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. 3 / 35

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. 8 / 35

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. 12 / 35

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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