Hirschey Chapter 4 DEMAND ANALYSIS

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Hirschey Chapter 4DEMAND ANALYSIS
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The Basis for Consumer Demand

• The ability of goods and services to satisfy
  consumer wants is the basis for consumer demand.
• Utility theory helps us understand the basis for
  demand since it explains the relationship between
  consumer satisfaction and the goods and services
  consumed.

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Utility Functions

• A mathematical representation of the relationship
  between total utility and the consumption of
  goods and services.
• Utility f(Goods, Services)
• The utility function is shaped by
• the tastes and preferences of consumers, and
• the quantity and quality of available products.

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Utility Functions

• The utility derived from consumption is
  intangible.
• Consumers reveal their preferences through
  purchase decisions and provide tangible evidence
  of the utility they derive from various products.

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Marginal Utility

• Measures the added satisfaction derived from
  one-unit increase in consumption of a particular
  good or service, holding consumption of all other
  goods and services constant.

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Total and Marginal Utility
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Total and Marginal Utility

• The marginal utility is diminishing as
  consumption of sandwiches is increasing.
• Each sandwich costs 1.
• 1st sandwich
• cost per unit of utility 1/5 0.20
• 2nd sandwich
• cost per unit of utility 1/4 0.25

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Total and Marginal Utility

• As a result of diminishing marginal utility, the
  cost of each marginal unit of satisfaction
  increases as we increase our consumption of
  sandwiches.
• Assume that the consumer has alternative
  consumption opportunities that would provide one
  additional unit of utility for 20.
• Then, the consumer will be willing to increase
  the consumption of sandwiches only if sandwich
  prices were to fall.

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Total and Marginal Utility

• If the required price/marginal utility trade-off
  for sandwiches is 20 per unit of satisfaction,
  then the consumer will pay 1 for a single
  sandwich.
• In order for the consumer to purchase one more
  sandwich, the second sandwich should cost only
  80 (20 x 4 units of satisfaction).
• Similarly, in order for the consumer to purchase
  the third sandwich, the third sandwich should
  cost only 60 (20 x 3 units of satisfaction).

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The Law of Diminishing Marginal Utility

• As an individual increases consumption of a given
  product, the marginal utility gained from
  consumption eventually declines.
• This law gives rise to a downward-sloping demand
  curve for all goods and services.

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The Demand Curve
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Consumer Choice

• Products are frequently consumed as parts of a
  basket of goods and services.
• Within this basket, products can be substituted
  for each other.
• The substitution occurs at different degrees for
  different pairs of products.

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Consumer ChoiceTotal and Marginal Utility
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Consumer ChoiceIndifference Curves

• E.g. A consumer can choose to buy a basket with a
  high proportion of total expenditures devoted to
  services or vice versa.
• For this consumer, a large number of baskets can
  be created that provide the same level of utility
  to the consumer.
• An indifference curve represents all market
  baskets among which the consumer is indifferent
  about choosing.

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Indifference Curves
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Indifference Curves

• Indifference curves will never intersect with
  each other.
• Higher curves will represent higher levels of
  utility.
• The consumer will want to consume a basket on a
  relatively higher indifference curve in order to
  increase/maximize his/her utility.

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Marginal Rate of Substitution

• The slope of each indifference curve equals the
  change in goods (?Y) divided by the change in
  services (?X).
• Marginal rate of substitution is the slope
  relation that shows the change in the consumption
  of Y (goods) necessary to offset a given change
  in the consumption of X (services) if the
  consumers overall level of utility is to remain
  constant.
• MRS ?Y / ?X slope of an indifference curve

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Marginal Rate of Substitution

• MRS is not constant along an indifference curve.
• MRS usually declines as the amount of
  substitution increases.
• MRS declines because of the law of diminishing
  marginal utility.

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Marginal Rate of Substitution

• When we move from a left-hand-side point to a
  right-hand-side point on a given indifference
  curve
• the loss in utility associated with a reduction
  in Y is equal to ?U MUY x ?Y.
• the gain in utility associated with an increase
  in X is equal to ?U MUX x ?X.

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Marginal Rate of Substitution

• Along an indifference curve, the utility level
  does not change.
• Therefore, the absolute value of the change in
  utility for reducing Y needs to be equal to the
  change in utility for increasing X.
• So, the following must be true
• MUY x ?Y - (MUX x ?X )
• The absolute value of the changes utility must be
  the same and the signs must be opposite in order
  for U to stay constant.

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Marginal Rate of Substitution

• When MUY x ?Y - (MUX x ?X ) is true, the
  following must also be true
• MRSXY Slope of an indifference curve
• The slope of the indifference curve is
  determined by the ratio of the marginal utilities
  derived from each product.

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Consumer ChoiceBudget Lines

• The second important determinant of the consumer
  choice is the existence of a budget constraint.
• A budget line represents all combinations of
  products that can be purchased for a fixed
  dollar/lira amount

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Consumer ChoiceBudget Lines

• Total Budget Spending on Goods Spending on
  Services
• B PY Y PX X
• The expression for the budget line becomes

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Budget Line
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Decrease in Price of Y
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Effect of Price Changes

• Consumer is affected in two ways
• 1. Income Effect With the same budget, a price
  decrease allows higher consumption (higher
  indifference curve) and a price increase causes
  lower consumption (lower indifference curve).
• Change in the quantity demanded as a result of a
  change in the consumers real income (real income
  changes as result of a change in the price level)

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Effect of Price Changes

• 2. Substitution Effect With the same budget, a
  price increase makes the product relatively more
  expensive and shifts the overall consumption away
  and more towards the cheaper product (movement
  along the indifference curve).
• Change in the quantity demanded that is the
  result of only a change in the relative prices of
  goods, given a constant real income.

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Effect of Price Changes

• 3. Total Effect Total effect is the sum of
  income and substitution effects.

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Effect of Price Changes

• Price of X decreases

• Nominal income is the same.
• Same combination can be bought
• by spending less of the nominal
• income.
• Consumer has money left to purchase
• more of X or Y.
• Consumers real income has increased.
• Income effect is the change in the combination
  due to the new real income.

• Nominal income is the same.
• If the real income were kept at the original
  level, what is the combination that the consumer
  would buy?
• Substitution effect is the change in the
  combination due to the new price ratio, under the
  original real income.

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Decrease in Price of Y
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Optimal Consumption

• Optimal consumption will occur when utility for
  the consumer is maximized.
• Utility is maximized when a consumer chooses a
  basket of products on the highest indifference
  curve possible, for a given budget expenditure.

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Consumer ChoiceBudget Constraint and Utility

• The budget constraint will impose a limit on the
  level of utility a consumer can derive from
  consumption of the basket of products.
• The highest indifference curve a consumer can
  reach will be determined by the budget
  constraint.

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DEMAND ELASTICITY
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Elasticity

• Percentage relationship between two variables
• elasticity change in A / change in B
• Price elasticity shows the sensitivity of demand
  to changing prices
• price elasticity change Q / change in P

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Price Elasticity

• Mathematically,
• change in Q ? Quantity / Initial Quantity
• and,
• change in P ? Price / Initial Price
• Therefore,

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Arc Elasticity

• Measures the sensitivity of Q to changes in P
  over a range of price values

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Arc Elasticity

• E.g. If the price of a product rises from 11 to
  12, the quantity demanded falls from 7 to 6
  units. The arc elasticity of demand over this
  price range is

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Arc Elasticity

• We use averages in the denominators because
• 1. If we had used the beginning values (Q7,
  P11), Ep would equal to -1.57.
• 2. If the price decreases from 12 to 11, then
  Q increases from 6 to 7. If we use beginning
  values (Q6, P12), this time Ep equals -2.0.
• 3. It looks like we have a different sensitivity
  depending on whether we have a price increase or
  a price decrease.
• Using averages avoids this ambiguity.

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Point Elasticity

• Measures the sensitivity of Q to changes in P
  when the change is very small
• where dQ/dP is the derivative of Q with respect
  to P.

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Point Elasticity

• E.g. Q 18 - P
• When Q 6 and P 12,
• Ep -1 x (12/6) -2
• Note that when the demand curve is linear,
  (dQ/dP) is constant along the demand curve.
  However, Ep changes as Q and P values change.

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Point Elasticity

• E.g. Q 100 - P2
• When Q 75 and P 5,
• Ep -2P x (5/75) -50 / 75 -0.67
• E.g. Q 100 / P1.7
• When Q 10 and P 3.875, Ep ?
• Rewrite the demand equation
• log Q log 100 - 1.7 log P

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Elasticity Definitions

• Ep gt 1 ? relatively elastic demand
• ( ? in Q gt ? in P)
• 0 lt Ep lt 1 ? relatively inelastic demand
• ( ? in Q lt ? in P)
• Ep 1 ? unitary elasticity
• ( ? in Q ? in P)
• Ep ? ? perfect elasticity
• ( ? in Q gtgt ? in P since ? in P 0)
• Ep 0 ? perfect inelasticity
• ( ? in Q 0)

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Determinants of Elasticity

• Ease of substitution
• Proportion of total expenditures
• Durability of product
• Possibility of postponing purchase
• Possibility of repair
• Used product market
• Length of time period

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Demand Elasticity and Revenue(TR Q x P)

• Price increase
• Ep gt 1 ? ( decrease in Q gt increase in P)
• TR is decreasing.
• 0 lt Ep lt 1 ? ( ? decrease in Q lt ? increase
  in P)
• TR is increasing.
• Ep 1 ? ( ? decrease in Q ? increase in
  P)
• TR does not change.

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Demand Elasticity and Revenue(TR Q x P)

• Price decrease
• Ep gt 1 ? ( increase in Q gt decrease in P)
• TR is increasing.
• 0 lt Ep lt 1 ? ( increase in Q lt decrease in
  P)
• TR is decreasing.
• Ep 1 ? ( increase in Q ? decrease in P)
• TR does not change.

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Elastic
Unitary
Inelastic
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Demand and Marginal Revenue
P
Elastic
Ep -1
Inelastic
MR
D
Q
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Demand and Revenue

• Demand Curve P a - bQ
• Total Revenue PxQ aQ - bQ2
• Marginal Revenue dTR/dQ a - 2bQ
• Note that the demand curve and the marginal
  revenue curve share the y-intercept.
• Marginal revenue curve has twice the slope of the
  demand curve.

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Cross-Elasticity of Demand

• Shows the impact on the quantity demanded of a
  particular product created by a price change in a
  related product (substitutes or complements)
• Ex gt 0 for substitutes.
• Ex lt 0 for complements.

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Income Elasticity of Demand

• Sensitivity of quantity demanded to changes in
  the consumers income
• EY gt 1.0 for superior goods.
• 0 ? EY? 1.0 for normal goods.
• EY lt 0 for inferior goods.