Download 5. Theory of Demand. 5.1 Types of Competition

5. Theory of Demand. 5.1 Types of Competition
a. Perfect Competition Producers sell goods that cannot be
differentiated: e.g. agricultural products - class 1 corn.
It is assumed that there are a large number of producers who have
no control over the price (how this price is set will be considered in
the chapter on supply and demand).
On agricultural markets e.g. by charging a higher price, a producer
would not sell anything, by charging a lower price, he could not sell
any more than he has.
The total demand (and supply) over a given period for such a
product depends on the market price.
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b. Monopolistic Competition
In the case of monopolistic competition, there are a large number
of producers who sell very similar (competing - substitute), but
differentiated goods, e.g. pepsi, coke.
Each producer has some control over the price they set.
For example, even if coke costs slightly more than pepsi, people
will still buy coke, as they ”prefer” it to pepsi.
However, raising the price of coke will reduce the demand for it.
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c. A monopoly
In this case, there is only one producer of a particular good, e.g.
electricity, (possibly) transport between two locations, some
computer packages.
The producer has a lot of control over price, but price affects
demand due to the income effect (as the price increases, real
income decreases and so a client buys less).
If there is an alternative product, demand is affected by the
substitution effect (if the price of train travel increases, I might
prefer to travel by car).
However, often there is inertia, i.e. some time might pass before
patterns of demand change, e.g. if electricity prices significantly
rise, people will switch to gas, but they need to first invest in new
heaters, ovens etc.
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d. An oligopoly
In this case, there are a small number of producers of a particular
good, e.g. computers, air flights between cities, oil.
In such cases, producers have a lot of control over price and may
collude (explicit collusion is usually illegal, but implicit collusion is
common).
The behaviour of oligopolies will be considered in the section on
game theory.
This and the following chapters consider in turn the behaviour of
competitive markets and the behaviour of monopolies (or firms
under the conditions of monopolistic competition).
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5.2 The Demand Curve
The demand for normal goods (as opposed to luxury goods) is
decreasing in the price of the good.
Suppose the demand for a good (quantity demanded) given its
price p is given by the function qd = d(p).
Note it is assumed that this function describes the short term
demand for a product (i.e. the prices of other goods do not
change, nor do wages change).
From the above assumptions d 0 (p) < 0, where d 0 (p) denotes the
first derivative of demand with respect to price.
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The Demand Curve
When drawing demand and supply curves, price is on the y -axis.
Hence, the demand curve is given by price as a function of
quantity, pd = f (q), where f = d −1 , i.e. f is the inverse function
to the demand function.
pd is the price according to demand.
Since, d 0 (p) < 0, f 0 (q) < 0, i.e. as the quantity of a good
increases, the price according to demand decreases.
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The Demand Curve - Diagram
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5.3 Elasticity of Demand
The empirical elasticity of demand with respect to price, ˆ,
measures how observed demand changes in relation to the
observed price.
By definition, it is the percentage change in demand divided by the
percentage change in price, i.e.
ˆ =
p0
d1 − d0
×
,
d0
p1 − p0
where d0 , p0 are the original demand and price and d1 , p1 are the
new price and demand.
If price increases, then demand decreases. Hence, the empirical
elasticity of demand will be negative.
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Example 5.1
Suppose the price of a good changes and we observe the following
demands. Calculate the empirical elasticity of demand.
Price
Demand
Old
50
200
New
55
190
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Example 5.1
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Example 5.1
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Elasticity of Demand
Suppose we can estimate the quantity demanded as a function of
price, qd = d(p).
Letting the change in price tend to zero in the expression for the
empirical elasticity of demand, we obtain the (theoretical) elasticity
of demand with respect to price, p , where
p =
pd 0 (p)
d(p)
Since d 0 (p) < 0, this value will be negative.
The more negative the value of the elasticity (the greater its
absolute value), the more strongly demand falls when the price is
increased.
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Example 5.2
Assume that the demand for a good is given by d(p) =
100
p .
Calculate the elasticity of demand for the good when i) p = 5, ii)
p = 10.
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Example 5.2
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Example 5.2
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Relation between Revenue and Elasticity of Demand
It can be shown that for any p > 0, the elasticity of demand when
d(p) = pc is always equal to -1.
Note that the revenue, r (p) = pd(p) = c.
This corresponds to the following statement.
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Relation between Revenue and Elasticity of Demand
When the elasticity of demand is -1, then a marginal (very small)
change in the price of a good does not affect the revenue obtained.
When the elasticity of demand is between 0 and -1, then a
marginal (very small) increase in the price of a good increases the
revenue obtained. Demand is said to be inelastic.
When the absolute value of the elasticity of demand is greater than
1, then a marginal (very small) increase in the price of a good
decreases the revenue obtained. Demand is said to be elastic.
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Substitute and Complimentary Goods
Two goods are substitutes when they play similar roles, e.g. fish
and meat, different brands of a given product (i.e. it is natural that
two substitute products are not bought together).
Two goods are complements when in order to consume one good,
one tends to consume another, e.g. CDs and CD players, flights to
Italy and accommodation in Italy.
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Factors influencing the Elasticity of Demand
The elasticity of demand tends to be high when a good has many
substitutes (when the price of a brand of milk increases, then
people choose another brand of milk).
However, milk is regarded as a necessity. Hence, the overall
demand for milk is relatively inelastic with respect to an increase in
the price of milk in general.
Similarly, tobacco and insulin have a low elasticity of demand.
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Factors influencing the Elasticity of Demand
When the user of a good/service does not actually pay for that
good, then price elasticity is low (e.g. business flights).
Brand loyalty decreases elasticity of demand (e.g. individual brands
of cigarettes will have a less elastic demand than brands of milk).
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Cross-Price Elasticities of Demand
Suppose the demands for goods 1 and 2 are given by d1 (p1 , p2 )
and d2 (p1 , p2 ), respectively where p1 and p2 are the prices of
goods 1 and 2, respectively.
Then the same price elasticities of demand of the two goods are
given by
1,1 =
p1
∂d1
×
;
d1 (p1 , p2 ) ∂p1
2,2 =
p2
∂d2
×
;
d2 (p1 , p2 ) ∂p2
These elasticities describe how the demand for a good is affected
by a change in the price of that (same) good.
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Cross-Price Elasticities of Demand
In addition, any change in the price of the second good might
affect the demand for the first good and vice versa. Hence, we
consider cross-price elasticities of demand.
The cross-price elasticity of demand for good 1 with respect to the
price of good 2, 1,2 and the cross-price elasticity of demand for
good 2 with respect to the price of good 1, 2,1 are given by
1,2 =
∂d1
p2
×
;
d1 (p1 , p2 ) ∂p2
2,1 =
p1
∂d2
×
;
d2 (p1 , p2 ) ∂p1
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Cross-Price Elasticities of Demand
The cross-price elasticity of demand of a good with respect to a
substitute good is positive, i.e. demand increases when the price of
the substitute good goes up (e.g. when the price of vodka goes up,
the demand for beer goes up).
This is equivalent to the condition
∂d1
∂p2
> 0.
The cross-price elasticity of demand for a good with respect to a
complementary good is negative, i.e. demand decreases when the
price of the complementary good goes up (when CDs increase in
price, the demand for CD players goes down).
This is equivalent to the condition
∂d1
∂p2
< 0.
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Example 5.3
The demands for two goods are given by
d1 (p1 , p2 )=20 − 5p1 + 2p2
d2 (p1 , p2 )=40 − 8p2 + p1
Calculate the price elasticities and cross-price elasticities for these
goods when p1 = 2, p2 = 3.
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Example 5.3
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Example 5.3
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Cross-Price Elasticities of Demand
Hence, the cross-price elasticities are positive.
Note this is equivalent to
∂d1
∂p2
> 0 and
∂d2
∂p1
> 0.
Hence, the two goods are substitutes.
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5.4 Consumer Surplus
When the price of a good is fixed, various purchasers would have
be willing to pay a higher price to purchase the good.
Consumer surplus is a measure of the general happiness of
customers buying a product with the purchasing price.
In more strict terms, it is the extra amount of revenue a firm could
obtain by selling the product to each customer at the maximum
price that the customer is willing to pay.
This value is given by the area both under the demand curve and
above the selling price.
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Customer Surplus - Graph
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Customer Surplus
It follows that customer surplus Cs when the set price is p0 is given
by
Z
p max
Cs =
d(p)dp,
p0
where d(p) = 0 for all p ­ p max .
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Example 5.4
Suppose the price of a good is equal to 5.
Calculate the consumer surplus when the demand function is
i) d(p) = 10 − p, p ¬ 10.
ii) d(p) = 64 − p 2 , p ¬ 8.
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Example 5.4
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Example 5.4
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Example 5.4
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Example 5.4
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