Download Golden rule of cost minimization

MICROECONOMICS: Theory & Applications
Chapter 8: The Cost of Production
By
Edgar K. Browning & Mark A. Zupan
John Wiley & Sons, Inc.
11th Edition, Copyright 2012
PowerPoint prepared by Della L. Sue, Marist College
The Nature of Cost

Recall:



Explicit costs – arise from transactions in which
the firm purchases inputs or the services of
inputs from other parties
Implicit costs – costs associated with the use of
the firm’s own resources and reflect the fact
that these resources could be employed
elsewhere
Opportunity cost reflects both explicit and
implicit costs.
Copyright 2012
John Wiley & Sons, Inc.
2
Measures of Short-Run Cost
Total fixed cost (TFC) – the cost
incurred by the firm that does not
depend on how much output it
produces
 Total variable cost (TVC) – the cost
incurred by the firm that depends on
how much output it produces

Copyright 2012
John Wiley & Sons, Inc.
3
Five Other Measures of
Short-Run Cost





Total cost (TC) – the sum of total fixed and
total variable cost at each output level
Marginal cost (MC) – the change in total
cost that results from a one-unit change in
output
Average fixed cost (AFC) – total fixed cost
divided by the amount of output
Average variable cost (AVC) – total variable
cost divided by the amount of output
Average total cost (ATC) – total cost divided
by the output
Copyright 2012
John Wiley & Sons, Inc.
4
Table 8.1
Copyright 2012
John Wiley & Sons, Inc.
5
Behind Cost Relationships

A firm’s costs are determined by its
production function:



Input combinations (quantities)
Input prices
The shape of the TVC curve is determined by
the shape of the TP curve, which in turn
reflects diminishing marginal returns.
Copyright 2012
John Wiley & Sons, Inc.
6
Figure 8.1 – From Total Product to
Total Variable Cost
Copyright 2012
John Wiley & Sons, Inc.
7
Figure 8.2 - Short-Run Total and Per-Unit
Cost Curves
Copyright 2012
John Wiley & Sons, Inc.
8
Marginal Cost




Law of diminishing marginal returns => marginal product
curve of the variable input generally rises and then falls as
output increases.
The marginal product of labor varies with output => marginal
cost also varies with output
As a result, the MC curve will first fall and then rise.
Thus, the law of diminishing marginal returns lies behind the
MC curve.
Copyright 2012
John Wiley & Sons, Inc.
9
Average Cost




The average product curve rises, reaches a maximum, and
then falls, due to the law of diminishing marginal
productivity.
As a result, the AVC curve will fall and then rise.
The AFC curve declines over the entire range of output as
the amount of total fixed cost is spread over ever-larger
rates of output.
The ATC curve is the sum of AFC and AVC. It measures the
average unit cost of all inputs, both fixed and variable, and
must also be U-shaped.
Copyright 2012
John Wiley & Sons, Inc.
10
Marginal-Average Relationships
When marginal cost is below average
(total or variable) cost, average cost
will decline.
 When marginal cost is above average
cost, average cost rises.
 When average cost is at a minimum,
marginal cost is equal to average cost.

Copyright 2012
John Wiley & Sons, Inc.
11
Figure 8.3 – Graphical Derivation of Average
and Marginal Cost Curves
Copyright 2012
John Wiley & Sons, Inc.
12
Isocost Lines

An isocost line is a line that identifies all the
combinations of capital and labor, two factor
inputs, that can be purchased at a given total
cost.
 The line intersects each axis at the quantity
of that input that the firm could purchase if
only that input were purchased.
 The slope of an isocost line is (minus) the
ratio of input prices, w/r, indicating the
relative prices of inputs.
Copyright 2012
John Wiley & Sons, Inc.
13
Least Costly Input Combination
A point of tangency between an isocost
line and an isoquant show the least
costly way of producing a given output
level.
 Alternatively, a point of tangency shows
the maximum output attainable at a
given cost as well as the minimum cost
necessary to produce that output.

Copyright 2012
John Wiley & Sons, Inc.
14
Interpreting the Tangency Points

Golden rule of cost minimization: a rule
that says that to minimize cost, the firm
should employ inputs in such a way that the
marginal product per dollar spent is equal
across all inputs
Copyright 2012
John Wiley & Sons, Inc.
15
If the firm is not producing at a
tangency point…
Whenever MPL/w > MPK/r, a firm
can increase output without
increasing production cost by
shifting outlays from capital to labor.
 Whenever MPL/w < MPK/r, a firm
can increase output without
increasing production cost by
shifting outlays from labor to capital.

Copyright 2012
John Wiley & Sons, Inc.
16
The Expansion Path

The expansion path is a curve
formed by connecting the points of
tangency between isocost lines and
the highest respective attainable
isoquants.
Copyright 2012
John Wiley & Sons, Inc.
17
Figure 8.4 - Isocost Lines and
the Long-Run Expansion Path
Copyright 2012
John Wiley & Sons, Inc.
18
Is Production Cost Minimized?

Cost minimization is NOT the same as
profit maximization…

Cost minimization occurs at all points on
the expansion path, but profit
maximization involves selecting the
most profitable output from among those
on the expansion path.
Copyright 2012
John Wiley & Sons, Inc.
19
Table 8.2 – The Productivity Gains
from Privatization
Copyright 2012
John Wiley & Sons, Inc.
20
Input Price Changes and
Cost Curves
The input substitution effect is the
effect of a change in the price of an
input on a firm’s relative use of the
input to produce a given level of
output.
Copyright 2012
John Wiley & Sons, Inc.
21
Figure 8.5 – A Higher Input Price Shifts
Cost Curves Upward
Copyright 2012
John Wiley & Sons, Inc.
22
Long-Run Cost Curves

LTC shows the minimum cost at which each rate of
output may be produced, just as the expansion path
does.

LMC and LAC are derived from the LTC in the same
way that the short-run marginal and average curves
are derived from the short-run total cost curve.

LAC is U-shaped…why?


Economies of scale
Diseconomies of scale
Copyright 2012
John Wiley & Sons, Inc.
23
Figure 8.6 - Long-Run Cost Curves
Copyright 2012
John Wiley & Sons, Inc.
24
Economies of Scale and
Diseconomies of Scale

Economies of scale – a situation in which a
firm can increase its output more than
proportionally to its total input cost


Reflects increasing returns to scale
Diseconomies of scale – a situation in
which a firm’s output increases less than
proportionally to its total input cost

Copyright 2012
Reflects decreasing returns to scale
John Wiley & Sons, Inc.
25
The Long Run and Short Run Revisited

Summary:

Long-run average cost curve (LAC): the
lowest average cost attainable when all
inputs are variable

Each point on the LAC is associated with a
different short-run scale of operation that
the firm could choose.
Copyright 2012
John Wiley & Sons, Inc.
26
FIGURE 8.7 - Short- and Long-Run
Average Cost Curves
Copyright 2012
John Wiley & Sons, Inc.
27
Learning by Doing

Learning by doing is associated with improvements in
productivity resulting from a firm’s cumulative output
experience

Advantages of Learning by Doing to Pioneering Firms



Attainment of lower production costs
Incentive to produce more in any given period
Limits to Advantages:


Benefits spill over to other firms
New products can give newer firms a competitive advantage
Copyright 2012
John Wiley & Sons, Inc.
28
Figure 8.8 - Learning by Doing Versus
Economies of Scale
Copyright 2012
John Wiley & Sons, Inc.
29
Importance of Cost Curves to Market
Structure

Minimum efficient scale – the scale of
operations at which average cost per unit
reaches a minimum

Impact on industry structure



Number of firms
Proportion of industry output by each firm
Degree of competition
Copyright 2012
John Wiley & Sons, Inc.
30
Figure 8.3 – Minimum Efficient Plant
Scales
Copyright 2012
John Wiley & Sons, Inc.
31
Figure 8.9 - Cost Curves and
the Structure of Industry
Copyright 2012
John Wiley & Sons, Inc.
32
Using Cost Curves: Controlling Pollution

Question: Can the government’s program to reduce
pollution be accomplished at the lowest possible cost?

If marginal costs of firms differ, the total cost of
pollution abatement can be reduced:



Increase abatement when MC is less
Decrease abatement where MC is greater
Result: firms should operate where their MC are equal.
Copyright 2012
John Wiley & Sons, Inc.
33
Figure 8.10 – Cost of Pollution
Abatement
Copyright 2012
John Wiley & Sons, Inc.
34
Economies of Scope and
Diseconomies of Scope

Economies of scope – a case where it is
cheaper for one firm to produce products
jointly than it is for separate firms to produce
the same products independently

Diseconomies of scope – a case where it is
cheaper for separate products to be
produced independently than for one firm to
produce the same products jointly
Copyright 2012
John Wiley & Sons, Inc.
35
Copyright © 2012 John Wiley & Sons, Inc. All rights
reserved. Reproduction or translation of this work
beyond that permitted in section 117 of the 1976
United States Copyright Act without express
permission of the copyright owner is unlawful.
Request for further information should be
addressed to the Permissions Department, John
Wiley & Sons, Inc. The purchaser may make backup copies for his/her own use only and not for
distribution or resale. The Publisher assumes no
responsibility for errors, omissions, or damages
caused by the use of these programs or from the
use of the information herein.
Copyright 2012
John Wiley & Sons, Inc.
36