Using Economics to Analyze Pricespersonal.psu.edu/faculty/r/2/r2w/AGBM420-2017Fall/LectureNotes/W2-… · Single market model of price determination ... Product category vs. product

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Markets & Prices (c) R.D. Weaver Penn State

Using Economics to Analyze Prices

Intuition and concepts review

Single market model of price determination

What is a product?

Think of bananas……..

What is the price of a banana?

what is a banana !?@#$%$*&

We all have an idea of: the general concept of a banana

So we could say what – in general – the price is.

But specifically, we need to add detail to specification of what we mean by a banana!


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Categories, groups, and products

Define a product category If a group of products can be thought of as composed of close substitutes and consumers typically allocate budget to that group, versus other groups, we label that product group as a product category.

Examples: Fresh fruit, beef, cars, sports equipment


Product category vs. product types

Within a product category, it is useful to define

product groups or “types” in which products are nearly perfect substitutes, so consumers buy only one product type in each group.

Typically, only one product type is chosen from a product category.

Examples: Bananas, apples,….pick-up trucksMarkets & Prices (c) R.D. Weaver Penn State

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Consumer choice as nested choice

Budget is allocated through a nested series of product categories…


Total income

DiscretionaryNon-

Discretionary

Housing Food CommTrans SavingEducEntertTravel

Consumer choice as nested choice….it keeps branching down to greater detail and eventual purchase


Food budget

DiscretionaryNon-

Discretionary

Meat Carbs FruitVegs SavingUpgradesSnacks

This makes sense since consumer preferences reflect this type of independence across trade-offs. You think about travel vs. education, transportation vs. housing, etc. Then within each product category, the trade-offs are independent of your decisions in other categories….

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Consumer’s nested choices also result in picking the product’s market position across market dimensions


Fruit

FrozenFresh

Bananas Oranges KiwiApples

Grocery i Grocery jBackyard

…where…when....exactly what

horizontal

…stage of processing (vertical)

Producers do the same in choosing what to produce…..nested choice


Fruit

FrozenFresh

Bananas Oranges KiwiApples

Grocery i Grocery jBackyard

…where…when....exactly what

horizontal

…stage of processing (vertical)

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So, in the real world……….multiple markets…..considerable complexity within each dimension! Over time

Over geography (space)

Over vertical position of the product

Over horizontal position of the product

Let’s shift now to the market level

Conceptually, at the market level consumers and producers come together to buy and sell a product.

The aggregation of those transactions result in what we can call “aggregate demand” and “aggregate supply”

In each case, “aggregate” means the summation across all purchases, or all sales.

We can think of these aggregates as defining a “quantity flow” from sellers to buyers.


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Price & quantity flows are determined by simultaneous adjustment across all those markets!

Quantity flow:

At the micro-level,the product quantity that is transacted between a buyer and a seller.

At the market-level, the aggregate quantity sold = aggregate quantity bought.

quantity flows decomposed


As we will see, when we step away from the single isolate market in basic economics, we see need to consider the spectrum of interacting markets for a product. To do so, we need to generalize our concept of demand and supply, e.g.

Total demand components

Current demand for use (maybe many types)

Demand for exports (spatial)

Demand for carry-out, closing stocks ..ending inventory

Total supply components

Current supply just produced (maybe many forms)

Supply from imports

Supply from carry-in, opening stocks…..opening inventory

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Composition of demand and supply

Market Dimension Demand Component Supply Component

Intertemporal(at time t)

Current demandInventory demand

Current supplyInventory supply

Spatial (at location s) Demand for export Supply from imports

Vertical (at stage v) Demand derived from next stage of processing

Supply to next stage of processing

Horizontal (at product type i)

Demand for product variation Supply to product variation

Market aggregate(t, s, v, i )

Total demand Total supply


Price is determined in competitive markets by equilibirum between total demand and supply.

Total demand = YD (Pt, s, v, i ) = YS (Pt, s, v, i ) = Total supply

Price determination

How is price determined? Producers have to set prices, BUT…….

If they set price > market price, their sales 0

If they set price < market price, they would loose $

So they need to set their price at market price.

Market price is not always observable! But, in principle

it adjusts such that

YD (Pt, s, v, i ) = YS (Pt, s, v, i )


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Quantity flows & structure of a market To understand price, we need to understand what

dimensions of the market are important….and what are the drivers affecting those dimensions.

We need to break down Total demand and Total supply

We can learn about the structure of the market by considering quantity flow data.

For many products, not all market dimensions are relevant!


Quantity flow data


the key to understanding the structure of a market …if it is available!

Wheat: Supply and Disappearance, 1996 - 2009

ERS/USDA Data - Wheat Data: Yearbook Tables

It can be considered at Product Category, product group or type, or specific product level!

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Vast data is available on prices and quantity flows

Section: FEEDSTOCKSWheat: Supply and Disappearance, 1996-2009

(million bushels)

Year (beginning

September 1)

Supply Disappearance

Ending stocks May 31

Beginning stocks Production Importsa Total

Domestic use

Food Seed Feedb Total Exportsa

Total disappear

ance1996 376 2,277 92 2,746 891 102 308 1,301 1,002 2302 4441997 444 2,481 95 3,020 914 92 251 1,257 1,040 2,298 7221998 722 2,547 103 3,373 909 81 391 1,381 1,046 2,427 9461999 946 2,296 95 3,336 929 92 279 1,300 1,086 2,386 9502000 950 2,228 90 3,268 950 79 300 1,330 1,062 2,392 8762001 876 1,947 108 2,931 926 83 182 1,192 962 2,154 7772002 777 1,606 77 2,460 919 84 116 1,119 850 1,969 4912003 491 2,344 63 2,899 912 80 203 1,194 1,158 2,353 5462004 546 2,157 71 2,774 910 78 181 1,168 1,066 2,234 5402005 540 2,103 81 2,725 917 77 157 1,151 1,003 2,154 5712006 571 1,808 122 2,501 938 82 117 1,137 908 2,045 4562007 456 2,051 113 2,620 947 88 115 1,050 1,264 2,314 3062008 306 2,499 127 2,932 927 78 255 1,260 1,015 2,275 657

2009 c 657 2,216 119 2,991 917 70 149 1,137 881 2,018 973

Source:U.S. Department of Agriculture, 2010 Agricultural Statistics, Table 1-7, and previous annual editions,http://www.nass.usda.gov/Publications/Ag_Statistics/index.asp

a Imports and exports include flour and other products expressed in wheat equivalent.b Approximates feed and residual use and includes negligible quantities used for distilled spirits.c Preliminary. Totals may not add due to independent rounding.


Data shows

Extent of specific sources of supplyBeginning stocks, imports, current production

Extent of specific types of use – illustrates relevance of particular dimensions of the market Where and when is it consumed

Current consumption

Vertical downstream processing

Exports


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By the end of the course

You will need to understand The quantity flows that are relevant for you product

The drivers of each component of total demand and of total supply.

You will need to be able to find data on quantity flows and drivers.

You will be begin to think about how the drivers affect change quantity flows and price!



But……lets start with a single market………

Recall we noted prices exhibit substantial systematic variation

What is the system?

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System concept

System

Drivers = Zt

Outcome

We want to break open this “ black box “ to

1) identify the drivers

2) Understand how the drivers affect price


Economic system concept

Product Market

Drivers = Zt

exogenous variables

Pt

We want to break open this “ black box “ to

1) identify the drivers

2) Understand how the drivers affect price

What are the nuts & bolts of this

system?

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Product Market

Demand Drivers = ZDt

Pt

Pt = P(ZDt ZS

t ) + et

Three aspects of the market system

Demand drivers demand(price)

Supply drivers supply(price)

Equilibrium demand(price) = supply(price) price (drivers)+error

Supply Drivers = ZSt



Product Market

Demand Drivers = ZDt

Pt

Pt = P(ZDt ZS

t ) + et

Three aspects of the market system

Demand drivers demand(price)

Supply drivers supply(price)

Equilibrium demand(price) = supply(price) price (drivers)+error

Supply Drivers = ZSt

Structural form

Reduced form

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what we will cover in this section

Single Market Model of Price Determination Intuition

Algebraic

Back-of-the-envelop

Using a single market model Setting up data

Tracking Change

Reduced-form price models


The single market model - remember the parts?

P1

Y1

P1*

Y1*

Notation: P for price Y for quantity

* means “the equilibrium value”$/apple

Lbs apples

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To understand price, we need to understand drivers or determinants of demand, supply, and how equilibrium occurs

P1

Y1

P1*

Y1*

Demand is a function of own price and other

stuff

Supply is a function of own price and other

stuff


What are the drivers of demand or of supply?

P1

Y1

P1*

Y1*

What is the theory of demand?

What is the theory of supply?

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What is so magic about the X? Why is P* determined at the intersection?

P1

Y1

P1*

Y1*

What is the theory of

equilibrium?


Single Market Model: Intuition

Review at home……..

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We use three theories to motivate our ideas of how price is determined

Consider textbook case

Consumer demand

Producer supply

Equilibrium: how price is determined

(Later we will consider producer demand for inputs…)


System involves three subsystems

Demand determinants

Consumer Demand

Competitive Equil

Producer Supply

Supply determinants PriceQuantity Traded

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note

In this single market, we do not consider

1) Markets over time (inventories)

2) Markets over space (imports, exports)

3) Markets linked vertically (stages of processing)

4) Horizontal markets for close substitutes

We are starting with a simple model!


1) Theory of Consumer Demand(quick review of AGBM 101, 102, 302)

Schematic

Prices

IncomePreferences

Over Y1 vs. Y2

Demand

Let’s look at it graphically

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Summarizing demand Demand:

Yd1 = Yd1(P1,Ps,Pc,Inc)

Yd1 is demand quantity of good 1P1 is own price, the price of good 1Ps is price of a substitute (or a set of prices….)Pc is the price of a complement (s)Inc is income

Example: Yd1 = a0 + a1 P1 + a2 Ps + a3 Pc + a4 Inc

Inverse demand: To graph the demand curve, we want price on the vertical axis, so we

use what is called the inverse demand curve….P1= P1d( Y1, Ps, Pc, Inc)

Example P1d = [Yd1 – (a0 + a2 Ps + a3 Pc + a4 Inc )]/a1

We call the a’s parameters


2) Theory of Supply(quick review of AGBM 101, 102, 302)

Schematic

Prices (output & input)

Fixed Inputs

Preferences (profits)

Subject to

Technology

Supply

Input demands

Objective

Reality constraint!

Let’s look at it graphically

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Summarizing supply

Supply for good 1: Ys1 = Ys1(P1,R, K)

Ys1 is quantity supplied for good 1P1 is price of good 1R is a set of input prices for inputs used in producing good 1K is capital or quantity of fixed goods and services used in

producing good 1Example: Ys1 = b0 + b1 P1 + b2 R + a3 K

Inverse demand: P1= P1s( Y1, R,K) Example: P1s = [Ys1 – (b0 + b2 R + a3 K )]/b1


3) Theory of how price is determined

Roulette wheel?

Bureaucratically (think California electricity!)

Competition (what do we mean by this???)

A game among a small set of agents

By a dominant firm….

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Graphing the inverse demand and supply curves……

P1

Y1

P1*

Y1*

We note equilibrium occurs when Quantity demanded = Quantity supplied

or quivalentlyDemand price = supply price


How can you graph the demand function?

P1

Y1

You first have to set values for Ps, Pc, & Inc….why?

Demand: Yd1 = Yd1(P1,Ps,Pc,Inc)

Inverse demand: Pd1= P1d( Yd1, Ps’ , Pc’, Inc’)

If you change those values,

you would get a different graph, why?

Yd1 ‘

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P1

Y1




Yd1 ‘

Yd1 ‘”

Suppose income decreased from Inc’ to Inc”



P1

Y1




Yd1 +

Yd1 ‘

Suppose income increased from Inc’ to Inc+

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Drivers except own price are called “demand shifters”Why?

P1

Y1



Yd1 +

Yd1 ‘

Suppose income increased from Inc’ to Inc+


What determines the slope of the demand curve?

P1

Y1

Preferences………..why? Think of organic vs. conventional preferences….

Yd1

Yd1

Person with “green” preferences will be less price responsive (sensitive) than conventional preferences

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What determines position and slope of the supply curve? Review


Summarizing………..for particular values for drivers preferences and technology

we can graph demand and supplyP1

Y1

P1*

Y1*

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But….what causes equilibrium………..??P1d P1s Y1dY1s

P1

Y1

P1*

Y1*

Supply: Ys1 = Ys1(P1,R, K)

Inverse demand: P1= P1s( Y1,R,K)


Inverse demand: P1= P1d( Y1, Ps, Pc, Inc)


Competitive Equilibrium

At the market level, we assume

1) Free entry and exit

2) Products and goods are “private goods”

a) Exclusive

b) Exhaustive consumption

Why does that matter?

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Price is determined where Yd1=Ys1

P1

Y1

P1*

Y1*

Demand: Yd1 = Yd1(P1,Ps,Pc,Inc) = Ys1 = Ys1(P1,R, K) = Supply

If we had actual functions, and values for Ps, Pc, Inc, R, K,

we could solve for P1!


Start with bureaucratic prices how would they work?

Friday afternoon after a long and IMPORTANT meeting, 12 people decide what the price of a bushel of soybeans should be:

Pbt = $8.10/ unit

Demand YDt = YD (Pb

t )

Supply YSt = YS (Pb

t )

We could have two possible outcomes

Excess demand = YD (Pbt ) - YS (Pb

t ) ) ≥ 0 ? or

Excess supply = YD (Pbt ) - YS (Pb

t ) ) ≤ 0 ?

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Why bureaucrats fail1) Bureaucratic pricing is not likely to clear the market!

P1

Y1

P1*

Y1*

P1b

P1 b

Who cares! Why is it important that prices clear markets????

Why would anyone expect a

bureaucrat to have special

knowledge?


Why bureaucrats fail2) Bureaucratic pricing determines who gets the product, leaving buyers and sellers disappointed!

P1

Y1

P1*

Y1*

P1b

P1 b

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Examples of bureaucratic prices Pa electricity Milk prices? License plates Bridge tolls Parking tickets Tickets to your favorite band’s concert (football

game)(Price = $/seat + pain and effort to get a ticket!)

The price of public educationWhat’s wrong with this picture?


What else??????

Interest rates (Fed tries to influence them! )

Exchange rates

(Govs & Feds try to influence them! )

Available credit

(Govs & Feds try to influence them! )

Price of health care

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Competitive markets - how would they work? Consider “ short-run” first….Key assumptions

Buyers and sellers take the price, they can adjust their demand and supply as price changes….but do not “set price”.

Private good characteristics imply people have to compete for the right to consume a product

(remember long lines for whatever “ must have “ you didn’t have! )

Free entry implies that if there is excess demand, someone will enter and expand supply………


The price adjustment story – suppose price is too highIf price were too high, supply at that price would exceeed demand, producers

could not sell what they produced. Soon, those with more to sell would reduce their price and market price would fall…..until the market clears…

P1

Y1

P1*

Y1*

P1 b

Y1D

Y1S

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The price adjustment story – suppose price is too lowIf price were too low, demand at that price would exceed supply, consumers

would not be able to find all they wanted to buy. Soon, some would offer to pay more increasing the price and market price would increase…..until the market clears…

P1

Y1

P1*

Y1*

P1 b

Y1D

Y1S


Bottom line

Competitive market determines Price that signals

Cost of resources

Consumer willingness to pay for the product

Quantity that exactly equals demand and supply

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What happens if P* results in profits?

In the long-run, we assume free entry and exit.

If P* results in profits, more people will enter the industry, expanding supply, driving price down and profits to zero.

If P* results in some people losing money (neg. profits), people will close businesses, decreasing supply, driving price up, and profits to zero.


Implications of competitive markets in the long-run Resources move into or out of the market to adjust

supply such that profits are driven to zero

That implies!.........

P* is driven to equal average cost of production (AC)

P* = average cost of production

And that means………..prices have social value!

P* reflects cost and preferences! Leads to max social welfare (societal standard of living given available resources!)

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We need to use a concept - functions

A function “processes” a value of a variable x

into another value or new variable, call it y

We can write a function symbolically as f( )

And if it transforms every value of x into a value of y

We can write it as:

y = f(x)


Example functions in economics?

Cost of production

For value of output y, there is an associated cost C

C = C(y)

That cost might be influenced by the values of other variables, e.g. capacity K C= C(y, K)


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Example cost function

Cost

Y1Y1*

TC1

For each value of Y output, there is a unique value for cost

Total cost could be broken down to variable and fixed cost.


Cost of production and profits

Define “ variable cost of production” as the sum of all costs that can be varied in the short-run.

Define the cost function C=C(YS|Θ) it measures the variable cost of producing each level of output YS that is feasible given available fixed resources Θ.

Note: this cost reflects how technology can combine and transform inputs into the output.

Example???

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If some resources are fixed, the position of cost curve will change when we change the level of those resources.

Cost

Y1Y1*

C(Y|Θ”)

C(Y|Θ’)


Average cost of production and profits

If we divide variable cost by quantity of output, we get average cost of producing that quantity of output!

AC1(YS | Θ) = C(YS |Θ)/YS

Define profits as π = P YS - C(YS |Θ)

that is, the left-over revenue after you pay all your variable costs!

note,……this is a return you have left to pay for use of your fixed resources Θ

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Profits, zero profits and prices

If entry and exit drive profits to zero, what does that mean for price?

as π = P YS - C(YS |Θ) 0

divide both sides by YS

P YS - C(YS |Θ) = 0 P - AC = 0


The long-run story

P1

Y1

P1*

Y1*

Y1D

Y1S

AC1

Here, P* exceeds AC, profits are positive. New firms would enter and expand supply, shifting supply outward, driving price down until profits=0

Can you calc profits?

AC(Y*1 )

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The long-run story

P1

Y1

P1*

Y1*

Y1D

Y1S

AC1

Here, P* exceeds AC, profits are positive. New firms would enter and expand supply, shifting supply outward, driving price down until profits=0

1) Supply shifts outward as more firms enter

2) But, AC shifts up as costs increase for new entrants

3) Over time, innovation reduces costs (not shown here!)

P1**

Two effects make this happen

Conclusions – what makes a market work? Price and quantity adjusts in response to profit

opportunities

If price exceeds average cost, profits entice increased supply, driving price down, average cost up….until profit 0

AND at that price (P*) Demand = supply !


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Why does the competitive mechanism work?


Markets naturally emerge

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Review again?


Ingredients necessary for competitive markets to work Human initiative …….a.k.a. “hedonism”

Institutional infrastructure Legal system

Currency

Physical infrastructure

Market technologies: Information, data, analysis,……

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System involves three subsystems

Demand determinants (drivers)

Consumer Demand

Competitive Equil

Producer Supply

Supply determinants (drivers) Price &Quantity Traded


Implications

Three subsystems

Consumer choicesDemand

Producer choices Supply

Equilibrium

price

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Important implication

For consumer, price is predetermined

For producer, price is predetermined

At the market level, price is determined


Boiling it down……we need three theories……….

Demand determinants

Consumer Demand

Competitive Equil

Producer Supply

Supply determinants Price &Quantity Traded

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Think of it as a balanced system

Newton’s which law??? For every action there is an accompanying reaction….

Demand

YD1(P1)

Supply

YS1 (P1)

Change in supply driver increase supply

Price has to change to rebalance the system

P


Think of it as a balanced system

Demand

YD1(P1)

Supply

YS1 (P1)

Change in Determinants

Price has to change to rebalance the system

Price

Price has to fall when supply increases

Price is the pivot!

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Home Thoughts….

Think of your product

Can you identify three key determinants of demand for that product?

Can you identify three key determinants of supply of that product?

Documents

Using Economics to Analyze Pricespersonal.psu.edu/faculty/r/2/r2w/AGBM420-2017Fall/LectureNotes/W2-… · Single market model of price determination ... Product category vs. product