 Optimization
Assumption: an assumption that
suggests that the person in question is trying to
maximize some objective
 Marginal Benefit: the increase in the benefit
that results from an action
 Marginal Cost: the increase in the cost that
results from an action
 Total Net Benefits: the difference between all
benefits and all costs
 The Box Example
 If the marginal benefit
of an extra unity of the
activity is greater than its marginal cost,
increasing the activity will increase total net
benefits.
 If the marginal cost of an extra unit of the
activity is greater than its marginal cost,
increasing the activity will decrease total net
benefits.
 Therefore, to maximize total net benefits the
level of an activity that maximizes total net
benefits is where the marginal benefit equals
the marginal cost of an extra unit of the activity.
 If
an extra unit of the activity (trades)
results in getting more boxes (MB) than
are being given up (MC) the stack of boxes
grows (TNB).
 If an extra unit of the activity (trades)
results in getting less boxes (MB) than are
being given up (MC) the stack of boxes
shrinks (TNB).
 If an extra unit of the activity (trades)
results in getting the same amount of
boxes (MB) that are being given up (MC)
the stack of boxes is at its tallest (
maximum TNB).
 Total
Way – select the level of the activity
that maximizes the difference between
total benefits and total costs
 Marginal Way – set the marginal benefit of
to the marginal cost of an extra unit
 Economist prefer the later because many
decisions are not all or nothing. Most
times people are deciding to increase or
decrease the amount of something that
they are doing.
MB=∆TB/ ∆Q=(TBNew-TBOld)/(Qnew-Qold)
 MC=∆TC/ ∆Q=(TCNew-TCOld)/(Qnew-Qold)
 TB=∑MB + (any fixed benefits which we generally assume to

be zero)

TC=∑MC+
(any fixed costs which we generally assume to be
zero)
TNB =TB-TC
 Max TNB at that level of Q where MB=MC

 See
Hand out and Excel Spreadsheet
(Maximizing TNB)

The market simulation summarized


Each buyer had a buyer value (MB of the one book) and
each seller a seller cost (MC)
Both buyer and seller tried to maximize their gain





Buyer Gain=Buyer value – price
Seller Gain=Price - Seller cost
Repeated trials brought about a market price that
cleared the market
As the price approached the market price the total gain
to buyers and sellers together increased
Let´s generalize this by presenting the theory of
markets.


A market is simply an institution that bring buyers and sellers
together to agree on price and quantity traded.
Competitive Markets
many sellers and buyers →no one buyer or seller affect the price or
they are price takers
 identical or homogeneous goods→price is the only decision factor
 perfect information →there is only one price
 free entry and exit →profits (economic) will be zero in the long-run


Non-Competitive Markets
Monopoly – one seller
 Oligopoly – few sellers
 Monopolistically Competitive – differentiated products

Households or consumers buy goods and services for
a variety of reasons, but can we model it?
 Economics assume that individuals are rational –
they weigh the costs and benefits of their actions
and then try and maximize TNB.
 What are the benefits? Economists have modeled
benefits as satisfaction or utility (an injection is
useful but usually not pleasant – it provides utility).
 What are the costs? Economist argue that the costs
are opportunity costs – i.e. what does one give up to
get a good or service.





A person’s preferences or tastes, along with other factors,
determine the benefit from a good.
The price of the good, the price of similar or substitute
goods, a person’s limited income, along with other
factors, determine the opportunity costs of the good.
Basically, the theory of demand is getting the most
satisfaction from the goods and service one buys given
the prices of goods and one’s income.
While many factors affect demand, we begin by
concentrating on the price of the good. Why? In
competitive markets, the price of the good is the MC to
the buyer.
Law of Demand – the price of a good and the
quantity demanded are negatively (or inversely)
related, ceteris paribus (Latin – all other things
equal).
 Rational behavior suggests that as the MC↑,
ceteris paribus, an individual will ↓Q, it’s that
simple.
 Early theorists, however, concentrated on MB
rather than MC. The believed that utility was
measurable, so-called cardinal (after numbers)
utility.




Law of Diminishing Marginal Utility
Jelly bean example and Econ U$A tape on the drought in
California.
If people are to buy more (↑Q), since the MB↓, the price
must fall (↓P)



More recent theorists use the concept of ordinal utility to
come to a similar conclusion. A person is assumed to be
able to rank bundles from most preferred to least
preferred.
 Reaches the Law of Demand with less restrictive
assumptions than cardinal utility.
The Law if Demand and the Income and Substitution
Effects
Substitution Effect: as the price of a good falls its
opportunity cost relative to other similar or substitute
goods falls, so consumers use more of the good and less of
other goods
 Example: Papples=$1/lb of A ($1/A) and Poranges=$1/lb of O
($1/O) → the relative price of A in terms of O : PA/PO →
1 A requires us to give up 1 0. If the PA falls to $.5/A, the
PA/PO → 1 A requires us to give up only .5 O. Apples are
thus cheaper and we buy more apples and less oranges.
Oranges are now more expensive ( 2 A for every 1 O).
 Income
Effect: as the price of a good falls, the
real purchasing power of income increases and
consumers will buy more of the good (if the good
is normal).


Example: If PA=$1, A $100 a week of income will
allow us to buy 100 A. Or, the real income, measured
in apples, is 100 A. If the PA falls to $.5/A, our real
income is now 200 A.
The effect of incomes on demand is not clear. For
normal goods, increases in income, increase demand,
and for inferior goods the opposite happens.
 Cardinal
utility, ordinal utility, and MB=MC,
all arrive at Law of Demand.
 We now look at the Law of Demand and the
Theory of Demand using numbers/schedules,
graphs/curves, and mathematical functions
(don’t panic). These representations make it
easier to understand the implications of
theory, but they require study and practice.
 We will use the book example and then shift
to a handout to practice.
Price of
Ice-Cream Cone
$3.00
2.50
1. A decrease
in price ...
2.00
1.50
A movement
1.00
along the curve
0.50
is caused by
changes in P only
0 1 2 3 4 5 6 7 8 9 10 11 12 Quantity of
Ice-Cream Cones
2. ... increases quantity
of cones demanded.
Copyright © 2004 South-Western

The Demand Function

PR - Price of related goods







Complements
Substitutes
Y - Income
NB - Number of Buyers (added when all individuals curves are
summed together – see market demand)
T -Tastes
E -Expectations
G- Government: Taxes and Subsidies
In mathematical notation:
 Qd=F (P , PR ,Y,NB,T,E,G), where F() is “related to”
 Signing the determinants of demand. - is an inverse
relationship and + is a direct relationship.
 Market Demand Curve: The horizontal summation of
all the individual demand curves (handout). In our
Aplia experiment, the buyer values were ranked
from high to low.


Demand Curve versus the Demand Function



Schedules



Changes in price are described by the demand schedule.
Shifts are shown as increases in QD at every price.
Graphs/Curves



The demand curve is created assuming ceteris paribus, so it
maps only the relationship between P and QD.
The demand function shows all the determinants of demand.
All the factors other than P, such a PR and Y, are shift
factors.
A movement along the curve is a change in quantity
demanded and is only caused by the change in the price of
the good itself.
A shift of the curve is a change in demand is caused by any
other factor other than the price of the good itself.
Qd=F (P | PR,Y,NB,T,E,G)
Price of
Ice-Cream
Cone
Increase
in demand
Decrease
in demand
Demand
curve, D2
Demand
curve, D1
Demand curve, D3
0
Quantity of
Ice-Cream Cones
Copyright©2003 Southwestern/Thomson Learning
 Economists
assume that businesses are
rational as well. We assume their primary
interest is maximizing profits.
 Profits are the difference between total
revenues and total costs. Revenues are
analogous to benefits received by
consumers.
 Once again, we concentrate on price
first. Why? In competitive markets, price
is equal to MB (or marginal revenue) to
firms. Every time the firm sells another
unit, its revenue increases by the price of
the good.
 Law
of Supply - price and the quantity
supplied are positively related, ceteris paribus.



Rational behavior implies that firms try and maximize
profits, where the MB = P and MC is dependent on how
much output is produced.
As the P ↑, the MB ↑ → Q supplied ↑ to maximize profits.
Classical theorist approached the Law of Supply
from the costs perspective. They posited that
the MC ↑ as Q ↑.

Law of Diminishing Marginal Returns → LDMR comes
from the productivity decline as more and more of a
variable input is added to fixed input, eventually the
extra output for each additional variable input will fall,
ceteris paribus. Thus, MC ↑ of producing additional Q
will eventually

Drilling for oil in Economics U$A video, Dairy Queen
example, and growing the world’s food supply in a flower
pot.

Law of Increasing Costs: as the production of a
good increases, its opportunity cost increases
(re: PPF and specialized resources)

Remember that the L of IC occurs because of resource
specialization.
Both the LIC and LDMR predict that as Q ↑ up the
productivity of inputs will fall and MC ↑.
 The Law of Supply arises because prices must
rise to cover the higher MC of producing
additional units of output.
 We can better work with the Law of Supply using
schedules, graphs/curves, and mathematical
equations.

Price of
Ice-Cream
Cone
$3.00
1. An
increase
in price ...
2.50
2.00
1.50
Change in
Qs is a movement
And caused only by Price
1.00
0.50
0
1 2
3
4
5
6
7
8
9 10 11 12 Quantity of
Ice-Cream Cones
2. ... increases quantity of cones supplied.
Copyright©2003 Southwestern/Thomson Learning
 The






Supply Function
PI - Input prices
PI -Prices of other outputs
Te -Technology
E -Expectations
NS -Number of sellers (occurs when adding
individual supply curves together)
G - Government taxes and subsidies
 Qs=F(P,PI,PO,Te,E,NS,G)
 Market
Supply: The horizontal summation of
all the individual firms’ supply curves.
 Qs=F(P,PI,PO,Te,E,NS,G)
 The
price of the good itself causes
movements along the supply curve or
changes in the quantity supplied.
 Anything other than the price of the good
causes shifts in the supply curve or
changes in supply.
 Market supply comes from horizontally
adding all the individual supply curves
(see handout).
Price of
Ice-Cream
Cone
Supply curve, S3
Decrease
in supply
Supply
curve, S1
Supply
curve, S2
Increase
in supply
0
Quantity of
Ice-Cream Cones
Copyright©2003 Southwestern/Thomson Learning
Market – an institution that bring buyers and sellers
together to agree upon price and quantity traded.
 Remember buyers key off of price in competitive
markets because it is their MC and for sellers it is
their MB.
 Equilibrium price and quantity are those that clear
the market (neither shortages or surpluses) because
the Qd=Qs.
 Disequilibrium prices and quantities




Shortage – Excess Demand
Surplus – Excess Supply
At the Pe and Qe , buyers and sellers behavior are
coordinated.
Price of
Ice-Cream
Cone
Supply
Equilibrium
Equilibrium price
$2.00
Equilibrium
quantity
0
1
2
3
4
5
6
7
8
Demand
9 10 11 12 13
Quantity of Ice-Cream Cones
Copyright©2003 Southwestern/Thomson Learning
(a) Excess Supply
Price of
Ice-Cream
Cone
Supply
Surplus
$2.50
2.00
Demand
0
4
Quantity
demanded
7
10
Quantity
supplied
Quantity of
Ice-Cream
Cones
Copyright©2003 Southwestern/Thomson Learning
(b) Excess Demand
Price of
Ice-Cream
Cone
Supply
$2.00
1.50
Shortage
Demand
0
4
Quantity
supplied
7
10
Quantity of
Quantity
Ice-Cream
demanded
Cones
Copyright©2003 Southwestern/Thomson Learning
Price of
Ice-Cream
Cone
1. Hot weather increases
the demand for ice cream . . .
Supply
New equilibrium
$2.50
2.00
2. . . . resulting
in a higher
price . . .
Initial
equilibrium
D
D
0
7
3. . . . and a higher
quantity sold.
10
Quantity of
Ice-Cream Cones
Copyright©2003 Southwestern/Thomson Learning
Price of
Ice-Cream
Cone
S2
1. An increase in the
price of sugar reduces
the supply of ice cream. . .
S1
New
equilibrium
$2.50
Initial equilibrium
2.00
2. . . . resulting
in a higher
price of ice
cream . . .
Demand
0
4
7
3. . . . and a lower
quantity sold.
Quantity of
Ice-Cream Cones
Copyright©2003 Southwestern/Thomson Learning
 Animal
tracks help one to tell what kind of
an animal and the direction the animal went.
 Demand and supply shifts leave different
tracks to help us identify them and whether
they are increasing or decreasing.
 Movement of either D or S (confirm with
graphs)




D↓, S
D↑, S
S↓, D
S↑, D
constant
constant
constant
constant
→ P↓, Q↓
→ P↑, Q↑
→ P↑, Q↓
→ P↓, Q↑
 Price
play an important role in markets
because it:




Coordinates buyers and seller behavior
Provides information about MC and MB
Rations the good between buyers
Determines resource allocation
 Although
the equilibrium graph is
interested it is sterile, we are interested
in what happens when circumstances
change, i.e. demand and supply shocks
(shifts).
When either the demand curve or the supply
curve shift, Pe and Qe change predictably.
 These is done by comparing two static
equilibriums or comparative statics.
 Demand Shifts/Shocks:




Supply Shifts/Shocks:



D↑→P↑Q↑
D↓→P↓Q↓
S↑→P↓Q↑
S↓→P↑Q↓
Like animals, D and S shocks leave unique tracks.
 Predicting:



Demand can increase, remain the same, or
decrease.
Supply can increase, remain the same, or
decrease.
So comparative statics tells us that there are 9
different possible comparative static predictions
D↑
D unchanged
D↓
S↑
P↑Q↑
P↓Q↑
P? Q ↑
P Q
P↓Q↑
P↓Q↑
P↓Q↓
P↓Q↑
P↓Q?
S unchanged
P↑Q↑
P Q
P↑Q↑
P
P
P
P↓Q↓
P Q
P↓Q↓
S↓
P↑Q↑
P↑Q↓
P↑ Q ?
P Q
P↑Q↓
P↑Q↓
Q
Q
Q
P↓Q↓
P↑Q↓
P?Q↓
 If
P↑Q↑ , what kind of animal is it? D or S?
Which way is it going?
 If P↓Q↓, explain.
 If P↓Q↑, explain.
 If P↑Q↓, explain.
 Listening to market information on
movements of P and Q, help explain what
is the primary influence on the market, D
or S.
 NPR examples: Mad Cow and Tuition
Adam Smith summarized the remarkable
coordination that results even as people follow their
own self-interest. He called in the ¨Invisible Hand¨.
 As we saw in the Aplia experiment, consumer simply
try to maximise their utility (TNB or gain) and
producers try and maximize their profit (TNB or
gain).
 Market prices are






signals for resource allocation
coordinate consumer and producer behavior
incentives for buyers and sellers (MC for buyers and MB for
sellers)
Ration scarce goods and services
Provide information about scarcity and value
 Prices
help markets allocate resources
more efficiently. Markets are efficient
when
They produce what consumers want or most
highly value, and
 Produce those goods and services at least
possible cost
 In Aplia, we saw the total gain increased as we
moved to the equilibrium prices and
quantities.
 We will explore the implications of this
remarkable human creation as we proceed
through the course.
