chapter fifteen market demand. from individual to market demand functions the market demand curve...
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Chapter Fifteen
Market Demand
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From Individual to Market Demand Functions
The market demand curve is the “horizontal sum” of the individual consumers’ demand curves.
E.g. suppose there are only two consumers; i = A,B.
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From Individual to Market Demand Functions
p1 p1
x A1* x B
1*20 15
p1’
p1”
p1’
p1”
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From Individual to Market Demand Functions
p1 p1
x A1* x B
1*
x xA B1 1* +
p1
20 15
p1’
p1”
p1’
p1”
p1’
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From Individual to Market Demand Functions
p1 p1
x A1* x B
1*
x xA B1 1* +
p1
20 15
p1’
p1”
p1’
p1”
p1’
p1”
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From Individual to Market Demand Functions
p1 p1
x A1* x B
1*
x xA B1 1* +
p1
20 15
35
p1’
p1”
p1’
p1”
p1’
p1”
The “horizontal sum”of the demand curvesof individuals A and B.
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Elasticities
Elasticity measures the “sensitivity” of one variable with respect to another.
The elasticity of variable X with respect to variable Y is
εx yxy,
%%
.=ΔΔ
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Economic Applications of Elasticity
Economists use elasticities to measure the sensitivity ofquantity demanded of commodity
i with respect to the price of commodity i (own-price elasticity of demand)
demand for commodity i with respect to the price of commodity j (cross-price elasticity of demand).
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Economic Applications of Elasticity
demand for commodity i with respect to income (income elasticity of demand)
quantity supplied of commodity i with respect to the price of commodity i (own-price elasticity of supply)
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Economic Applications of Elasticity
quantity supplied of commodity i with respect to the wage rate (elasticity of supply with respect to the price of labor)
and many, many others.
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Own-Price Elasticity of Demand
Q: Why not use a demand curve’s slope to measure the sensitivity of quantity demanded to a change in a commodity’s own price?
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Own-Price Elasticity of Demand
X1*5 50
10 10slope= - 2
slope= - 0.2
p1 p1
In which case is the quantity demandedX1* more sensitive to changes to p1?
X1*
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Own-Price Elasticity of Demand
5 50
10 10slope= - 2
slope= - 0.2
p1 p1
10-packs Single Units
X1* X1
*
In which case is the quantity demandedX1* more sensitive to changes to p1?It is the same in both cases.
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Own-Price Elasticity of Demand
Q: Why not just use the slope of a demand curve to measure the sensitivity of quantity demanded to a change in a commodity’s own price?
A: Because the value of sensitivity then depends upon the (arbitrary) units of measurement used for quantity demanded.
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Own-Price Elasticity of Demand
εx p
xp1 1
1
1* ,
*%%
=ΔΔ
is a ratio of percentages and so has nounits of measurement. Hence own-price elasticity of demand is a sensitivity measure that is independent of units of measurement.
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Point Own-Price Elasticity
pi
Xi*
pi = a - bXi* εX p
i
ii i
pa p
* ,= −
−
p = ⇒ =0 0ε
ε =0
a
a/b
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Point Own-Price Elasticity
pi
Xi*
a
pi = a - bXi*
a/b
εX p
i
ii i
pa p
* ,= −
−
pa a
a a= ⇒ =−
−=−
222
1ε//
ε =−1
ε =0
a/2
a/2b
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Point Own-Price Elasticity
pi
Xi*
a
pi = a - bXi*
a/b
εX p
i
ii i
pa p
* ,= −
−
p aa
a a= ⇒ =−
−=−∞ε
ε =−1
ε =0
a/2
a/2b
ε =−∞
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Point Own-Price Elasticity
pi
Xi*
a
pi = a - bXi*
a/b
εX p
i
ii i
pa p
* ,= −
−
ε =−1
ε =0
a/2
a/2b
ε =−∞
own-price elastic
own-price inelastic(own-price unit elastic)
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Revenue and Own-Price Elasticity of Demand
If raising a commodity’s price causes little decrease in quantity demanded, then sellers’ revenues rise.
Hence own-price inelastic demand causes sellers’ revenues to rise as price rises.
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Revenue and Own-Price Elasticity of Demand
If raising a commodity’s price causes a large decrease in quantity demanded, then sellers’ revenues fall.
Hence own-price elastic demand causes sellers’ revenues to fall as price rises.