the firm would use L0 and face costs STC0.
q1
L1
STC1
Ch. 7 • 26

Capital
per
week
K
1
Labor
per
week
L0
STC0
q0
q1
L1
STC1
q2
L2
STC2
For which output level is the firm minimizing costs?
Ch. 7 • 27
q : only for this output is the RTS equal to
1
the ratio of input prices.

Shifts in Cost Curves
Ch. 7 • 28
• Three changes will affect the shape and position of a firm’s cost
curves.
1. Changes in input prices such as wages.
– An increase (decrease) in input prices will cause the cost
curves to shift up (down).
– Will depend on the firm’s ability to substitute inputs.

Shifts in Cost Curves
Ch. 7 • 29
1. Changes in input prices.
2. Technological innovation.
– Cost curves will shift down.
– Technological change may be “biased”.
3. Economies of scope.
– Relates to multiproduct firms.
– Expansion of one product may improve the ability to produce
another product.

A Numerical Example
• Back at Hamburger Heaven
– TC = $5K + $5L
– q = 40
Ch. 7 • 30

Capital
per
hour
4
Labor
per
hour
4
Ch. 7 • 31
E
40 hamburgers per hour
Total Cost = $40
A Numerical Example

A Numerical Example
Total
Cost
Quantity
per week
20 40 60 80
80
60
40
20
Total Cost
Ch. 7 • 32

A Numerical Example
Average and
marginal cost
Quantity
per week
20 40 60 80
AC and MC
$1
Ch. 7 • 33

A Numerical Example
• Suppose we now fix the number of grills to 4
SAC
falls
MC
rises
SAC
rises
Ch. 7 • 34

A Numerical Example
Average and
marginal cost
Quantity
per week
20 40 60 80
AC and MC
$1
Ch. 7 • 35
SMC (4 grills)
SAC (4 grills)

Summary
Ch. 7 • 36
• To minimize the cost of producing a given level of output, the firm
should choose a point on its isoquant so that the RTS = input price
ratio.
• To minimize the cost of producing a given level of output, the firm
should choose its inputs so MP/Input Price is the same for all
inputs.
• The expansion path shows the minimum cost way of producing
any level of output. From firm’s total cost curve can be derived
from the expansion path.

Summary
Ch. 7 • 37
• Average and marginal costs can be constructed from the total cost
curve. The shape of these curves depend on the nature of the
production process.
• In the short run at least one input is fixed and short run costs are
not generally the lowest cost the firm could achieve.
• Short run costs increase rapidly due to diminishing marginal
productivities.
• Cost curves will shift due to a change in input prices,
technological change, and economies of scope.

Cost Concepts and Curves in Microeconomics

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