Microeconomics 2
John Hey
I said that only economists know what indifference means,
but I found this quote while I was looking for jokes on
indifference:
“The opposite of love is not
hate, it's indifference. The
opposite of art is not ugliness,
it's indifference. The opposite of
faith is not heresy, it's
indifference. And the opposite of
life is not death, it's
indifference.”
Elie Wiesel
The only ‘joke’ I found is “Indifference will be the downfall of mankind, but who cares?”
By the way, I found an immense amount of activity on the Facebook page!
My Mum’s indifference curves
Was she mad?
q2
We will see at the end – remind me.
B
q1
Chapters 7 and 6
• In Chapter 7 income is in the form
of money m.
• In Chapter 6, income is in the
form of endowments of the two
goods: e1 and e2.
• Otherwise everything is the same.
• We will need this for Chapter 8 – the most important in
the module.
What was the structure of Chapter 7?
• Individual with given preferences and income
m faces prices p1 and p2 for two goods:1 and 2.
• He or she is going to allocate his or her income
buying quantities q1 and q2 of the two goods.
• What he or she buys/demands depends on her
preferences.
• The relationship between q1 and q2 (the
endogenous variables) and m, p1 and p2 (the
exogenous variables) is called the demand
function.
What do we know from Chapter 7? First the intuition
• Perfect Substitutes 1:a
(a>0)
• The individual buys either just Good 1 (if the relative
price of Good 2 is greater than a); just Good 2 otherwise.
• Perfect Complements 1 with a
(a>0)
• The ratio of the quantities bought is always equal to a.
• Cobb-Douglas with parameter a
(1>a>0)
• The individual always spends a proportion a of the
income on Good 1
• Stone-Geary with parameters s1, s2 and a (s >0 s >0 and1>a>0)
• The individual first buys the subsistence quantities and
then spends a proportion a of the residual income on
Good 1.
1
2
What do we know from Chapter 7? (now the maths)
• Perfect Substitutes 1:a
(a>0)
if p1/p2 < a then q1 = m/p1 q2 = 0
if p1/p2 = a then....
if p1/p2 >a then q1 = 0 q2 = m/p2
• Perfect Complements 1 with a
(a>0)
q1=m/(p1 + ap2) and q2 =am/(p1 + ap2)
• Cobb-Douglas with parameter a
(1>a>0)
q1 = am/p1 and q2 = (1-a)m/p2
• Stone-Geary with parameters s1, s2 and a (s >0 s >0 and1>a>0)
• q1 = s1+a(m-p1s1-p2s2)/p1 & q2 =s2+(1-a)(m-p1s1-p2s2)/p2
1
•
2
These formulas will be in the promemoria, but you should feel them.
The optimal point – the formal condition
• With indifference curves that are smoothly
convex...
• ... the optimal point is the point of
tangency between the budget line and the
highest possible indifference curve...
• ...at which the relative price (the slope of
the budget line) is equal to the marginal rate
of substitution (the slope of the
indifference curve).
•
Not true if they are not smoothly convex.
From Chapter 7 to Chapter 6: are we economists or not?
•
•
•
•
Economists are ...
... lazy ...
... efficient.
In Chapter 7 income is in the form of money m. In
Chapter 6, income is in the form of endowments of
the two goods: e1 and e2.
• What is the money value of this endowment? Call it
m.
• We have m = p1e1 + p2e2.
• Let us just replace m with p1e1 + p2e2 everywhere!
From Chapter 7 we have (gross demands)
• Perfect Substitutes 1:a
if p1/p2 < a then q1 = (
m
)/p1 and q2 = 0
if p1/p2 = a then....
if p1/p2 >a then q1 = 0 and q2 = (
m
)/p2
• Perfect Complements 1 with a
q1 = (
q2 =a(
m
m
)/(p1 + ap2) and
)/(p1 + ap2)
• Cobb-Douglas with parameter a
q1 = a(
m
)/p1 and
q2 = (1-a)(
m
)/p2
Hence for Chapter 6 (gross demands)
• Perfect Substitutes 1:a
if p1/p2 < a then q1 = (p1e1 + p2e2)/p1 and q2 = 0
if p1/p2 = a then....
if p1/p2 >a then q1 = 0 and q2 = (p1e1 + p2e2)/p2
• Perfect Complements 1 with a
q1= (p1e1 + p2e2)/(p1 + ap2) and
q2 =a(p1e1 + p2e2)/(p1 + ap2)
• Cobb-Douglas with parameter a
q1 = a(p1e1 + p2e2)/p1 and
q2 = (1-a)(p1e1 + p2e2)/p2
Stone-Geary from Chapter 7 and hence for Chapter 6 (gross demands)
•
•
•
•
•
•
•
q1 = s1+a( m -p1s1-p2s2)/p1
and
q2 =s2+(1-a)( m -p1s1-p2s2)/p2
hence
q1 = s1+a(p1e1 + p2e2 -p1s1-p2s2)/p1
and
q2 =s2+(1-a)(p1e1 + p2e2 -p1s1-p2s2)/p2
• Note linearity or otherwise in exogenous variables.
So ....
• We have done the maths but we now need to add
intuition. (Remember you want to be economists not mathematicians.)
• Note the difference between chapters 7 and 6 of a price
change:
• In both chapters this changes the slope of the budget
line.
• In chapter 6 it also changes the monetary value of the
endowment p1e1 + p2e2 but it does not change m in
Chapter 7.
• In chapter 6 it rotates the budget line around the
endowment point.
Notice also ....
• In this Chapter when we consider an individual
starting with an endowment of the two goods...
• ... if he or she wants more of one good then he
or she has to sell some of the other. So...
• Either q1 > e1 and the individual is a (net)
demander of good 1 and (hence) q2 < e2 and the
individual is a (net) supplier of good 2...
• Or q1 < e1 and the individual is a (net) supplier of
good 1 and (hence) q2 > e2 and the individual is
a (net) demander of good 2;
Chapter 6
• We consider an individual who starts with an
endowment of the two goods.
• We find his gross demands for the two goods
(and hence his net demands).
• We analyse how these demands change
when the prices and his income change.
(These variables are exogenous for the
individual).
• These are called comparative static
exercises.
Chapter 6
• We start with an individual with Cobb-Douglas
preferences with parameter a = 0.5.
• The Maple/html file contains other examples:
• Cobb-Douglas with parameter a = 0.3;
• Stone-Geary;
• Perfect Substitutes;
• Perfect Complements.
• The shape of the demand curve depends
upon the preferences.
Chapters 6 and 7
• We use two spaces:
• The first: to show the preferences of the individual
and the budget line:
• q1 on the horizontal axis and q2 on the vertical axis.
• The second: to show the effect of changes in an
exogenous variable on the demand:
• q1 (and q2 ) on the vertical axis and the exogenous
variable on the horizontal axis.
• Note that this is different from usual demand and
supply curves.
Chapter 6
• The indifference curves are given by the
preferences.
• The budget constraint is given by the individual’s
income and the prices of the two goods.
• We denote by (e1, e2) the endowment and by (q1, q2)
the quantities chosen to consume. The budget line
is given by the equation:
• p1q1 + p2 q2 = p1e1 + p2e2
• This is a line with slope
• - p1/ p2
• which passes through the endowment point.
• After showing this we go to the html file.
q2
the budget line: p1 q1 +p2 q2 = p1 e1 +p2 e2
(p1 e1 +p2 e2)/p2
has slope = -p1/p2
and passes through (e1,e2)
e2
X
(p1 e1 +p2 e2 )/p1
e1
q1
Let’s go to Maple
My Mum’s indifference curves
Was she mad?
q2
No – just contented.
B
q1
Chapter 6
• Goodbye!