DEMAND ANALYSIS AND OPTIMAL PRICING

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DEMAND ANALYSIS AND OPTIMAL PRICING
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DETERMINANTS OF DEMAND AND SUPPLY
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Market Demand

• The quantity of a good or service that people are
  ready to buy at various prices within some given
  time period, other factors besides price held
  constant.
• Ready willing (preference) and able (income)
• The combined demands of all participants is
  called the market demand.

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The Law of Demand

• As the price of a good or service increases, the
  quantity demanded decreases.
• The demand curve is downward sloping.

Price
Quantity demanded
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The Demand Curve

• Shows the relationship between quantity demanded
  and price, assuming that all other factors are
  held constant.
• If price changes, the quantity demanded changes
  and we have a movement along the demand curve.
• If one of the nonprice factors change, the demand
  changes and we have a shift of the demand curve.

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Nonprice Factors

• Tastes and preferences
• Income
• Prices of related products
• Substitute products
• Complementary products
• Future expectations
• Number of buyers

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Market Supply

• The quantity of a good or service that people are
  ready to sell at various prices within some given
  time period, other factors besides price held
  constant.
• The combined supplies of all participants is
  called the market supply.

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The Law of Supply

• As the price of the product increases, the
  quantity supplied increases.
• The supply curve is upward sloping.

Price
Quantity Supplied
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The Supply Curve

• Shows the relationship between quantity supplied
  and price, assuming that all other factors are
  held constant.
• If price changes, the quantity supplied changes
  and we have a movement along the supply curve.
• If one of the nonprice factors change, the supply
  changes and we have a shift of the supply curve.

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Nonprice Factors

• Costs and technology
• Prices of other products offered by the seller
• Substitute products
• Complementary products
• Future expectations
• Number of sellers
• Weather conditions

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Market Equilibrium

• The market will come to an equilibrium and clear
  at the point where the quantity demanded is equal
  to the quantity supplied.

Price
QS
Surplus
PE
Shortage
QD
Quantity
QE
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Comparative Statics Analysis

• It is a sensitivity analysis in which managers
  will ask What if questions regarding demand and
  supply.
• Analysis starts with one equilibrium point and
  jumps to the next equilibrium (statics), while
  comparing the differences in market conditions
  between the two situations.

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Comparative Statics Analysis

• Short run change Increase in demand causes price
  to increase.
• Long run change Supply increases as new sellers
  enter the market and original sellers increase
  production capacity.

QS,1
2
QS,2
P2
3
P3
P1
1
QD,2
QD,1
Q1
Q3
Q2
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Comparative Statics Analysis

• Short run change Decrease in demand causes price
  to fall.
• Long run change Supply decreases as less
  profitable firms or those experiencing losses
  exit the market or decrease production capacity.

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Comparative Statics Analysis

• Short run change Increase in supply causes price
  to fall.
• Long run change Demand increases as tastes and
  preferences of consumers eventually change in
  favor of the product relative to substitutes.

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Comparative Statics Analysis

• Short run change Decrease in supply causes price
  to rise.
• Long run change Demand decreases as tastes and
  preferences of consumers eventually change away
  from the product and toward the substitutes.

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ELASTICITY OF DEMAND
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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 in 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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(No Transcript)
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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.

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Price Discrimination

• When a company sells identical products in two or
  more markets, it may charge different prices in
  the markets.
• Price discrimination means
• products with identical costs are sold in
  different markets at different prices,
• the ratio of (price to marginal cost) differs for
  similar products.
• E.g. When an adult and a child are charged
  different prices for tickets of the same quality
  and at the same time, there is PD.

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Necessary Conditions for Price Discrimination

• The two or more markets in which the product is
  sold must be capable of being separated.
• There can be no transfer or resale of the product
  from one market to the other.
• The demand curves in the segmented markets must
  have different elasticities at given prices.

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Degrees of Price Discrimination

• First degree price discrimination
• when the seller can identify where each buyer
  lies on a demand curve and can charge each buyer
  the price s/he is willing to pay.
• The seller needs to have a lot of information
  about where the buyer lies on the demand curve.
• E.g. bargaining to buy a new automobile
• E.g. bargaining to buy a new house

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• In first degree price discrimination, the maximum
  price possible is charged for each unit of output.

A
P1
P2
Profit maximization suggests selling QD units at
PC dollars. If QgtQD, PltMC if QgtQD,
PgtMC. Consumer surplus (price consumer is
willing to pay) (actual price charged by the
producer) Consumer surplus without price
discrimination APCB By price discrimination,
the firm captures the consumer surplus as
economic profits.
P3
B
PC
D
MC AC
Q1 Q2 Q3
QD
MR
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• Second degree price discrimination
• when the seller charges differential prices for
  blocks of services
• The seller must be able to meter the services
  consumed by the buyers.
• E.g. public utility prices (highest fare for the
  smallest quantities)

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• In second-degree price discrimination, pricing is
  based on the quantities of output purchased by
  individual consumers.

The first Q1 units are purchased at price P1. Q2
Q1 units are purchased at P2. All additional
units are purchased at P3.
P1
P2
P3
Q2
Q1
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• Third degree price discrimination
• the monopolist separates the customers into
  different markets and charges different prices in
  each.
• E.g. market segmentation based on geography, age,
  sex, product use, income, etc.
• If the firm can segment the markets successfully,
  it can increase its profits above what they would
  be if a single price were charged.

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• In third-degree price discrimination, consumers
  or markets are separated in terms of their price
  elasticity of demand.

PI
PII
DT
DII
MC
MC
MC
MRI
MRII
DI
MRT
QII
QI
QT
A higher price is charged in Market I where
demand is relatively inelastic. In Market II,
price elasticity of demand is higher and hence
the profit-maximizing price is lower.
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• E.g. A firm sells its product in two markets.
• MC 2 per unit
• Market I PI 14 2QI
• MRI 14 4QI
• Market II PII 10 QII
• MRII 10 2QII
• Using third-degree price discrimination, what are
  the profit-maximizing prices and quantities in
  each market?
• MRI MC and MRII MC for profit maximization.
• MRI 14 4QI 2 ? QI 3 units, P 8
• MRII 10 2QII 2 ? QII 4 units, P 6
• Profit (P.Q) (MC.Q) in each market.
• Market I Profit 18 (3x8) (3x2)
• Market II Profit 16 (4x6) (4x2)
• Combined profit 34

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• How much would profits be in the absence of price
  discrimination?
• Use the combined demand and MR equations
• QI 7 P/2 and QII 10 P ? QT 17 3/2 P
• P 11.33 0.67 QT and MRT 11.33 1.33 QT
• Set combined MRT equal to MC
• MRT 11.33 1.33 QT 2 ? QT 7 units.
• When QT 7 units, profits 32.67
• Profit is increased by applying third-degree
  price discrimination.

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Examples of Price Discrimination

• Products going into the export market are priced
  lower than those sold domestically (for
  international competitiveness)
• Pubs and bars may have happy hours
• Restaurants may have lunch hours
• Theaters, cinemas, sporting events usually charge
  lower for children, students.
• Public transportation is offered at lower prices
  to senior citizens, students, physically impaired.

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• Public utilities charge higher rates to business
  customers.
• For academic publications, individuals are
  charged lower rates than libraries or other
  institutions.
• Theaters charge different ticket prices for
  matinees and evening performances.
• Theaters charge higher ticket prices on weekends
  than on weekdays.
• Daytime telephone rates are higher than nighttime
  rates.
• Hotels catering to business travelers charge
  lower room rates during weekends.

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Nonmarginal Pricing

• It is often claimed that businesses are not
  really profit-maximizers and that they have other
  objectives.
• Other objectives could be achieving
• a desired market share,
• a target profit margin,
• a target rate of return on assets,
• a target rate of return on equity.
• One common method used for pricing purposes is
  cost-plus (full-cost).

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Cost-Plus Pricing

• Most businesspeople are found to be pricing their
  products by applying cost-plus
• Calculate the variable cost of the product
• Add an allocation of fixed costs
• Add a profit percentage or markup
• E.g. Variable cost 8.00
• Allocated overhead 6.00
• Desired markup 25
• Price 8.00 6.00 (8.00 6.00) (0.25)
• 17.50

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Important Questions

• How are the variable costs calculated?
• Do they include the opportunity cost?
• How are fixed costs allocated?
• Is the firm using long-term costs? Are all the
  costs variable?
• How is the size of the markup determined?
• Does it reflect the demand conditions and the
  competitive environment?

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Cost-Plus Pricing and Marginal Pricing

• Under certain conditions, cost-plus pricing is
  consistent with the profit maximization rule of
  MR MC.
• When the average cost curve is constant,
  cost-plus pricing may give results identical to
  those that would be obtained if the managers were
  pursuing profit maximization.
• First, re-write MR

1 / Ep
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• Since for profit maximization, MR MC

• Further, if MC AC

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• Re-writing

• Under cost-plus,
• P AC (1 M) where M is the markup.
• Then,

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• There is an inverse relationship between markup
  and price elasticity
• The less elastic the demand curve, the larger
  the markup will be.
• When the average cost curve is constant,
  cost-plus pricing may give results identical to
  those that would be obtained if the managers were
  pursuing profit maximization.

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• E.g.
• If EP -1.5, M -1.5/(-1.51)-1 2.0.
• If EP -4.0, M -4.0/(-4.01)-1 0.33.
• If EP -1.0, M is undefined (division by 0).
• If -1 lt EP lt 0, M becomes negative.
• Both cases are irrelevant because
• A profit-maximizing firm will never operate on
  the inelastic portion of its demand curve.
• When MR gt 0, demand is elastic.
• For profit-maximization, MR MC.
• MC is always gt 0 (i.e., positive).
• Then, MR is always gt 0 (i.e., positive).
• So, at the profit-maximizing output, the firm is
  always on the elastic portion of its demand curve.