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

Add horizontally

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

15.5 Elasticity

Elasticity

(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

(c) (d)

----------------1-------------0-------------------

(a) (b)

(3) Example: Linear demand

q= a-bp

Eq,p=(-b)=

Note: Elasticity is in the linear case a function of p and q

(4) Demand curve with constant elastisticity

q= Apa (e<0. Why?)

E= a

(5) "Tendency":

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

R=qp

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

= 1

(2) Example: q(p) = 30 - 2q

G. Some other elasticities

15.11 Income Elasticity

(1) Income elasticity

Eq,m =

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

Important Points

15.1

1. The market demand curve is simply the sum of the individual demand

curves.

2. The reservation price measures the price at which a consumer is just

indifferent between purchasing or not purchasing a good.

15.2

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.

15.5 Elasticity

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.

15.6

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.

15.7

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.

15.9

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/| |].

15.10

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.

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