Post on 18-Jan-2016
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.