Buying & Selling (Chapter 9)
Daniel N. Tomkins
ECON 3020 – Intermediate Microeconomics
Daniel N. Tomkins
Buying & Selling
Buying & Selling
Income vs. Endowment
Earlier we thought about income as given, but in reality people
earn income by selling goods, assets, or labor
An Endowment is some bundle of goods that the consumer
brings to the market to trade
Net Demand and Gross Demand
Gross Demand for a good is the amount of the good the
consumer chooses to consume
Net Demand for a good is the difference between the gross
demand for that good and the endowment
Daniel N. Tomkins
Buying & Selling
Net and Gross Demand
Some notation. . .
Let’s consider a two-good model
The consumer has an Endowment bundle (ω1 , ω2 )
Gross Demand is the optimal choice bundle (x1 , x2 )
Finally, Net Demand is Gross Demand minus the Endowment
(x1 − ω1 , x2 − ω2 )
Gross Demand is generally positive but Net Demand may be
positive (the consumer is a buyer) or negative (the consumer is a
seller)
Daniel N. Tomkins
Buying & Selling
Budget Constraint
What will the budget constraint look like?
Before, the consumer’s budget constraint was m = p1 x1 + p2 x2
The right-hand side is total expenditures on both goods and the
left-hand side is money income
This same principle holds with our new budget constraint
Now, instead of money income we have the value of our
endowment so the consumer’s total expenditure is equal to the
value of their endowment
Imagine the consumer comes to the market and sells all their
endowment – this is simply their money income
The new budget constraint is
p1 ω1 + p2 ω2 = p1 x1 + p2 x2
Daniel N. Tomkins
Buying & Selling
Budget Constraint
What will the budget constraint look like?
Value of the Endowment must equal the value of Gross Demands
Useful to rewrite the budget constraint in terms of Net Demands
p1 (x1 − ω1 ) = −p2 (x2 − ω2 )
For any positive prices, where Net Demand for one good is positive
it must be that Net Demand for the other good is negative
This just means if the consumer is a buyer of one good it must be a
seller of the other
Necessary condition for trade!
Daniel N. Tomkins
Buying & Selling
Budget Constraint
What does the budget line look like graphically?
Solving the budget constraint for x2 , the budget line is
x2 = ω2 + ω1
p1 p1
− x1
p2 p2
The slope, or market exchange rate, is −p1 /p2 just as we saw in
Chapter 2
The vertical intercept is ω2 + ω1 pp12
The horizontal intercept is ω2 pp21 + ω1
The budget line must pass through the endowment point (the
consumer can not trade)
Daniel N. Tomkins
Buying & Selling
Budget Constraint
What does the budget line look like graphically?
Daniel N. Tomkins
Buying & Selling
Budget Constraint
Changing the Endowment
How does the budget line change as a result of an endowment shift
from (ω1 , ω2 ) to (ω10 , ω20 )?
Slope is unchanged, −p1 /p2
New budget line must pass through the new endowment (ω10 , ω20 )
The new endowment is worth less if
p1 ω1 + p2 ω2 > p1 ω10 + p2 ω20
This is another way of saying if the new endowment is ‘below’ the
original budget line it is worth less
Daniel N. Tomkins
Buying & Selling
Budget Constraint
Changing Prices
How does a change in the price affect the budget line?
In Chapter 2, when prices changed the money income remained
constant
We can no longer say this because money income is determined by
the endowment and prices, m = p1 ω1 + p2 ω2
The budget line must still pass through the endowment point
(ω1 , ω2 )
Consider an increase in price of good one to p10 > p1 , this will make
the budget line steeper and rotate it around the endowment point
p0
The new vertical intercept is larger ω2 + ω1 p12 and the horizontal
intercept is smaller ω2 pp20 + ω1
1
Daniel N. Tomkins
Buying & Selling
Budget Constraint
Changing Prices
How does the price change affect demand?
An increase in price of good 1 makes the consumer feel more
wealthy because her endowment is more valuable,
p1 ω1 + p2 ω2 < p10 ω1 + p2 ω2
Also, it is more expensive for the consumer to buy more of good 1
A change in price can cause a consumer to switch from being a
buyer to a seller of a good
We will revisit the Slutsky Equation to further examine the effect
of a price change on demand
Daniel N. Tomkins
Buying & Selling
Slutsky Equation
Slutsky Equation Revisited
Slutsky equation is the combination of the substitution effect and
income effect
Income effect is change in quantity demanded from a change in
price from change in purchasing power
Substitution is change in quantity demanded from a change in price
holding money income constant
Before money income was m, now money income is the value of the
endowment p1 ω1 + p2 ω2
Now, a price change necessarily changes the value of the endowment
– the money income
It is useful to distinguish the new income effect that arises now
from the old one
Daniel N. Tomkins
Buying & Selling
Slutsky Equation
Two Income Effects
Ordinary Income Effect is the effect from just changing
purchasing power (old income effect)
Endowment Income Effect is the change of demand resulting
from the change in endowment resulting from a change in price
The Slutsky Equation becomes
∆x m
∆x1s
∆x1
=
− x1 1 + Endowment Income Effect
∆p1
∆p1
∆m
What exactly is the Endowment Income Effect?
Daniel N. Tomkins
Buying & Selling
Slutsky Equation
Endowment Income Effect
What exactly is the Endowment Income Effect?
Change in demand from the change in money income due to the
price change
Money income is m = p1 ω1 + p2 ω2
Change in money income from change in p1 is
∆m
= ω1
∆p1
Endowment income effect is change in demand from change in
money income ∆x1m /∆m times the change in money income from
change in price ∆m/∆p1
Daniel N. Tomkins
Buying & Selling
Slutsky Equation
Endowment Income Effect
Endowment Income Effect is
∆x m
∆x1m ∆m
= ω1 1
∆m ∆p1
∆m
Combining this with our Slutsky Equation from before, the
Slutsky Equation becomes
∆x1
∆x1s
∆x m
=
− (x1 − ω1 ) 1
∆p1
∆p1
∆m
As before, the substitution effect is always negative
The income effect can be positive or negative
Daniel N. Tomkins
Buying & Selling
Labor Supply
Endowment and Labor Supply
We can use this analysis to analyze the individual’s labor supply
decision
If the individual chooses to work little, she earns little money and
consumes little
If the individual chooses to work lots, she earns lots of money and
consumes a lot
The budget constraint
The consumer is endowed with some amount of time L they can use
to either work (Labor L) or relax (Leisure `)
Time spent working earns a wage of w
Consumption C costs the price p
Daniel N. Tomkins
Buying & Selling
Labor Supply
Endowment and Labor Supply
The budget constraint
The consumer is endowed with some amount of time L they can use
to either work (Labor L) or relax (Leisure `)
Time spent working earns a wage of w
Consumption C costs the price p
Expenditure on consumption and opportunity cost of leisure must
value of endowment
pC + w` = wL
The consumer gets utility from Consumption C and Leisure `
Daniel N. Tomkins
Buying & Selling
Labor Supply
Endowment and Labor Supply
The consumer’s optimal choice is where the Marginal Rate of
Substitution between labor and leisure equals the real wage w/p
Comparative Statics
How would labor supply change as time endowment L changes?
What is response to a change in the wage rate w?
What is response to a change in the price of consumption p?
Daniel N. Tomkins
Buying & Selling