Chapter 2: Modeling Individual Choice

1
Chapter 2 Modeling Individual
Choice

• Purposes of Chapter
• Venture into microeconomics.
• Examining the economic decision process of
  consumers, a key component of the economic
  decision process of firms, and several
  complexities in modeling human behavior.

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Another Economic Fundamental Rationality

• Rationality the behavior of economic units
  (i.e. individuals, firms, government) reflects
  the pursuit of an underlying goal.

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The Underlying Goals in Rational Economic
Behavior

• Based upon values, what the economic unit
  (consumer, firm, government) holds to be
  important.
• Varies across different units.
• Typically includes one or more constraints,
  reflecting scarcity.
• Generally phrased in terms of maximizing or
  minimizing, possibly subject to (constraint).

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Individual Choice in Buying
GoodsTheory

• Individuals want to be as happy as possible.
• Individuals gain happiness from the consumption
  of goods.
• The more consumption the better, at least to a
  satiation point.
• The happiness we gain becomes less and less as we
  consume more and more of any good.

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Individual Choice in Buying
GoodsModel

• Utility happiness that individuals feel
  (measured in utils).
• Utility caused by levels of the various goods
  that we consume.
• Utility Function A explicit relationship which
  specifies the level of utility based upon the
  amounts of all the goods that we consume.

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Marginal Utility

• Marginal Utility (MU) -- the change in utility
  (U) resulting from a change in the quantity of an
  individual good (Q) consumed.
• In mathematical terms,
• MU ?U/?Q.

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Positive and Diminishing Marginal Utility

• The more consumption the better,
• i.e. Q? ? U?,
• ? Positive Marginal Utility
• The happiness we gain becomes less and less as we
  consume more and more of any good
  
• i.e. Q? ? MU?,
• ? Diminishing Marginal Utility

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Utility and Marginal Utility
An Example

• Suppose I get utility from consuming coffee (and
  other goods).
• Suppose my utility from coffee, holding
  consumption of all other goods constant, looks as
  follows.

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My Utility From Coffee (All Other Goods
Constant)

• Coffee (Cups) Utility (Utils)
• 0 0
• 1 100
• 2 185
• 3 245
• 4 295
• 5 325
  
• 6 340
• 7 340
• 8 320
  

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My Marginal Utility From Coffee (All Else
Constant)

• Coffee (Cups) Utility Marginal Utility
• 0 0
  --
• 1 100
  100
• 2 185
  85
• 3 245
  60
• 4 295
  50
• 5 325
  30
• 6 340
  15
• 7 340
  0
• 8 320
  -20

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Ceteris Paribus

• Ceteris Paribus Latin term, meaning all else
  constant, or in the context of theories and
  models, all other causes constant.
• Fundamental concept in theories and models most
  behavior has multiple causes.
• One can only look sensibly at responses to
  changes in one cause at a time, therefore one
  needs to hold others constant.

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Utility and Marginal Utility Multiple Goods

• My utility is determined by consumption of a
  number of goods (call it n goods).
• Notation
• Q1 quantity consumed of good 1,
• Q2 quantity consumed of good 2, etc.
• MU1 marginal utility of good 1,
• MU2 marginal utility of good 2, etc.

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Condition for Maximizing Utility, No Scarcity of
Goods

• I can have as much as I want of any good for
  free.
• Then to maximize utility, I should choose to
  consume quantities of each good until each of
  their marginal utilities equals zero.
• In mathematical notation I choose quantities of
  goods so that
• MU1 MU2 MU3 MUn 0.

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Maximizing Utility With Scarcity and Finite Budget

• Scarcity ? every good as a price.
• Notation
• P1 price of good 1,
• P2 price of good 2, etc.
• A related issue finite budget
• I have so much I can spend.
• Also called Budget Constraint.

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Maximizing Utility Scarcity and
Finite Budget

• Then to maximize utility subject to being within
  my budget constraint, I should choose to consume
  quantities of each good according to two
  conditions.
• (1) I spend my entire budget.
• (2) The marginal benefit-cost ratio is
• equal across all goods, i.e.
• MU1/P1 MU2/P2 MUn/Pn.

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An Example

• Suppose my world has two goods, steak dinners (S)
  and bottled water (W), and I get similar utility
  from consumption of each one.
• The price of a steak dinner (PS) equals 25,
  while the price of bottled water (PW) equals 1.

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Maximizing Utility Subject to Budget Constraint

• I should seek to consume quantities of steak
  dinners and water so that I spend my entire
  budget and
• MUS/PS MUW/PW, or equivalently
• MUS/25 MUW/1.

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The Solution

• Thus, I should choose my consumption of steak
  dinners and water where the marginal utility of
  steak dinners is 25 times the marginal utility of
  water.
• Diminishing marginal utility for both steak
  dinners and water ? I should consume a small
  amount of steak dinners and a lot of water.

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Behavior of the Firm The Production
Function

• The Production Function A relationship for the
  individual firm that specifies how inputs
  (natural resources, labor, and capital) are
  combined to produce output.
• Capital physical capital (machines) and human
  capital (skills, innate and acquired).

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Marginal Product of Labor

• Marginal Product of Labor (MPN) -- the change in
  output (Q) resulting from a change in the amount
  of labor employed (N), ceteris paribus on the
  other inputs.
• In mathematical terms,
• MPN ?Q/?N.

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The Law of Diminishing Returns

• The Law of Diminishing Returns as a firm uses
  more and more of a given input such as labor,
  ceteris paribus on the other inputs, there will
  come a time when the marginal product of labor
  will decrease (i.e. Diminishing Marginal
  Product of Labor).

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Production and Marginal Product An Example

• Suppose King Davids (a Marshall Street eatery)
  employs labor and other inputs (e.g. food,
  electricity, cooking machines) to produce
  lunches.
• Suppose their production function with labor,
  ceteris paribus on the other inputs, looks as
  follows.

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King Davids Production Function

• Labor Input (People) Output (Lunches)
• 0
  0
• 1
  10
• 2
  25
• 3
  50
• 4
  70
• 5
  86
• 6
  95
• 7
  101
• 8
  104
• 9
  93

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King Davids Marginal Product of
Labor

• Labor Input (N) Output (Q) MPN
  
• 0 0
  --
• 1 10
  10
• 2 25
  15
• 3 50
  25
• 4 70
  20
• 5 86
  16
• 6 95
  9
• 7 101
  6
• 8 104
  3
• 9 93
  -11

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So How Much Should King Davids Produce and
Employ?

• Assumption King Davids seeks to maximize
  profits.
• Therefore, not enough information for them to
  make this decision.
• Need additional information on
• -- cost per unit of each input
• -- price of their output
• -- market structure, or degree of
• competitiveness with other lunch
  
• eateries

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The Relevant Region of Production and Employment

• Increased usage of inputs, ceteris paribus, imply
  more output,
• i.e. N? ? Q?,
• ? Positive
  
• Marginal Product of Labor.
• The Law of Diminishing Returns has set in,
  i.e. N? ? MPN?,
• ? Diminishing
• Marginal Product of Labor.

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Additional Complexities in the Economic Decision
Process

• Realistically, life places complexities that
  influence the rational economic decisions of both
  consumers and firms.
• Here, we just introduce two of them and motivate
  how they can be influential.

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Complexity 1 The Present Versus The Future

• Consumers Should I buy and/or work now or later
  (existence of interest on savings, investment in
  human capital)?
• Firms Should I expand my physical capital by
  buying this machine (trading current costs versus
  future benefits)?

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Intertemporal Decisions

• Intertemporal Decisions rational economic plans
  for consumers and firms in assessing the future
  along with the present.
• Mechanisms for weighing the present versus the
  future.
• The Discount Rate
• Present Value

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The Discount Rate

• The Discount Rate the rate, in percentage
  terms, that we are willing to trade off money
  received one year from now versus money received
  today.
• Equivalent amounts received today and in the
  future are worth more today need to discount
  future amounts.

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The Discount Rate An Example

• Suppose you have a choice between 300 today and
  a higher amount next year. Suppose as well that
  you decide that youre indifferent between 300
  today and 360 next year.
• Your discount rate
• (360 ? 300)/(300)x100
• 20

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Characteristics of the Discount Rate

• Consumers depends upon different individuals
  utility or preferences.
• High Discount Rate devalues the future sharply,
  wants it now.
• Low Discount Rate more willing to forego the
  present for the future.
• Firms the market interest rate is their
  ultimate discount rate.

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Present Value

• Present Value an explicit formula for
  converting the value of dollars received in
  future years to their current value equivalents.
• Hugely important in many aspects of financial
  world (interest rates).

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Complexity 2 Risk and
Uncertainty

• Key Issue future is unknown, affects economic
  decisions.
• Risk unknown events to which we can attach a
  probability.
• Uncertainty absolutely un-thought of events
  which may end up occurring.
• Uncertain events which in fact occur will convert
  into risky events.

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Incorporating Riskin Economic Decisions

• We develop expectations of unknown events our
  best guess of what we think will happen, then we
  act upon those (right or wrong).
• We practice risk aversion of different events
  with the same expected return, we prefer less
  risk.

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Conclusions Economic Decisions

• Intertemporal issues and risk/uncertainty place
  complexities on the rational decisions of
  consumers, firms, and even government
• We wont use them explicitly here, the basics
  still tell us a lot.
• We covered the decision rule for consumers, for
  firms we got the process started.