Uncertainty and Consumer Behavior

1
Chapter 5

• Uncertainty and Consumer Behavior

2
Introduction

• Choice with certainty is reasonably
  straightforward
• How do we make choices when certain variables
  such as income and prices are uncertain (making
  choices with risk)?

3
Describing Risk

• To measure risk we must know
• All of the possible outcomes
• The probability or likelihood that each outcome
  will occur

4
Describing Risk

• Interpreting Probability
• Objective Interpretation
• Based on the observed frequency of past events
• Subjective Interpretation
• Based on perception that an outcome will occur

5
Interpreting Probability

• Subjective Probability
• Different information or different abilities to
  process the same information can influence the
  subjective probability
• Based on judgment or experience

6
Describing Risk

• With an interpretation of probability, must
  determine 2 measures to help describe and compare
  risky choices
• Expected value
• Variability

7
Describing Risk

• Expected Value
• The weighted average of the payoffs or values
  resulting from all possible outcomes
• Expected value measures the central tendency the
  payoff or value expected on average

8
Expected Value An Example

• Investment in offshore drilling exploration
• Two outcomes are possible
• Success the stock price increases from 30 to
  40/share
• Failure the stock price falls from 30 to
  20/share

9
Expected Value An Example

• Objective Probability
• 100 explorations, 25 successes and 75 failures
• Probability (Pr) of success 1/4 and the
  probability of failure 3/4

10
Expected Value An Example
11
Expected Value

• In general, for n possible outcomes
• Possible outcomes having payoffs X1, X2, , Xn
• Probabilities of each outcome is given by Pr1,
  Pr2, , Prn

12
Describing Risk

• Variability
• The extent to which possible outcomes of an
  uncertain event may differ
• How much variation exists in the possible choice

13
Variability An Example

• Suppose you are choosing between two part-time
  sales jobs that have the same expected income
  (1,500)
• The first job is based entirely on commission
• The second is a salaried position

14
Variability An Example

• There are two equally likely outcomes in the
  first job 2,000 for a good sales job and 1,000
  for a modestly successful one
• The second pays 1,510 most of the time (.99
  probability), but you will earn 510 if the
  company goes out of business (.01 probability)

15
Variability An Example
16
Variability An Example

• Income from Possible Sales Job
• Job 1 Expected Income

Job 2 Expected Income
17
Variability

• While the expected values are the same, the
  variability is not
• Greater variability from expected values signals
  greater risk
• Variability comes from deviations in payoffs
• Difference between expected payoff and actual
  payoff

18
Variability An Example
19
Variability

• Average deviations are always zero so we must
  adjust for negative numbers
• We can measure variability with standard
  deviation
• The square root of the average of the squares of
  the deviations of the payoffs associated with
  each outcome from their expected value

20
Variability

• Standard deviation is a measure of risk
• Measures how variable your payoff will be
• More variability means more risk
• Individuals generally prefer less variability
  less risk

21
Variability

• The standard deviation is written

22
Standard Deviation Example 1
23
Standard Deviation Example 1

• Standard deviations of the two jobs are

24
Standard Deviation Example 1

• Job 1 has a larger standard deviation and
  therefore it is the riskier alternative
• The standard deviation also can be used when
  there are many outcomes instead of only two

25
Standard Deviation Example 2

• Job 1 is a job in which the income ranges from
  1000 to 2000 in increments of 100 that are all
  equally likely
• Job 2 is a job in which the income ranges from
  1300 to 1700 in increments of 100 that, also,
  are all equally likely

26
Outcome Probabilities - Two Jobs
Job 1 has greater spread greater standard
deviation and greater risk than Job 2.
Probability
0.2
0.1
Income
1000
1500
2000
27
Decision Making Example 1

• What if the outcome probabilities of two jobs
  have unequal probability of outcomes?
• Job 1 greater spread and standard deviation
• Peaked distribution extreme payoffs are less
  likely that those in the middle of the
  distribution
• You will choose job 2 again

28
Unequal Probability Outcomes
The distribution of payoffs associated with Job 1
has a greater spread and standard deviation than
those with Job 2.
Probability
0.2
0.1
Income
1000
1500
2000
29
Decision Making Example 2

• Suppose we add 100 to each payoff in Job 1 which
  makes the expected payoff 1600
• Job 1 expected income 1,600 and a standard
  deviation of 500
• Job 2 expected income of 1,500 and a standard
  deviation of 99.50

30
Decision Making Example 2

• Which job should be chosen?
• Depends on the individual
• Some may be willing to take risk with higher
  expected income
• Some will prefer less risk even with lower
  expected income

31
Risk and Crime Deterrence

• Attitudes toward risk affect willingness to break
  the law
• Suppose a city wants to deter people from double
  parking
• Monetary fines may be better than jail time

32
Risk and Crime Deterrence

• Costs of apprehending criminals are not zero,
  therefore
• Fines must be higher than the costs to society
• Probability of apprehension is actually less than
  one

33
Risk and Crime Deterrence - Example

• Assumptions
• Double-parking saves a person 5 in terms of time
  spent searching for a parking space
• The driver is risk neutral
• Cost of apprehension is zero

34
Risk and Crime Deterrence - Example

• A fine greater than 5.00 would deter the driver
  from double parking
• Benefit of double parking (5) is less than the
  cost (6.00) equals a net benefit that is
  negative
• If the value of double parking is greater than
  5.00, then the person would still break the law

35
Risk and Crime Deterrence - Example

• The same deterrence effect is obtained by either
• A 50 fine with a 0.1 probability of being caught
  resulting in an expected penalty of 5
• or
• A 500 fine with a 0.01 probability of being
  caught resulting in an expected penalty of 5

36
Risk and Crime Deterrence - Example

• Enforcement costs are reduced with high fine and
  low probability
• Most effective if drivers dont like to take risks

37
Preferences Toward Risk

• Can expand evaluation of risky alternative by
  considering utility that is obtained by risk
• A consumer gets utility from income
• Payoff measured in terms of utility

38
Preferences Toward Risk - Example

• A person is earning 15,000 and receiving 13.5
  units of utility from the job
• She is considering a new, but risky job
• 0.50 chance of 30,000
• 0.50 chance of 10,000

39
Preferences Toward Risk - Example

• Utility at 30,000 is 18
• Utility at 10,000 is 10
• Must compare utility from the risky job with
  current utility of 13.5
• To evaluate the new job, we must calculate the
  expected utility of the risky job

40
Preferences Toward Risk

• The expected utility of the risky option is the
  sum of the utilities associated with all her
  possible incomes weighted by the probability that
  each income will occur

E(u) (Prob. of Utility 1) (Utility 1)
(Prob. of Utility 2)(Utility 2)
41
Preferences Toward Risk Example

• The expected is
• E(u) (1/2)u(10,000) (1/2)u(30,000)
• 0.5(10) 0.5(18)
• 14
• E(u) of new job is 14, which is greater than the
  current utility of 13.5 and therefore preferred

42
Preferences Toward Risk

• People differ in their preference toward risk
• People can be risk averse, risk neutral, or risk
  loving

43
Preferences Toward Risk

• Risk Averse
• A person who prefers a certain given income to a
  risky income with the same expected value
• The person has a diminishing marginal utility of
  income
• Most common attitude towards risk
• Ex Market for insurance

44
Risk Averse - Example

• A person can have a 20,000 job with 100
  probability and receive a utility level of 16
• The person could have a job with a 0.5 chance of
  earning 30,000 and a 0.5 chance of earning
  10,000

45
Risk Averse Example

• Expected Income of Risky Job
• E(I) (0.5)(30,000) (0.5)(10,000)
• E(I) 20,000
• Expected Utility of Risky Job
• E(u) (0.5)(10) (0.5)(18)
• E(u) 14

46
Risk Averse Example

• Expected income from both jobs is the same risk
  averse may choose current job
• Expected utility is greater for certain job
• Would keep certain job
• Risk averse persons losses (decreased utility)
  are more important than risky gains

47
Risk Averse

• Can see risk averse choices graphically
• Risky job has expected income 20,000 with
  expected utility 14
• Point F
• Certain job has expected income 20,000 with
  utility 16
• Point D

48
Risk Averse Utility Function
Utility
The consumer is risk averse because she would
prefer a certain income of 20,000 to an
uncertain expected income 20,000
Income (1,000)
49
Preferences Toward Risk

• A person is said to be risk neutral if they show
  no preference between a certain income, and an
  uncertain income with the same expected value
• Constant marginal utility of income

50
Risk Neutral

• Expected value for risky option is the same as
  utility for certain outcome
• E(I) (0.5)(10,000) (0.5)(30,000)
• 20,000
• E(u) (0.5)(6) (0.5)(18) 12
• This is the same as the certain income of 20,000
  with utility of 12

51
Risk Neutral
Utility
The consumer is risk neutral and is
indifferent between certain events and uncertain
events with the same expected income.
Income (1,000)
0
10
20
30
52
Preferences Toward Risk

• A person is said to be risk loving if they show a
  preference toward an uncertain income over a
  certain income with the same expected value
• Examples Gambling, some criminal activities
• Increasing marginal utility of income

53
Risk Loving

• Expected value for risky option point F
• E(I) (0.5)(10,000) (0.5)(30,000)
• 20,000
• E(u) (0.5)(3) (0.5)(18) 10.5
• Certain income is 20,000 with utility of 8
  point C
• Risky alternative is preferred

54
Risk Loving
Utility
The consumer is risk loving because she would
prefer the gamble to a certain income.
Income (1,000)
10
20
30
0
55
Preferences Toward Risk

• The risk premium is the maximum amount of money
  that a risk-averse person would pay to avoid
  taking a risk
• The risk premium depends on the risky
  alternatives the person faces

56
Risk Premium Example

• From the previous example
• A person has a .5 probability of earning 30,000
  and a .5 probability of earning 10,000
• The expected income is 20,000 with expected
  utility of 14

57
Risk Premium Example

• Point F shows the risky scenario the utility of
  14 can also be obtained with certain income of
  16,000
• This person would be willing to pay up to 4000
  (20 16) to avoid the risk of uncertain income
• Can show this graphically by drawing a straight
  line between the two points line CF

58
Risk Premium Example
Here, the risk premium is 4,000 because a
certain income of 16,000 gives the person the
same expected utility as the uncertain income
with expected value of 20,000.
Utility
Income (1,000)
0
10
16
20
59
Risk Aversion and Indifference Curves

• Can describe a persons risk aversion using
  indifference curves that relate expected income
  to variability of income (standard deviation)
• Since risk is undesirable, greater risk requires
  greater expected income to make the person
  equally well off
• Indifference curves are therefore upward sloping

60
Risk Aversion and Indifference Curves
Expected Income
Highly Risk Averse An increase in
standard deviation requires a large increase in
income to maintain satisfaction.
Standard Deviation of Income
61
Risk Aversion and Indifference Curves
Expected Income
Slightly Risk Averse A large increase in
standard deviation requires only a small
increase in income to maintain satisfaction.
Standard Deviation of Income
62
Reducing Risk

• Consumers are generally risk averse and therefore
  want to reduce risk
• Three ways consumers attempt to reduce risk are
• Diversification
• Insurance
• Obtaining more information

63
Reducing Risk

• Diversification
• Reducing risk by allocating resources to a
  variety of activities whose outcomes are not
  closely related
• Example
• Suppose a firm has a choice of selling air
  conditioners, heaters, or both
• The probability of it being hot or cold is 0.5
• How does a firm decide what to sell?

64
Income from Sales of Appliances
65
Diversification Example

• If the firm sells only heaters or air
  conditioners their income will be either 12,000
  or 30,000
• Their expected income would be
• 1/2(12,000) 1/2(30,000) 21,000

66
Diversification Example

• If the firm divides their time evenly between
  appliances, their air conditioning and heating
  sales would be half their original values
• If it were hot, their expected income would be
  15,000 from air conditioners and 6,000 from
  heaters, or 21,000
• If it were cold, their expected income would be
  6,000 from air conditioners and 15,000 from
  heaters, or 21,000

67
Diversification Example

• With diversification, expected income is 21,000
  with no risk
• Better off diversifying to minimize risk
• Firms can reduce risk by diversifying among a
  variety of activities that are not closely related

68
Reducing Risk The Stock Market

• If invest all money in one stock, then take on a
  lot of risk
• If that stock loses value, you lose all your
  investment value
• Can spread risk out by investing in many
  different stocks or investments
• Ex Mutual funds

69
Reducing Risk Insurance

• Risk averse are willing to pay to avoid risk
• If the cost of insurance equals the expected
  loss, risk averse people will buy enough
  insurance to recover fully from a potential
  financial loss

70
The Law of Large Numbers

• Insurance companies know that although single
  events are random and largely unpredictable, the
  average outcome of many similar events can be
  predicted
• When insurance companies sell many policies, they
  face relatively little risk

71
Reducing Risk Actuarially Fair

• Insurance companies can be sure total premiums
  paid will equal total money paid out
• Companies set the premiums so money received will
  be enough to pay expected losses

72
The Value of Information

• Risk often exists because we dont know all the
  information surrounding a decision
• Because of this, information is valuable and
  people are willing to pay for it

73
The Value of Information

• The value of complete information
• The difference between the expected value of a
  choice with complete information and the expected
  value when information is incomplete

74
The Value of Information Example

• Per capita milk consumption has fallen over the
  years
• The milk producers engaged in market research to
  develop new sales strategies to encourage the
  consumption of milk

75
The Value of Information Example

• Findings
• Milk demand is seasonal with the greatest demand
  in the spring
• Price elasticity of demand is negative and small
• Income elasticity is positive and large

76
The Value of Information Example

• Milk advertising increases sales most in the
  spring
• Allocating advertising based on this information
  in New York increased profits by 9 or 14
  million
• The cost of the information was relatively low,
  while the value was substantial (increased
  profits)

77
Behavioral Economics

• Sometimes individuals behavior contradicts basic
  assumptions of consumer choice
• More information about human behavior might lead
  to better understanding
• This is the objective of behavioral economics
• Improving understanding of consumer choice by
  incorporating more realistic and detailed
  assumptions regarding human behavior

78
Behavioral Economics

• There are a number of examples of consumer choice
  contradictions
• You take at trip and stop at a restaurant that
  you will most likely never stop at again. You
  still think it fair to leave a 15 tip rewarding
  the good service.
• You choose to buy a lottery ticket even though
  the expected value is less than the price of the
  ticket

79
Behavioral Economics

• Reference Points
• Economists assume that consumers place a unique
  value on the goods/services purchased
• Psychologists have found that perceived value can
  depend on circumstances
• You are able to buy a ticket to the sold out Cher
  concert for the published price of 125. You find
  out you can sell the ticket for 500 but you
  choose not to, even though you would never have
  paid more than 250 for the ticket.

80
Behavioral Economics

• Reference Points (cont.)
• The point from which an individual makes a
  consumption decision
• From the example, owning the Cher ticket is the
  reference point
• Individuals dislike losing things they own
• They value items more when they own them than
  when they do not
• Losses are valued more than gains
• Utility loss from selling the ticket is greater
  than original utility gain from purchasing it

81
Behavioral Economics

• Experimental Economics
• Students were divided into two groups
• Group one was given a mug with a market value of
  5.00
• Group two received nothing
• Students with mugs were asked how much they would
  take to sell the mug back
• Lowest price for mugs, on average, was 7.00

82
Behavioral Economics

• Experimental Economics (cont.)
• Group without mugs was asked minimum amount of
  cash they would except in lieu of the mug
• On average willing to accept 3.50 instead of
  getting the mug
• Group one had reference point of owning the mug
• Group two had reference point of no mug

83
Behavioral Economics

• Fairness
• Individuals often make choices because they think
  they are fair and appropriate
• Charitable giving, tipping in restaurants
• Some consumers will go out of their way to punish
  a store they think is unfair in their pricing
• Manager might offer higher than market wages to
  make for happier working environment or more
  productive worker

84
Chapter 6

• Production

85
Introduction

• Our study of consumer behavior was broken down
  into 3 steps
• Describing consumer preferences
• Consumers face budget constraints
• Consumers choose to maximize utility
• Production decisions of a firm are similar to
  consumer decisions
• Can also be broken down into three steps

86
Production Decisions of a Firm

• Production Technology
• Describe how inputs can be transformed into
  outputs
• Inputs land, labor, capital and raw materials
• Outputs cars, desks, books, etc.
• Firms can produce different amounts of outputs
  using different combinations of inputs

87
Production Decisions of a Firm

• Cost Constraints
• Firms must consider prices of labor, capital and
  other inputs
• Firms want to minimize total production costs
  partly determined by input prices
• As consumers must consider budget constraints,
  firms must be concerned about costs of production

88
Production Decisions of a Firm

• Input Choices
• Given input prices and production technology, the
  firm must choose how much of each input to use in
  producing output
• Given prices of different inputs, the firm may
  choose different combinations of inputs to
  minimize costs
• If labor is cheap, firm may choose to produce
  with more labor and less capital

89
Production Decisions of a Firm

• If a firm is a cost minimizer, we can also study
• How total costs of production vary with output
• How the firm chooses the quantity to maximize its
  profits
• We can represent the firms production technology
  in the form of a production function

90
The Technology of Production

• Production Function
• Indicates the highest output (q) that a firm can
  produce for every specified combination of inputs
• For simplicity, we will consider only labor (L)
  and capital (K)
• Shows what is technically feasible when the firm
  operates efficiently

91
The Technology of Production

• The production function for two inputs
• q F(K,L)
• Output (q) is a function of capital (K) and labor
  (L)
• The production function is true for a given
  technology
• If technology increases, more output can be
  produced for a given level of inputs

92
The Technology of Production

• Short Run versus Long Run
• It takes time for a firm to adjust production
  from one set of inputs to another
• Firms must consider not only what inputs can be
  varied but over what period of time that can
  occur
• We must distinguish between long run and short run

93
The Technology of Production

• Short Run
• Period of time in which quantities of one or more
  production factors cannot be changed
• These inputs are called fixed inputs
• Long Run
• Amount of time needed to make all production
  inputs variable
• Short run and long run are not time specific

94
Production One Variable Input

• We will begin looking at the short run when only
  one input can be varied
• We assume capital is fixed and labor is variable
• Output can only be increased by increasing labor
• Must know how output changes as the amount of
  labor is changed (Table 6.1)

95
Production One Variable Input
96
Production One Variable Input

• Observations
• When labor is zero, output is zero as well
• With additional workers, output (q) increases up
  to 8 units of labor
• Beyond this point, output declines
• Increasing labor can make better use of existing
  capital initially
• After a point, more labor is not useful and can
  be counterproductive

97
Production One Variable Input

• Firms make decisions based on the benefits and
  costs of production
• Sometimes useful to look at benefits and costs on
  an incremental basis
• How much more can be produced when at incremental
  units of an input?
• Sometimes useful to make comparison on an average
  basis

98
Production One Variable Input

• Average product of Labor - Output per unit of a
  particular product
• Measures the productivity of a firms labor in
  terms of how much, on average, each worker can
  produce

99
Production One Variable Input

• Marginal Product of Labor additional output
  produced when labor increases by one unit
• Change in output divided by the change in labor

100
Production One Variable Input
101
Production One Variable Input

• We can graph the information in Table 6.1 to show
• How output varies with changes in labor
• Output is maximized at 112 units
• Average and Marginal Products
• Marginal Product is positive as long as total
  output is increasing
• Marginal Product crosses Average Product at its
  maximum

102
Production One Variable Input
Output per Month
At point D, output is maximized.
Labor per Month
0
2
3
4
5
6
7
8
9
10
1
103
Production One Variable Input
Output per Worker

• Left of E MP gt AP AP is increasing
• Right of E MP lt AP AP is decreasing
• At E MP AP AP is at its maximum
• At 8 units, MP is zero and output is at max

30
20
10
104
Marginal and Average Product

• When marginal product is greater than the average
  product, the average product is increasing
• When marginal product is less than the average
  product, the average product is decreasing
• When marginal product is zero, total product
  (output) is at its maximum
• Marginal product crosses average product at its
  maximum

105
Product Curves

• We can show a geometric relationship between the
  total product and the average and marginal
  product curves
• Slope of line from origin to any point on the
  total product curve is the average product
• At point B, AP 60/3 20 which is the same as
  the slope of the line from the origin to point B
  on the total product curve

106
Product Curves
AP is slope of line from origin to point on TP
curve
q
q/L
112
TP
30
AP
10
MP
107
Product Curves

• Geometric relationship between total product and
  marginal product
• The marginal product is the slope of the line
  tangent to any corresponding point on the total
  product curve
• For 2 units of labor, MP 30/2 15 which is
  slope of total product curve at point A

108
Product Curves
MP is slope of line tangent to corresponding
point on TP curve
TP
15
10
4
8
0
2
3
5
6
7
9
1
Labor
109
Production One Variable Input

• From the previous example, we can see that as we
  increase labor the additional output produced
  declines
• Law of Diminishing Marginal Returns As the use
  of an input increases with other inputs fixed,
  the resulting additions to output will eventually
  decrease

110
Law of Diminishing Marginal Returns

• When the use of labor input is small and capital
  is fixed, output increases considerably since
  workers can begin to specialize and MP of labor
  increases
• When the use of labor input is large, some
  workers become less efficient and MP of labor
  decreases

111
Law of Diminishing Marginal Returns

• Typically applies only for the short run when one
  variable input is fixed
• Can be used for long-run decisions to evaluate
  the trade-offs of different plant configurations
• Assumes the quality of the variable input is
  constant

112
Law of Diminishing Marginal Returns

• Easily confused with negative returns decreases
  in output
• Explains a declining marginal product, not
  necessarily a negative one
• Additional output can be declining while total
  output is increasing

113
Law of Diminishing Marginal Returns

• Assumes a constant technology
• Changes in technology will cause shifts in the
  total product curve
• More output can be produced with same inputs
• Labor productivity can increase if there are
  improvements in technology, even though any given
  production process exhibits diminishing returns
  to labor

114
The Effect of Technological Improvement
Moving from A to B to C, labor productivity is
increasing over time
Output
100
50
115
Production Two Variable Inputs

• Firm can produce output by combining different
  amounts of labor and capital
• In the long run, capital and labor are both
  variable
• We can look at the output we can achieve with
  different combinations of capital and labor
  Table 6.4

116
Production Two Variable Inputs
117
Production Two Variable Inputs

• The information can be represented graphically
  using isoquants
• Curves showing all possible combinations of
  inputs that yield the same output
• Curves are smooth to allow for use of fractional
  inputs
• Curve 1 shows all possible combinations of labor
  and capital that will produce 55 units of output

118
Isoquant Map
Ex 55 units of output can be produced with 3K
1L (pt. A) OR 1K 3L (pt. D)
119
Production Two Variable Inputs

• Diminishing Returns to Labor with Isoquants
• Holding capital at 3 and increasing labor from 0
  to 1 to 2 to 3
• Output increases at a decreasing rate (0, 55, 20,
  15) illustrating diminishing marginal returns
  from labor in the short run and long run

120
Production Two Variable Inputs

• Diminishing Returns to Capital with Isoquants
• Holding labor constant at 3 increasing capital
  from 0 to 1 to 2 to 3
• Output increases at a decreasing rate (0, 55, 20,
  15) due to diminishing returns from capital in
  short run and long run

121
Diminishing Returns
Increasing labor holding capital constant (A, B,
C) OR Increasing capital holding labor constant
(E, D, C
122
Production Two Variable Inputs

• Substituting Among Inputs
• Companies must decide what combination of inputs
  to use to produce a certain quantity of output
• There is a trade-off between inputs, allowing
  them to use more of one input and less of another
  for the same level of output

123
Production Two Variable Inputs

• Substituting Among Inputs
• Slope of the isoquant shows how one input can be
  substituted for the other and keep the level of
  output the same
• The negative of the slope is the marginal rate of
  technical substitution (MRTS)
• Amount by which the quantity of one input can be
  reduced when one extra unit of another input is
  used, so that output remains constant

124
Production Two Variable Inputs

• The marginal rate of technical substitution
  equals

125
Production Two Variable Inputs

• As labor increases to replace capital
• Labor becomes relatively less productive
• Capital becomes relatively more productive
• Need less capital to keep output constant
• Isoquant becomes flatter

126
Marginal Rate ofTechnical Substitution
Capital per year
5
Negative Slope measures MRTS MRTS decreases as
move down the indifference curve
4
3
2
1
Labor per month
1
2
3
4
5
127
MRTS and Isoquants

• We assume there is diminishing MRTS
• Increasing labor in one unit increments from 1 to
  5 results in a decreasing MRTS from 1 to 1/2
• Productivity of any one input is limited
• Diminishing MRTS occurs because of diminishing
  returns and implies isoquants are convex
• There is a relationship between MRTS and marginal
  products of inputs

128
MRTS and Marginal Products

• If we increase labor and decrease capital to keep
  output constant, we can see how much the increase
  in output is due to the increased labor
• Amount of labor increased times the marginal
  productivity of labor

129
MRTS and Marginal Products

• Similarly, the decrease in output from the
  decrease in capital can be calculated
• Decrease in output from reduction of capital
  times the marginal produce of capital

130
MRTS and Marginal Products

• If we are holding output constant, the net effect
  of increasing labor and decreasing capital must
  be zero
• Using changes in output from capital and labor we
  can see

131
MRTS and Marginal Products

• Rearranging equation, we can see the relationship
  between MRTS and MPs

132
Isoquants Special Cases

• Two extreme cases show the possible range of
  input substitution in production
• Perfect substitutes
• MRTS is constant at all points on isoquant
• Same output can be produced with a lot of capital
  or a lot of labor or a balanced mix

133
Perfect Substitutes
Capital per month
Same output can be reached with mostly capital or
mostly labor (A or C) or with equal amount of
both (B)
Labor per month
134
Isoquants Special Cases

• Perfect Complements
• Fixed proportions production function
• There is no substitution available between inputs
• The output can be made with only a specific
  proportion of capital and labor
• Cannot increase output unless increase both
  capital and labor in that specific proportion

135
Fixed-ProportionsProduction Function
Capital per month
Same output can only be produced with one set of
inputs.
Labor per month
136
Returns to Scale

• In addition to discussing the tradeoff between
  inputs to keep production the same
• How does a firm decide, in the long run, the best
  way to increase output?
• Can change the scale of production by increasing
  all inputs in proportion
• If double inputs, output will most likely
  increase but by how much?

137
Returns to Scale

• Rate at which output increases as inputs are
  increased proportionately
• Increasing returns to scale
• Constant returns to scale
• Decreasing returns to scale

138
Returns to Scale

• Increasing returns to scale output more than
  doubles when all inputs are doubled
• Larger output associated with lower cost (cars)
• One firm is more efficient than many (utilities)
• The isoquants get closer together

139
Increasing Returns to Scale
The isoquants move closer together
A
140
Returns to Scale

• Constant returns to scale output doubles when
  all inputs are doubled
• Size does not affect productivity
• May have a large number of producers
• Isoquants are equidistant apart

141
Returns to Scale
Constant Returns Isoquants are
equally spaced
142
Returns to Scale

• Decreasing returns to scale output less than
  doubles when all inputs are doubled
• Decreasing efficiency with large size
• Reduction of entrepreneurial abilities
• Isoquants become farther apart

143
Returns to Scale
Capital (machine hours)
Decreasing Returns Isoquants get further apart
Labor (hours)
144
Chapter 7

• The Cost of Production

145
Measuring CostWhich Costs Matter?

• For a firm to minimize costs, we must clarify
  what is meant by costs and how to measure them
• It is clear that if a firm has to rent equipment
  or buildings, the rent they pay is a cost
• What if a firm owns its own equipment or
  building?
• How are costs calculated here?

146
Measuring CostWhich Costs Matter?

• Accountants tend to take a retrospective view of
  firms costs, whereas economists tend to take a
  forward-looking view
• Accounting Cost
• Actual expenses plus depreciation charges for
  capital equipment
• Economic Cost
• Cost to a firm of utilizing economic resources in
  production, including opportunity cost

147
Measuring CostWhich Costs Matter?

• Economic costs distinguish between costs the firm
  can control and those it cannot
• Concept of opportunity cost plays an important
  role
• Opportunity cost
• Cost associated with opportunities that are
  foregone when a firms resources are not put to
  their highest-value use

148
Opportunity Cost

• An Example
• A firm owns its own building and pays no rent for
  office space
• Does this mean the cost of office space is zero?
• The building could have been rented instead
• Foregone rent is the opportunity cost of using
  the building for production and should be
  included in the economic costs of doing business

149
Opportunity Cost

• A person starting their own business must take
  into account the opportunity cost of their time
• Could have worked elsewhere making a competitive
  salary

150
Measuring CostWhich Costs Matter?

• Although opportunity costs are hidden and should
  be taken into account, sunk costs should not
• Sunk Cost
• Expenditure that has been made and cannot be
  recovered
• Should not influence a firms future economic
  decisions

151
Sunk Cost

• Firm buys a piece of equipment that cannot be
  converted to another use
• Expenditure on the equipment is a sunk cost
• Has no alternative use so cost cannot be
  recovered opportunity cost is zero
• Decision to buy the equipment might have been
  good or bad, but now does not matter

152
Prospective Sunk Cost

• An Example
• Firm is considering moving its headquarters
• A firm paid 500,000 for an option to buy a
  building
• The cost of the building is 5 million for a
  total of 5.5 million
• The firm finds another building for 5.25 million
• Which building should the firm buy?

153
Prospective Sunk Cost

• The first building should be purchased
• The 500,000 is a sunk cost and should not be
  considered in the decision to buy
• What should be considered is
• Spending an additional 5,250,000 or
• Spending an additional 5,000,000

154
Measuring CostWhich Costs Matter?

• Some costs vary with output, while some remain
  the same no matter the amount of output
• Total cost can be divided into
• Fixed Cost
• Does not vary with the level of output
• Variable Cost
• Cost that varies as output varies

155
Fixed and Variable Costs

• Total output is a function of variable inputs and
  fixed inputs
• Therefore, the total cost of production equals
  the fixed cost (the cost of the fixed inputs)
  plus the variable cost (the cost of the variable
  inputs), or

156
Fixed and Variable Costs

• Which costs are variable and which are fixed
  depends on the time horizon
• Short time horizon most costs are fixed
• Long time horizon many costs become variable
• In determining how changes in production will
  affect costs, must consider if fixed or variable
  costs are affected.

157
Fixed Cost Versus Sunk Cost

• Fixed cost and sunk cost are often confused
• Fixed Cost
• Cost paid by a firm that is in business
  regardless of the level of output
• Sunk Cost
• Cost that has been incurred and cannot be
  recovered

158
Measuring CostWhich Costs Matter?

• Personal Computers
• Most costs are variable
• Largest component labor
• Software
• Most costs are sunk
• Initial cost of developing the software

159
Measuring Costs

• Marginal Cost (MC)
• The cost of expanding output by one unit
• Fixed costs have no impact on marginal cost, so
  it can be written as

160
Measuring Costs

• Average Total Cost (ATC)
• Cost per unit of output
• Also equals average fixed cost (AFC) plus average
  variable cost (AVC)

161
A Firms Short Run Costs
162
A Firms Short Run Costs
163
Determinants of Short Run Costs

• The rate at which these costs increase depends on
  the nature of the production process
• The extent to which production involves
  diminishing returns to variable factors
• Diminishing returns to labor
• When marginal product of labor is decreasing

164
Determinants of Short Run Costs

• If marginal product of labor decreases
  significantly as more labor is hired
• Costs of production increase rapidly
• Greater and greater expenditures must be made to
  produce more output
• If marginal product of labor decreases only
  slightly as increase labor
• Costs will not rise very fast when output is
  increased

165
Determinants of Short Run Costs An Example

• Assume the wage rate (w) is fixed relative to the
  number of workers hired
• Variable costs is the per unit cost of extra
  labor times the amount of extra labor wL

166
Determinants of Short Run Costs An Example

• Remembering that

• And rearranging

167
Determinants of Short Run Costs An Example

• We can conclude

• and a low marginal product (MPL) leads to a high
  marginal cost (MC) and vice versa

168
Determinants of Short Run Costs

• Consequently
• MC decreases initially with increasing returns
• 0 through 4 units of output
• MC increases with decreasing returns
• 5 through 11 units of output

169
Cost Curves for a Firm
Total cost is the vertical sum of FC and VC.
Variable cost increases with production and the
rate varies with increasing and decreasing
returns.
Fixed cost does not vary with output
170
Cost Curves
171
Cost Curves

• When MC is below AVC, AVC is falling
• When MC is above AVC, AVC is rising
• When MC is below ATC, ATC is falling
• When MC is above ATC, ATC is rising
• Therefore, MC crosses AVC and ATC at the minimums
• The Average Marginal relationship

172
Cost Curves for a Firm

• The line drawn from the origin to the variable
  cost curve
• Its slope equals AVC
• The slope of a point on VC or TC equals MC
• Therefore, MC AVC at 7 units of output (point A)

173
Cost in the Long Run

• In the long run a firm can change all of its
  inputs
• In making cost minimizing choices, must look at
  the cost of using capital and labor in production
  decisions

174
Cost Minimizing Input Choice

• How do we put all this together to select inputs
  to produce a given output at minimum cost?
• Assumptions
• Two Inputs Labor (L) and capital (K)
• Price of labor wage rate (w)
• The price of capital
• r depreciation rate interest rate
• Or rental rate if not purchasing
• These are equal in a competitive capital market

175
Cost in the Long Run

• The Isocost Line
• A line showing all combinations of L K that can
  be purchased for the same cost
• Total cost of production is sum of firms labor
  cost, wL, and its capital cost, rK
• C wL rK
• For each different level of cost, the equation
  shows another isocost line

176
Cost in the Long Run

• Rewriting C as an equation for a straight line
• K C/r - (w/r)L
• Slope of the isocost
• -(w/r) is the ratio of the wage rate to rental
  cost of capital.
• This shows the rate at which capital can be
  substituted for labor with no change in cost

177
Choosing Inputs

• We will address how to minimize cost for a given
  level of output by combining isocosts with
  isoquants
• We choose the output we wish to produce and then
  determine how to do that at minimum cost
• Isoquant is the quantity we wish to produce
• Isocost is the combination of K and L that gives
  a set cost

178
Producing a Given Output at Minimum Cost
Q1 is an isoquant for output Q1. There are three
isocost lines, of which 2 are possible choices in
which to produce Q1.
Isocost C2 shows quantity Q1 can be produced
with combination K2,L2 or K3,L3. However, both of
these are higher cost combinations than K1,L1.
179
Input Substitution When an Input Price Change

• If the price of labor changes, then the slope of
  the isocost line changes, -(w/r)
• It now takes a new quantity of labor and capital
  to produce the output
• If price of labor increases relative to price of
  capital, and capital is substituted for labor

180
Input Substitution When an Input Price Change
Capital per year
If the price of labor rises, the isocost
curve becomes steeper due to the change in the
slope -(w/L).
The new combination of K and L is used to produce
Q1. Combination B is used in place of combination
A.
Labor per year
181
Cost in the Long Run

• How does the isocost line relate to the firms
  production process?

182
Cost in the Long Run

• The minimum cost combination can then be written
  as
• Minimum cost for a given output will occur when
  each dollar of input added to the production
  process will add an equivalent amount of output.

183
Cost in the Long Run

• If w 10, r 2, and MPL MPK, which input
  would the producer use more of?
• Labor because it is cheaper
• Increasing labor lowers MPL
• Decreasing capital raises MPK
• Substitute labor for capital until

184
Cost in the Long Run

• Cost minimization with Varying Output Levels
• For each level of output, there is an isocost
  curve showing minimum cost for that output level
• A firms expansion path shows the minimum cost
  combinations of labor and capital at each level
  of output
• Slope equals ?K/?L

185
A Firms Expansion Path
The expansion path illustrates the least-cost
combinations of labor and capital that can be
used to produce each level of output in the
long-run.
50
186
Expansion Path and Long Run Costs

• Firms expansion path has same information as
  long-run total cost curve
• To move from expansion path to LR cost curve
• Find tangency with isoquant and isocost
• Determine min cost of producing the output level
  selected
• Graph output-cost combination

187
A Firms Long Run Total Cost Curve
188
Long Run Versus Short Run Cost Curves

• In the short run, some costs are fixed
• In the long run, firm can change anything
  including plant size
• Can produce at a lower average cost in long run
  than in short run
• Capital and labor are both flexible
• We can show this by holding capital fixed in the
  short run and flexible in long run

189
The Inflexibility of Short Run Production
Capital per year
Capital is fixed at K1. To produce q1, min cost
at K1,L1. If increase output to Q2, min cost is
K1 and L3 in short run.
In LR, can change capital and min costs falls to
K2 and L2.
Labor per year
190
Long Run VersusShort Run Cost Curves

• Long-Run Average Cost (LAC)
• Most important determinant of the shape of the LR
  AC and MC curves is relationship between scale of
  the firms operation and inputs required to
  minimize cost
• Constant Returns to Scale
• If input is doubled, output will double
• AC cost is constant at all levels of output

191
Long Run Versus Short Run Cost Curves

• Increasing Returns to Scale
• If input is doubled, output will more than double
• AC decreases at all levels of output
• Decreasing Returns to Scale
• If input is doubled, output will less than double
• AC increases at all levels of output

192
Long Run Versus Short Run Cost Curves

• In the long run
• Firms experience increasing and decreasing
  returns to scale and therefore long-run average
  cost is U shaped.
• Source of U-shape is due to returns to scale
  instead of decreasing returns to scale like the
  short-run curve
• Long-run marginal cost curve measures the change
  in long-run total costs as output is increased by
  1 unit

193
Long Run Versus Short Run Cost Curves

• Long-run marginal cost leads long-run average
  cost
• If LMC lt LAC, LAC will fall
• If LMC gt LAC, LAC will rise
• Therefore, LMC LAC at the minimum of LAC
• In special case where LAC is constant, LAC and
  LMC are equal

194
Long Run Average and Marginal Cost
Cost ( per unit of output
Output
195
Long Run Costs

• As output increases, firms AC of producing is
  likely to decline to a point
• On a larger scale, workers can better specialize
• Scale can provide flexibility managers can
  organize production more effectively
• Firm may be able to get inputs at lower cost if
  can get quantity discounts. Lower prices might
  lead to different input mix.

196
Long Run Costs

• At some point, AC will begin to increase
• Factory space and machinery may make it more
  difficult for workers to do their jobs
  efficiently
• Managing a larger firm may become more complex
  and inefficient as the number of tasks increase
• Bulk discounts can no longer be utilized.
  Limited availability of inputs may cause price to
  rise.

197
Long Run Costs

• When input proportions change, the firms
  expansion path is no longer a straight line
• Concept of return to scale no longer applies
• Economies of scale reflects input proportions
  that change as the firm changes its level of
  production

198
Economies and Diseconomies of Scale

• Economies of Scale
• Increase in output is greater than the increase
  in inputs
• Diseconomies of Scale
• Increase in output is less than the increase in
  inputs
• U-shaped LAC shows economies of scale for
  relatively low output levels and diseconomies of
  scale for higher levels

199
Long Run Costs

• Increasing Returns to Scale
• Output more than doubles when the quantities of
  all inputs are doubled
• Economies of Scale
• Doubling of output requires less than a doubling
  of cost

200
Long Run Costs

• Economies of scale are measured in terms of
  cost-output elasticity, EC
• EC is the percentage change in the cost of
  production resulting from a 1-percent increase in
  output

201
Long Run Costs

• EC is equal to 1, MC AC
• Costs increase proportionately with output
• Neither economies nor diseconomies of scale
• EC lt 1 when MC lt AC
• Economies of scale
• Both MC and AC are declining
• EC gt 1 when MC gt AC
• Diseconomies of scale
• Both MC and AC are rising

202
Long Run Versus Short Run Cost Curves

• We will use short and long run costs to determine
  the optimal plant size
• We can show the short run average costs for 3
  different plant sizes
• This decision is important because once built,
  the firm may not be able to change plant size for
  a while

203
Long Run Cost with Economiesand Diseconomies of
Scale
204
Long Run Cost withConstant Returns to Scale

• The optimal plant size will depend on the
  anticipated output
• If expect to produce q0, then should build
  smallest plant AC 8
• If produce more, like q1, AC rises
• If expect to produce q2, middle plant is least
  cost
• If expect to produce q3, largest plant is best

205
Long Run Cost with Economiesand Diseconomies of
Scale
206
Long Run Cost withConstant Returns to Scale

• What is the firms long run cost curve?
• Firms can change scale to change output in the
  long run
• The long run cost curve is the dark blue portion
  of the SAC curve which represents the minimum
  cost for any level of output
• Firm will always choose plant that minimizes the
  average cost of production

207
Long Run Cost with Economiesand Diseconomies of
Scale
208
Long Run Cost withConstant Returns to Scale

• The long-run average cost curve envelops the
  short-run average cost curves
• The LAC curve exhibits economies of scale
  initially but exhibits diseconomies at higher
  output levels

209
Chapter 8

• Profit Maximization and Competitive Supply

210
Perfectly Competitive Markets

• The model of perfect competition can be used to
  study a variety of markets
• Basic assumptions of Perfectly Competitive
  Markets
• Price taking
• Product homogeneity
• Free entry and exit

211
Perfectly Competitive Markets

• Price Taking
• The individual firm sells a very small share of
  the total market output and, therefore, cannot
  influence market price
• Each firm takes market price as given price
  taker