3Chapter_3 Salvatore
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Transcript of 3Chapter_3 Salvatore
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Law of Demand
• Holding all other things constant (ceteris paribus), there is an inverse relationship between the price of a good and the quantity of the good demanded per time period.– Substitution Effect– Income Effect
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Components of Demand:The Substitution Effect
• Assuming that real income is constant:– If the relative price of a good rises, then
consumers will try to substitute away from the good. Less will be purchased.
– If the relative price of a good falls, then consumers will try to substitute away from other goods. More will be purchased.
• The substitution effect is consistent with the law of demand.
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Components of Demand:The Income Effect
• The real value of income is inversely related to the prices of goods.
• A change in the real value of income:– will have a direct effect on quantity
demanded if a good is normal.– will have an inverse effect on quantity
demanded if a good is inferior.
• The income effect is consistent with the law of demand only if a good is normal.
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Individual Consumer’s DemandQdX = f(PX, I, PY, T)
quantity demanded of commodity X by an individual per time period
price per unit of commodity X
consumer’s income
price of related (substitute or complementary) commodity
tastes of the consumer
QdX =
PX =
I =
PY =
T =
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QdX = f(PX, I, PY, T)
QdX/PX < 0
QdX/I > 0 if a good is normal
QdX/I < 0 if a good is inferior
QdX/PY > 0 if X and Y are substitutes
QdX/PY < 0 if X and Y are complements
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Market Demand Curve
• Horizontal summation of demand curves of individual consumers
• Exceptions to the summation rules– Bandwagon Effect
• collective demand causes individual demand
– Snob (Veblen) Effect• conspicuous consumption• a product that is expensive, elite, or in short
supply is more desirable
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Market Demand FunctionQDX = f(PX, N, I, PY, T)
quantity demanded of commodity X
price per unit of commodity X
number of consumers on the market
consumer income
price of related (substitute or complementary) commodity
consumer tastes
QDX =
PX =
N =
I =
PY =
T =
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Demand Curve Faced by a Firm Depends on Market Structure
• Market demand curve
• Imperfect competition– Firm’s demand curve has a negative slope– Monopoly - same as market demand– Oligopoly– Monopolistic Competition
• Perfect Competition– Firm is a price taker– Firm’s demand curve is horizontal
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Demand Curve Faced by a Firm Depends on the Type of Product
• Durable Goods– Provide a stream of services over time– Demand is volatile
• Nondurable Goods and Services
• Producers’ Goods– Used in the production of other goods– Demand is derived from demand for final
goods or services
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Linear Demand Function
QX = a0 + a1PX + a2N + a3I + a4PY + a5T
PX
QX
Intercept:a0 + a2N + a3I + a4PY + a5T
Slope:QX/PX = a1
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Linear Demand Function Example Part 1
Demand Function for Good X
QX = 160 - 10PX + 2N + 0.5I + 2PY + T
Demand Curve for Good X
Given N = 58, I = 36, PY = 12, T = 112
Q = 430 - 10P
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Linear Demand Function Example Part 2
Inverse Demand Curve
P = 43 – 0.1Q
Total and Marginal Revenue Functions
TR = 43Q – 0.1Q2
MR = 43 – 0.2Q
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Price Elasticity of Demand
/
/P
Q Q Q PE
P P P Q
Linear Function
Point Definition
1P
PE a
Q
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Price Elasticity of Demand
Arc Definition 2 1 2 1
2 1 2 1P
Q Q P PE
P P Q Q
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Marginal Revenue and Price Elasticity of Demand
11
P
MR PE
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Marginal Revenue and Price Elasticity of Demand
PX
QX
MRX
1PE
1PE
1PE
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Marginal Revenue, Total Revenue, and Price Elasticity
TR
QX
1PE MR<0MR>0
1PE
1PE MR=0
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Determinants of Price Elasticity of Demand
The demand for a commodity will be more price elastic if:
• It has more close substitutes
• It is more narrowly defined
• More time is available for buyers to adjust to a price change
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Determinants of Price Elasticity of Demand
The demand for a commodity will be less price elastic if:
• It has fewer substitutes
• It is more broadly defined
• Less time is available for buyers to adjust to a price change
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Income Elasticity of Demand
Linear Function
Point Definition/
/I
Q Q Q IE
I I I Q
3I
IE a
Q
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Income Elasticity of Demand
Arc Definition 2 1 2 1
2 1 2 1I
Q Q I IE
I I Q Q
Normal Good Inferior Good
0IE 0IE
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Cross-Price Elasticity of Demand
Linear Function
Point Definition/
/X X X Y
XYY Y Y X
Q Q Q PE
P P P Q
4Y
XYX
PE a
Q
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Cross-Price Elasticity of Demand
Arc Definition
Substitutes Complements
2 1 2 1
2 1 2 1
X X Y YXY
Y Y X X
Q Q P PE
P P Q Q
0XYE 0XYE
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Example: Using Elasticities inManagerial Decision Making
A firm with the demand function defined below expects a 5% increase in income (M) during the coming year. If the firm cannot change its rate of production, what price should it charge?
• Demand: Q = – 3P + 100M– P = Current Real Price = 1,000– M = Current Income = 40
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Solution
• Elasticities– Q = Current rate of production = 1,000– P = Price = - 3(1,000/1,000) = - 3– I = Income = 100(40/1,000) = 4
• Price– %ΔQ = - 3%ΔP + 4%ΔI– 0 = -3%ΔP+ (4)(5) so %ΔP = 20/3 = 6.67%– P = (1 + 0.0667)(1,000) = 1,066.67
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Other Factors Related to Demand Theory
• International Convergence of Tastes– Globalization of Markets– Influence of International Preferences on
Market Demand
• Growth of Electronic Commerce– Cost of Sales– Supply Chains and Logistics– Customer Relationship Management
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Chapter 3 Appendix
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Indifference Curves
• Utility Function: U = U(QX,QY)
• Marginal Utility > 0– MUX = ∂U/∂QX and MUY = ∂U/∂QY
• Second Derivatives– ∂MUX/∂QX < 0 and ∂MUY/∂QY < 0
– ∂MUX/∂QY and ∂MUY/∂QX • Positive for complements• Negative for substitutes
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Marginal Rate of Substitution
• Rate at which one good can be substituted for another while holding utility constant
• Slope of an indifference curve– dQY/dQX = -MUX/MUY
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Indifference Curves:Complements and Substitutes
QY
QX
QY
QX
Perfect Complements
Perfect Substitutes
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The Budget Line
• Budget = M = PXQX + PYQY
• Slope of the budget line– QY = M/PY - (PX/PY)QX
– dQY/dQX = - PX/PY
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Budget Lines: Change in Price
GF: M = $6, PX = PY = $1
GF’: PX = $2
GF’’: PX = $0.67
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Budget Lines: Change in Income
GF: M = $6, PX = PY = $1
GF’: M = $3, PX = PY = $1
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Consumer Equilibrium
• Combination of goods that maximizes utility for a given set of prices and a given level of income
• Represented graphically by the point of tangency between an indifference curve and the budget line– MUX/MUY = PX/PY
– MUX/PX = MUY/PY
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Mathematical Derivation
• Maximize Utility: U = f(QX, QY)
• Subject to: M = PXQX + PYQY
• Set up Lagrangian function– L = f(QX, QY) + (M - PXQX - PYQY)
• First-order conditions imply– = MUX/PX = MUY/PY
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