Chapter 6: Demand
Course: Eco201: Intermediate
Microeconomics
Dr. Qaiser Munir
Text: Varian’s
This lecture explains what does the consumer's demand function for a
good depend on,
what are normal and inferior goods, ordinary and Giffen goods, and
substitutes and complements,
what is the inverse demand function.
Changes in Price: Ordinary Goods and Giffen Goods
Let us now consider price changes. Suppose that we
decrease the price of good 1 and hold the price of good 2
and money income fixed. Then what can happen to the
quantity demanded of good 1
When the price of good 1
decreases, the budget line becomes
flatter. Or said another way, the
vertical intercept is fixed and the
horizontal intercept moves to the
right.
Ordinary good: decrease in price increases demand
x1
0
p1
Giffen good: decrease in price decreases demand
x1
0
p1
Intuition behind Giffen good: Suppose you consume a little
of meat and a lot of potatoes. A reduction of price of
potatoes gives you extra money for meat. Then you might
need less potatoes.
Copyright © 2019 Hal R. Varian
Own-Price Changes
• How does x1*(p1, p2, m) change as p1 changes, holding p2 and m constant?
• Suppose only p1 increases, from p1′ to p1″ and then to p1‴.
• Own-Price Changes – Fixed p2 and m
Changes in price lead to
a tilts or pivots of the
budget line.
Copyright © 2019 Hal R. Varian
Own-Price Changes – Fixed p2 and m
Suppose only p1 increases
The relationship between
the optimal choice and a
price, with income and
the other price fixed, is
called the demand curve.
Copyright © 2019 Hal R. Varian
Own-Price Changes – Fixed p2 and m
• The Price Offer Curve
• The curve containing all the
utility-maximizing bundles
traced out as p1 changes, with
p2 and y constant, is the p1price offer curve.
• The plot of the x1-coordinate of
the p1-price offer curve against
p1 is the ordinary demand
curve for commodity 1.
Suppose only p1 increases
• As price changes
the optimal choice
moves along the
price offer curve.
The price offer curve and demand curve. Panel A contains a price offer curve, which depicts the optimal choices as the price of
good 1 changes. Panel B contains the associated demand curve, which depicts a plot of the optimal choice of good 1 as a function of
its price.
Copyright © 2019 Hal R. Varian
Ordinary Goods: Fixed p2 and y
• A good is called ordinary if the quantity demanded of it always increases as its own price
decreases.
• ordinary goods should not be confused with normal goods. Normal goods are characterized by their
relationship between income and quantity demanded. Meanwhile, ordinary goods are classified
according to their relationship between price and quantity demanded.
Copyright © 2019 Hal R. Varian
Giffen Goods: Fixed p2 and y
• Giffen goods (low income goods) are goods that experience an increase in
quantity demanded when price rises or conversely a decrease in quantity
demanded when the price falls. That results in an upward sloping demand
curve, which contradicts the law of demand.
Copyright © 2019 Hal R. Varian
Own-Price Changes: Perfect Complements
• What does a p1 price offer curve look like for a perfect complements utility
function?
• Then the ordinary demand functions for commodities 1 and 2 are . . .
m
x ( p1 , p2 , m)  x ( p1 , p2 , m) 
.
p1  p2
*
1
*
2
• With p2 and y fixed, higher p1 causes smaller x1* and x2*.
As
p1  0
m
x x 
.
p2
As
p1  
x1*  x2*  0.
*
1
*
2
Copyright © 2019 Hal R. Varian
Own-Price Changes – Fixed p2 and m
Copyright © 2019 Hal R. Varian
Own-Price Changes – Fixed p2 and m
Copyright © 2019 Hal R. Varian
Own-Price Changes – Fixed p2 and m
Copyright © 2019 Hal R. Varian
Own-Price Changes – Fixed p2 and m
Price offer curve
Copyright © 2019 Hal R. Varian
Own-Price Changes: Perfect Substitutes
• What does a p1 price-offer curve look like for a perfect-substitutes utility
function?
• Then the ordinary demand functions for commodities 1 and 2 are . . .
and
Copyright © 2019 Hal R. Varian
Own-Price Changes – Perfect Substitutes
Fixed p2 and m
Copyright © 2019 Hal R. Varian
Own-Price Changes – Perfect Substitutes
Fixed p2 and m
Copyright © 2019 Hal R. Varian
Own-Price Changes – Fixed p2 and m - 23
Copyright © 2019 Hal R. Varian
Own-Price Changes – Fixed p2 and m - 24
Copyright © 2019 Hal R. Varian
Copyright © 2019 Hal R. Varian
Own-Price Changes: Inverse demand function
• Usually we ask “Given the price for commodity 1 what is the
quantity demanded of commodity 1?”
• But we could also ask the inverse question “At what price for
commodity 1 would a given quantity of commodity 1 be
demanded?”
• Given p1′, what quantity is demanded of commodity 1?
In the inverse demand function, price is a
function of the quantity demanded. That
contrasts with the demand function, where
the quantity demanded is a function of
price.
Qd = f(P)
the inverse demand function can be
formulated as P = f-1(Q)
p
1
Answer: x1′ units.
p1’
• The inverse question is:
Given x1′ units are demanded, what is the price of commodity
1?
Answer: p1
X1’
X1*
Copyright © 2019 Hal R. Varian
Own-Price Changes: Inverse demand function
• Taking quantity demanded as given and then asking what must be price describes
the inverse demand function of a commodity.
am
is the ordinary demand function and
( a  b) p1
am
is the inverse demand function. p1 
(a  b) x1*
*
A Cobb-Douglas example: x1 
m
is the ordinary demand
A perfect-complements example: x 
p1  p2
*
1
m
function and p1  *  p2 is the inverse demand function.
x1
Copyright © 2019 Hal R. Varian
Copyright © 2019 Hal R. Varian
Cross-Price Effects
• If an increase in p2
• increases demand for commodity 1 then commodity 1 is a gross
substitute for commodity 2.
• reduces demand for commodity 1 then commodity 1 is a gross
complement for commodity 2.
• Cross Demand can be either Positive or Negative:
i. Cross demand is positive in case of substitute goods as demand
for the given commodity varies directly with the prices of substitute
goods.
ii. Cross demand is negative in case of complementary goods as
demand for the given commodity varies inversely with the prices of
complementary goods.
Copyright © 2019 Hal R. Varian
Cross-Price Effects: Substitutes goods:
• A change (increase or decrease) in the price of
substitutes directly affects the demand for a
given commodity.
i) Increase in Price of Substitute Goods:
• When price of substitute goods (say, coffee) rises,
demand for the given commodity (say, tea) also
rises from OQ to OQ1 at its same price of OP. It
leads to a rightward shift in the demand curve of
the given commodity from DD to D1D1
(ii) Decrease in Price of Substitute Goods:
• With decrease in price of substitute goods
(coffee), demand for the given commodity (tea)
also decreases from OQ to OQ1 at the same price
of OP. It shifts the demand curve of the given
commodity towards left from DD to D1D1.
Copyright © 2019 Hal R. Varian
Cross-Price Effects: Complementary Goods:
• An increase or decrease in the prices of
complementary goods inversely affects the demand
for the given commodity.
(i) Increase in Price of Complementary Goods:
• When price of complementary goods (say, sugar)
rises, demand for the given commodity (say, tea)
falls from OQ to OQ1 at the same price of OP. As a
result, the demand curve of the given commodity
shifts to the left from DD to D1D1.
(ii) Decrease in Price of Complementary
Goods:
• With decrease in price of complementary goods
(sugar), demand for the given commodity (tea)
increases from OQ to OQ1 at the same price of
OP. As a result, the demand curve of the given
commodity shifts to the right from DD to D1D1.
Copyright © 2019 Hal R. Varian
Thank you!
Copyright © 2019 Hal R. Varian
Appendix
Copyright © 2019 Hal R. Varian
Own-Price Changes: Cobb-Douglas Preferences
• What does a p1 price offer curve look like for Cobb-Douglas preferences? Take:
U ( x1 , x2 )  x1a x2b .
• Then the ordinary demand functions for commodities 1 and 2 are . . .
a
m
x ( p1 , p2 , m) 

a  b p1
*
1
and
b
m
x ( p1 , p2 , m) 
 .
a  b p2
*
2
• Notice that x2* does not vary with p1 so the p1 price offer curve is flat.
Copyright © 2019 Hal R. Varian
Own-Price Changes – Cobb-Douglas Preferences
Fixed p2 and m
Copyright © 2019 Hal R. Varian
Own-Price Changes – Cobb-Douglas Preferences
Fixed p2 and m
Copyright © 2019 Hal R. Varian