Chapter 15 MARKET DEMAND

15.1 From Individual to Market Demand

Consumer i’s demand for good 1: xi1(p1,p2,mi)

Consumer i’s demand for good 2: xi2(p1,p2,mi)

n consumers in the economy: i=1, …,n Market demand for good 1: the sum of these

individual demands over all consumers.1 1

1, 2 1 1, 21

( , , ) ( , )n

n i ii

X p p m m x p p m

15.1 From Individual to Market Demand If we fix all the

monetary incomes and the price of good 2, we can illustrate the relation between the aggregate demand for good 1 and its price.

15.1 From Individual to Market Demand Substitutes: increasing the price of good 2 will tend to

shift the aggregate demand curve for good 1 outward. Complements: increasing the price of good 2 will

shift the aggregate demand curve for good 1 inward. Normal good: increasing monetary income, holding

everything else fixed, will shift the aggregate demand curve outward.

15.2 The Inverse Demand Function

Inverse demand function, P(X)It measures what the market price for good 1

would have to be for X units of it to be demanded.

EXAMPLE: Adding Up “Linear” Demand Curves

Since the demand curves are only linear for positive quantities, there will be a kink in the market demand curve.

15.3 Discrete Goods

15.4 The Extensive and the Intensive Margin Adjustment on the intensive margin: when

the price changes, the consumer changes the quantities demanded, but still ends up consuming both goods.

Adjustment on the extensive margin: when the price changes, the consumers enter or exit the market for one of the goods.

15.5 Elasticity Elasticity: a measure of responsiveness. Price elasticity of demand: the percent

change in quantity divided by the percent change in price.

0 0lim limp p

q q q p dq p

p p q p dp q

ln

ln

dq p dq q d q

dp q dp p d p

EXAMPLE: The Elasticity of a Linear Demand Curve Linear demand curve: q=a-bp. Elasticity: =-bp/q=-bp/(a-bp)

p=0: =0;p=a/b : =-;p=a/2b: =-1;p>a/2b: <-1;p<a/2b: >-1;

EXAMPLE: The Elasticity of a Linear Demand Curve

15.6 Elasticity and Demand

Elastic Demand: elasticity of demand is greater than 1 in absolute value.

Inelastic Demand: elasticity of demand is less than 1 in absolute value.

Unit Elastic Demand: elasticity of demand is exactly -1.

15.7 Elasticity and Revenue

Revenue: R=pq Price change: p+△p Quantity change: q+△q New revenue:R=(p+△p)(q+△q)=pq+q△p+p△q+△p△q Change in revenue:

△R= q△p+p△q+△p△q

15.7 Elasticity and Revenue

15.7 Elasticity and Revenue

Small values of △p and △q: the last term can safely be neglected.

△R= q△p+p△q or △R/△p=q+p△q/△p △R/△p>0: p△q/q△p>-1 or |(p)|<1 Revenue increases when price increases if the

elasticity of demand is less than 1 in absolute value. Revenue decreases when price increases if the

elasticity of demand is greater than 1 in absolute value.

15.7 Elasticity and Revenue Differential approach

R pq

1 1dR dq p dq

q p q qdp dp q dp

| |>1: dR/dp<0; | |<1: dR/dp>0.

15.8 Constant Elasticity Demands A unit elastic

demand curve has a constant elasticity of -1. For this demand curve, price times quantity is constant at every point.

15.9 Elasticity and Marginal Revenue △R= q△p+p△q Marginal revenue:

MR=△R/△q = p+ q△p/△q

MR = p(1+ q△p/p△q)

=p(1+ 1/(p))

=p(1-1/|(p)|)

15.9 Elasticity and Marginal Revenue =-1: MR=0

Revenue doesn’t change when the firm increases output.

| |<1: MR<0Revenue will decrease when the firm increases

output. | |>1: MR>0

Revenue will increase when the firm increases output.

15.10 Marginal Revenue Curves

Linear (inverse) demand curve: p(q)=a-bq Marginal revenue:

MR=△R/△q = p(q)+q△p(q)/△q

= p(q)-bq

=a-bq-bq

=a-2bq

15.10 Marginal Revenue Curves

The marginal revenue curve has the same vertical intercept as the demand curve, but has twice the slope.

15.11 Income Elasticity

Income elasticity of demand: it describes how the quantity demanded responds to a change in income.

0 0lim limm m m

q q q m dq m

m m q m dm q

15.11 Income Elasticity

Normal good: an increase in income leads to an increase in demand.

Inferior good: an increase in income leads to a decrease in demand.

Luxury good: a one percent increase in income leads to more than one percent increase in demand.

15.11 Income Elasticity

Two different levels of income: m and m0

Budget constraints:

p1x1+p2x2=mp1x1

0+p2x20=m0

Substraction:

p1△x1+ p2△x2=△m Further manipulation:

(p1x1/m)(△x1/x1)+ (p2x2/m)(△x2/x2)=△m/m

15.11 Income Elasticity

Finally:

s1(△x1/x1)/(△m/m)+ s2(△x2/x2)/(△m/m)=1

Expenditure share of good i: si= pixi/m

The weighted average of the income elasticity

is unity.The weights are the expenditure shares.