Chapter 8
The Basic Market Equation
Geog 3890: ecological economics
The Big Idea
► How
do the decentralized decisions of thousands of
firms and households communicated through
markets result in optimal allocations?
► Markets
appear to have spontaneous order
(the invisible hand)
► In
what sense is market
► allocation efficient?
► Are
outcomes fair or sustainable?
5 Concepts & 3 Principles
► Marginal
Utility
► Market Price of a Good
► Market Price of Factor
► Marginal Physical Product
► Competitive Market
► Law
of Diminishing Marginal Utility
► Law of Diminishing Marginal Physical Product
► Equimarginal Principle of Maximization
Marginal Utility = MUxn
► The
marginal utility of good ‘x’ to consumer
‘n’. The extra or additional satisfactaion one
gets from consuming one more unit of the
good, other things being held equal (ceteris
paribus & partial derivatives).
Market Price of Good ‘x’ = Px
► Goods
are typically denoted by ‘x’ and ‘y’
► E.g. Gallon of gas, slice of pizza, lift ticket,
etc.
Market Price of Factor ‘a’ = Px
► To
produce a slice of pizza there are
factor prices of Capital (kitchen & Stove);
Labor (chef & dishwasher);
and ingredients (sauce,
dough, cheese, etc.).
►
►
What is the market price
of Labor?
How much does minimum
wage really raise the ‘floor’
of the labor factor price?
Marginal Physical Product
of Factor ‘a’ = MPPa
► The
extra output produced as a result of
using one more unit of factor ‘a’ as input
(ceteris paribus )
► How
many more
pizzas are made
per night by the
addition of one
more oven or one
more chef?
Competitive Market
►A
market in which there are many buyers and
sellers of identical product.
► ‘Many’ means “enough that no single buyer or
seller is sufficiently large to affect the market
price” – e.g. no firm is ‘too big to fail’ 
► Every
‘player’ is a “Price Taker” rather than a
“Price Maker”.
► Question: What goods and services do you
think are provided in truly competitive
markets? Cell phone service, coffee, gasoline?
The Law of
Diminishing Marginal Utility
► As
one consumes successive units of a good,
the additional satisfaction decreases, that is,
total satisfaction increases but at a decreasing
rate.
►
The marginal utility
of one’s first slice of
pizza on an empty
stomach is great.
The marginal utility of
the 5th slice is much less.
Proof by
contrapositive
The Law of
Diminishing Marginal Physical Product
(aka The Law of Diminishing Returns)
►
Law of diminishing returns – as more and more of a
variable factor is added to a fixed factor, output will
rise initially but will eventually fall.
Output (total product)
initially rises at an
increasing rate , but
marginal output then
starts to diminish. This
means that total output
still increases, but at a
decreasing rate (the slope
of the curve tails off). There
may eventually be a point
where returns become
negative and output falls.
Economies of Scale
► The
law of diminishing marginal product should not
be confused with economies or diseconomies of scale.
An economy of scale occurs when a 1% increase in all
the factors of production together leads to more than
a 1% increase in output. This does not contradict the
law of diminishing marginal
physical product. In reality,
economies of scale are
likely to occur over a limited
range of production, usually
followed by diseconomies
of scale. (Carpenters and House Building example)
The Equimarginal Principle of Maximization
(aka the ‘When to Stop’ rule)
► This
is true for firms and households – we
stop changing our allocations when
marginal costs = marginal benefits
► Q: When does a consumer stop reallocatng
her income among different goods?
► A: When she has found an allocation that
maximizes her total satisfaction or total
‘utility’.
► Examples: Shoes vs. Pizza, guns vs. butter,
Wall Street vs. Main Street
The Equimarginal Principle of Maximization
(aka the ‘When to Stop’ rule)
► True
for Consumers (households)
► True for Producers (firms)
► Pizza
Parlor Example:
Hire another cook or buy a bigger oven?
Cook costs $1600/mnth Oven $1600/mnth
Additional Cook – 20 more pizzas per day
Additonal Oven – 18 more pizzas per day
20 Pizzas/day boosts revenue by $1700 / month
Failed Assumptions of
equimarginal principle of maximization
► Homo
Economicus
► Local vs. Global Optima in reallocation
decisions
► ‘Lumpiness’ of units
► Ceteris Paribus
Marginal Physical Product for Labor
► Pizzeria
and Shoe Store Story
► 1) The town is small – only labor available
must be taken from pizzeria and attracted by
higher wages.
► Diminished MPPshoes and increased MPPpizza
results in labor transfer
► Step ‘2’ continues until equilibrium which is
when: MPPshoes = MPPpizzas
► Comment: There is a ‘fairy tale’ element to ‘1’
The Basic Market Equation
► (x
& y) are goods; ‘a’ is a factor of
production (e.g. labor, capital, resources)
► Px is Price of one unit of good ‘x’
► ‘n’ is a given individual consumer
How do we know the equation holds
for ‘Ends’ or CONSUMPTION
More Pizza or more Beer?
More Studying time or More Playing Time?
How do we know the equation holds
for ‘Means’ or PRODUCTION
What does the Market Equation mean?
The Parametric or ‘Fulcrum Function’ of relative prices
The central role of Px/Py is worth emphasizing. It brings about an
equality of the marginal utility ratios with the marginal productivity
ratios. Things equal to the same thing are equal To each other –
Prices serve as a kind of sliding fulcrum on a seesaw that balances the
Weight of relative possibility with the weight of relative desirability,
of means with ends.
Types of Substitution
► Psychological
rate of substitution
 The rate at which consumers are willing to
substitute one good for another.
► Market
rate of substitution
 The rate at which consumers are able to
substitute one good for another
► Technical
rate of substitution or transformation
 The rate at which producers are able to produce
one good rather than another by reallocation of
factors of production.
Key Ideas
► The
basic market equation defines an optimal
allocation of resources, one in which no one
would want to reallocate any factor to any
alternative use because doing so would only
decrease that person’s total satisfaction. No
firm would want to reallocate any factor to any
other use because doing so would lower profit.
► Prices in competitive markets lead to an
efficient allocation of resources in the sense
that no one can be made better off in his own
judgment by reallocating resources to produce
a different mix of goods.
Pareto Optimum
►A
Pareto Optimum occurs when no other
allocation could make at least one person
better off without making anyone else
worse off. This is also known as a Pareto
Efficient Allocation.
► Pareto
Optimality accepts a given
distribution of wealth and income and does
not care about the ‘scale’ of the economy.
NCE recognized Market Failure: Monopoly
►
The fulcrum function of
relative prices depends
on pure competition.
Firms produce up to where
MC = MR
►
In a competitive market marginal revenue is equal to price and
price is given. Producers are price takers. Monopolists can
control supply and be price makers.
►
Consequently Monopolists will underproduce and over charge
to maximize profits.
Assumptions and Limitations
► 1)
► 2)
► 3)
► 4)
► 5)
► 6)
Ignore distribution of wealth and income
All goods are market goods
(rival & excludable)
Factors of production are substitutes for
each another
External costs and Benefits are negligible
All players have perfect information
Markets are competitive
Non-Price Adjustments
► There
are myriad pareto optima for every
distribution of income; every set of wants and
preferences; and every set of technologies,
and all the combos thereof.
 Advertising and Social Movements are a non-price
adjustment that can change relative desirability.
 Technological change can be a non-price
adjustment that changes ratios of MPPax/MPPay
 Price adj - Psychological adj – Techno adj
are all possible.
Advertising and creation of demand
►
If wants are created and
preferences altered through
advertising, and if advertising is a
cost of production of the product,
then production begins to look like
a treadmill. If we produce the need
along with the product to satisfy it,
then we are not really making any
forward motion toward the
satisfaction of pre-existing needs.
The producer replaces the
consumer as sovereign. Then, the
moral earnestness of production, as
well as the concept of Pareto
Optimal allocation of resources in
the service of such production,
suffers a loss.
Quote for Discussion
► “There
is more to welfare than efficient
allocation – for example, there are distribution
and scale.”
►
Do you agree or disagree?
►
“Welfare ” – what a word….
 …promote the general welfare (U.S. constitution)
 “Welfare queens” and entitlement programs
 Welfare as “Utility Maximization”
Supply and Demand (intro)
► 1)
The Demand Curve 2) The Supply Curve
► “Watch
Your
► ‘P’s
► And
► ‘Q’s”
►
The Demand Curve
Question: What does it mean to be on one’s
demand curve?
Question: What is the Marginal Utility of Money?
Demand Curve for Water
The Supply Curve
Market Clearance
Summary
► The
Basic Market Equation defines and
brings about a pareto optimal allocation of
resources and establishes te decreasing
demand curve and incrreasiing supply curve
which produces market clearance at P*,Q*.
This is true for any pair of goods (x,y), and
pair of factors (a,b), and any consumer (n1,
n2, n3, …). This is a simplified picture of
overall market equilibrium.
Big Ideas to remember…
► Basic
Market Equation
Competitive Market
► Pareto Optimal allocation Monopoly & Misallocation
► Sliding Fulcrum Function of Relative Prices
► Law of diminishing marginal physical product
► Marginal Costs = Marginal Revenue “when to stop”
► Non-Price Adjustments
Equimarginal Principle
► Supply and Demand
Principle of Substitution
Minnesota Welfare Monies