15. Market Demand
Analysis of Elasticity
In this chapter, we see how to add up individual choices to get total market demand.
Once the market demand curve is obtained, we examine some of its properties, such as the relationship between demand and revenue (elasticity).
15.1 From Individual to Market Demand
To get M.D. - add up individual demands
X1(p1, p2, m1, m2 ... mn) =
Often think of market behaving like a single individual
(1) The "representative consumer model"
(2) Not true in general, but a reasonable assumption for this course
(1) Measures responsiveness of demand to price
(2) E = (the own price elasticity)
(a) E < 0: Normal goods
(b) E> 0: Giffen goods
(c) > 1 Elastic
(d) < 1 Inelastic
(3) Example: Linear demand
Note: Elasticity is in the linear case a function of p and q
(4) Demand curve with constant elastisticity
q= Apa (e<0. Why?)
Goods with many close substitutes - elastic demand
Goods without close substitutes - inelastic demand
15.7 Elasticity and Revenue
How does revenue change when you change price?
(1) Revenue= quantity x price
dR/dp = q + p(dq/dp)
dR/dp > 0 when < 1. Why?
Inelastic demand - 1 % price increase leads to less than 1% reduction in quantity sold.
dR/dp < 0 when > 1.
Monopolist: Maximizes R when
(2) Example: q(p) = 30 - 2q
G. Some other elasticities
15.11 Income Elasticity
(1) Income elasticity
Eq,m > 0 Normal good
Eq,m < 0 Inferior good
(2) Cross price elasticity
E q,p2 =
Good 1 and 2 are substitutes if
E q,p2 > 0
Good 1 and 2 are complementary goods if
E q,p2 < 0
1. The market demand curve is simply the sum of the individual demand
2. The reservation price measures the price at which a consumer is just
indifferent between purchasing or not purchasing a good.
3. The demand function measures quantity demanded as a function of
price. The inverse demand function measures price as a function of quantity.
A given demand curve can be described in either way.
4. The elasticity of demand measures the responsiveness of the quantity
demanded to price. It is formally defined as the percent change in quantity
divided by the percent change in price.
5. If the absolute value of the elasticity of demand is less than 1 at some
point, we say that demand is inelastic at that point. If the absolute value
of elasticity is greater than 1 at some point, we say demand is elastic at
that point. If the absolute value of the elasticity of demand at some point
is exactly 1, we say that the demand has unitary elasticity at that point.
6. If demand is inelastic at some point, then an increase in quantity will
result in a reduction in revenue. If demand is elastic, then an increase in
quantity will result in an increase in revenue.
7. The marginal revenue is the extra revenue one gets from increasing
the quantity sold. The formula relating marginal revenue and elasticity
is MR = p[1 + 1/ ] = p[1 − 1/| |].
8. If the inverse demand curve is a linear function p(q) = a − bq, then the
marginal revenue is given by MR = a − 2bq.
9. Income elasticity measures the responsiveness of the quantity demanded
to income. It is formally defined as the percent change in quantity divided
by the percent change in income.