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This is a PowerPoint presentation on the fundamentals of the concept of “elasticity” as used in principles of economics. A left mouse click or the enter key will add an element to a slide or move you to the next slide. The backspace key will take you back one element or slide. - PowerPoint PPT Presentation
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Fall '97Economics 205Principles of
Microeconomics
This is a PowerPoint presentation on the fundamentalsof the concept of “elasticity” as used in principles ofeconomics.
A left mouse click or the enter key will add an element to a slide or move you to the next slide. The backspace key will take you back one element or slide. The escape key will get you out ofthe presentation.
R. Larry Reynolds
Fall '97Economics 205Principles of
MicroeconomicsSlide 2
Elasticity
· Elasticity is a concept borrowed from physics· Elasticity is a measure of how responsive a
dependent variable is to a small change in an independent variable(s)
· Elasticity is defined as a ratio of the percentage change in the dependent variable to the percentage change in the independent variable
· Elasticity can be computed for any two related variables
Fall '97Economics 205Principles of
MicroeconomicsSlide 3
Elasticity [cont. . . ]
· Elasticity can be computed to show the effects of:· a change in price on the quantity demanded [ “a
change in quantity demanded” is a movement on a demand function]
· a change in income on the demand function for a good
· a change in the price of a related good on the demand function for a good
· a change in the price on the quantity supplied· a change of any independent variable on a
dependent variable
Fall '97Economics 205Principles of
MicroeconomicsSlide 4
“Own” Price Elasticity
· Sometimes called “price elasticity”· can be computed at a point on a demand
function or as an average [arc] between two points on a demand function
· ep, are common symbols used to represent price elasticity
· Price elasticity [ep] is related to revenue· “How will a change in price effect the total
revenue?” is an important question.
Fall '97Economics 205Principles of
MicroeconomicsSlide 5
Elasticity as a measure of responsiveness
· The “law of demand” tells us that as the price of a good increases the quantity that will be bought decreases but does not tell us by how much.
· ep [“own”price elasticity] is a measure of that information]
· “If you change price by 5%, by what percent will the quantity purchased change?
Fall '97Economics 205Principles of
MicroeconomicsSlide 6
pechange in quantity demanded
change in price%
%
or, ep % Q
% P
At a point on a demand function this can be calculated by:
ep =
Q2 - Q1
Q1
P2 - P1
P1
Q2 - Q1 = Q
P2 - P1 = P=
QQ1
PP1
Fall '97Economics 205Principles of
MicroeconomicsSlide 7
Q
Q1
P
P1
ep =
Price decreases from $7 to $5
3
Px
Qx/ut
D
$5B
5
$7A
P1 =
P2 =
P2- P1 = 5 - 7 = P = -2P = -2
Q1 = Q2 =
Q2 - Q1 = 5 - 3 = Q = +2
Q = +2
+2
7
3[2/3 = .66667]
[-2/7=-.28571]
= % Q = 67%
% P = -28.5%= -2.3 [rounded]
The “own” price elasticity of demandat a price of $7 is -2.3
This is “point” price elasticity. It is calculated at a pointon a demand function. It is not influenced by the directionor magnitude of the price change.
.
There is a problem! If theprice changes from $5 to$7 the coefficient of elasticity is different!
-2
Fall '97Economics 205Principles of
MicroeconomicsSlide 8
3
Px
Qx/ut
D
$5B
5
$7A
Q
Q1
P
P1
ep =
When the price increases from $5 to $7,
P1 =
P2 =P = +2
+2
5
Q1=Q2=
Q = -2
-2
5
[-2/5 = -.4]
[+2/5 = .4]
= % Q = -40%
% P = 40%= -1 [this is called “unitary elasticity]
the ep = -1 [“unitary”]
ep = -1
In the previous slide, when the price decreased from $7 to $5, ep = -2.3
ep = -2.3The point price elasticity is different at every point!
There is an easier way!
Fall '97Economics 205Principles of
MicroeconomicsSlide 9
An easier way!
Q1PP1
ep =
QQ1 =
Q
Q1
P1
P*
By rearranging terms
=P1
Q1*
Q
Pthis is the slope of thedemand function
this is a point onthe demandfunction
Q P1
Q1
= *Pep
Given that when:P1 = $7, Q1 = 3
P2 = $5, Q2= 5
P2- P1 = 5 - 7 = P = -2
Q2 - Q1 = 5 - 3 = Q = +2
Then,Q
P +2 -2
= = -1
This is the slope of the demand Q = f(P)
-1
P1 = $7, Q1 = 3
7
3= -2.33
On linear demand functions the slope remains constant so you just put in P and Q
Fall '97Economics 205Principles of
MicroeconomicsSlide 10
P1 = $7, Q1 = 3
P2 = $5, Q2= 5
P2- P1 = 5 - 7 = P = -2Q2 - Q1 = 5 - 3 = Q = +2
3
Px
Qx/ut
D
$5B
5
$7A
The following information wasgiven
Q = f (P)
The slope of the demand function
[Q = f(P)] is Q
P =+2
-2= -1
The slope-intercept form Q = a + m P- 1
What is the Qintercept?
Px must decreaseby 5.
The slope [-1] indicates that for every1 unit increase in Q, Px will decrease by 1. Since Px must decrease by 5, Q must increase by 5
Q increases by 5
Q = 10
Q = 10 when Px = 0
10
The equation for the demandfunction we have been using isQ = 10 - 1P. A table can beconstructed.
Fall '97Economics 205Principles of
MicroeconomicsSlide 11
For a simple demand function: Q = 10 - 1P
price quantity ep TotalRevenue
$0 10
$1 9
$2 8
$3 7
$4 6
$5 5
$6 4
$7 3
$8 2
$9 1
$10 0
The slope is -1 The intercept is 10using our formula,
ep=Q P1
Q1*P
ep =Q P1
Q1P *
the slope is -1,
(-1)
price is 7
7
at a price of $7, Q = 3
3= -2.3
-2.3
Calculate ep at P = $9Q = 1
ep = (-1) 91
= -9
Calculate ep for all other price and quantity combinations. -9
0-.11
-.25-.43-.67
-1.
-1.5
-4.
undefined
Fall '97Economics 205Principles of
MicroeconomicsSlide 12
For a simple demand function: Q = 10 - 1P
price quantity ep TotalRevenue
$0 10
$1 9
$2 8
$3 7
$4 6
$5 5
$6 4
$7 3
$8 2
$9 1
$10 0
-2.3
-9
0-.11
-.25-.43-.67
-1.-1.5
-4.
undefined
Notice that at higher prices the absolute value of the priceelasticity of demand, ep is greater.
Total revenue is price times quantity; TR = PQ.0
9162124
2524
211690
Where the total revenue [TR]is a maximum, epis equalto 1
In the range where ep< 1, [less than 1 or “inelastic”], TR increases asprice increases, TR decreases as Pdecreases.
In the range where ep> 1, [greater than 1 or “elastic”], TR decreases as price increases, TR increases as P decreases.
Fall '97Economics 205Principles of
MicroeconomicsSlide 13
3
Px
Qx/ut
D
$5B
5
$7A
To solve the problem of a point elasticity that is different for every price quantitycombination on a demand function, an arc price elasticity can be used. This arc priceelasticity is an average or midpoint elasticity between any two prices. Typically,the two points selected would be representative of the usual range of prices in the time frame under consideration.
The formula to calculate the average or arc price elasticity is:
ep=Q P1 + P2
Q1 + Q2*PThe average or arc ep between$5 and $7 is calculated,
ep=Q P1 + P2
Q1 + Q2*P
Slope of demand
QP = - 1
-1
P1 = $7, Q1 = 3
P2 = $5, Q2= 5
P2- P1 = 5 - 7 = P = -2Q2 - Q1 = 5 - 3 = Q = +2
P1 + P2 = 12
12
Q1 + Q2 = 8
8= - 1.5
The average ep between $5 and $7 is -1.5
Fall '97Economics 205Principles of
MicroeconomicsSlide 14
Given: Q = 120 - 4 P
Price Quantity e p T R
$ 10
$ 20
$ 25
$ 28
Calculate the point ep at eachprice on the table.
Calculate the TR at each priceon the table.
Calculate arc ep at between$10 and $20.
Calculate arc ep at between$25 and $28.
Calculate arc ep at between $20 and $28.
Graph the demand function [labeling all axis and functions], identify which ranges on the demand function are price elastic and which areprice inelastic.
Fall '97Economics 205Principles of
MicroeconomicsSlide 15
Given: Q = 120 - 4 P
Price Quantity e p T R
$ 10
$ 20
$ 25
$ 28
Calculate the point ep at eachprice on the table.
80
40
20
8
- . 5
-2
-5
-14
Calculate the TR at each priceon the table. TR = PQ
$800
$800
$500
$224
Calculate arc ep at between$10 and $20. ep = -1
Calculate arc ep at between$25 and $28. ep = -7.6
Calculate arc ep at between $20 and $28. ep = -4
Graph the demand function [labeling all axis and functions], identify which ranges on the demand function are price elastic and which areprice inelastic. At what price will TR by maximized? P = $15
Fall '97Economics 205Principles of
MicroeconomicsSlide 16
Q/ut
Price
120
30
ep = -115
60
|ep | > 1 [elastic]
The top “half” of the demand function is elastic.
|ep | < 1inelastic
The bottom “half” of the demand function is inelastic.
Graphing Q = 120 - 4 P,
TR
TR is a maximumwhere ep is -1 or TR’s slope = 0
When ep is -1 TR is a maximum.When |ep | > 1 [elastic], TR and P move in opposite directions. (P hasa negative slope, TR a positive slope.)
When |ep | < 1 [inelastic], TR and P move in the same direction. (P and TR both have a negative slope.)
Arc or average ep is the average elasticity between two point [or prices]
pointep is the elasticity at a point or price.
Price elasticity of demand describeshow responsive buyers are to change in the price of the good. The more “elastic,” the more responsive to P.
Fall '97Economics 205Principles of
MicroeconomicsSlide 17
Use of Price Elasticity
· Ruffin and Gregory [Principles of Economics, Addison-Wesley, 1997, p 101] report that:
· short run epof gasoline is = .15 (inelastic)
· long run epof gasoline is = .78 (inelastic)
· short run epof electricity is = . 13 (inelastic)
· long run epof electricity is = 1.89 (elastic)
· Why is the long run elasticity greater than short run?
· What are the determinants of elasticity?
Fall '97Economics 205Principles of
MicroeconomicsSlide 18
Determinants of Price Elasticity
· Availability of substitutes [greater availability of substitutes makes a good relatively more elastic]
· Portion of the expenditures on the good to the total budget [lower portion tends to increase relative elasticity]
· Time to adjust to the price changes [longer time period means there are more adjustment possible and increases relative elasticity
· Price elasticity for “brands” is tends to be more elastic than for the category of goods
Fall '97Economics 205Principles of
MicroeconomicsSlide 19
An application of price elasticity.The price elasticity of demand for milk is estimated between -.35 and -.5. Using -.5 as a reasonable figure, there are several important observations that can be made.
What effect does a10% increase in the Pmilk
have on the quantity thatindividuals are willing to buy?
ep % Q
% P
ep % Q
% P
Since ep = -.5
-.5 =+10%
To solve for % Q
Multiply both sides by +10%(+10%)x ( ) x (+10%)-5% = % QA 10% increase in the price of milk would reduce the quantity demanded by about5%.
Pmilk
Qmilk
DmilkP1
Q1
P2
A 10% increasein P
Q2
reduces Qby 5%
+10%
-5%
If price were decreased by 5%, whatwould be the effect on quantity demanded?
Fall '97Economics 205Principles of
MicroeconomicsSlide 20
ep % Q
% PThe price elasticity of demand is a measure ofthe % Q that will be “caused” by a % P.
If the price elasticity of demand for air travel was estimated at -2.5, whateffect would a 5% decrease in price have on quantity demanded ?
-2.5 = % Q
% P- 5%= +12.5% change in quantity demanded
If the price elasticity of demand for wine was estimated at -.8, whateffect would a 6% increase in price have on quantity demanded ?
-.8 = % Q
% P+6%= -4.8% decrease in quantity demanded
Fall '97Economics 205Principles of
MicroeconomicsSlide 21
If the price elasticity of demand for milk were -.5, the effects of a price change on total revenue [TR] can also be estimated.
Since ,
ep % Q
% P
When ep < 1, demand is “inelastic. “ This means that the % Q< % P. Since the % price decrease is greater than the % increase in Q,TR [TR = PQ] will decrease.
When ep < 1, a price decrease will decrease TR; a price increase willincrease TR, Price and TR “move in the same direction.” [inelastic demand with respect to price]
When ep > 1, demand is “elastic.” This means that the % Q> % P. When the % price decrease is less than the % increase in Q, TR [TR = PQ] will increase.
When ep > 1, a price decrease will increase TR; a price increase will decrease TR, price and TR “move in opposite directions.” [elastic demand wrt price]
Fall '97Economics 205Principles of
MicroeconomicsSlide 22
Graphically this can be shown
P
Q/ut
D
at the midpoint, ep = -1
P1
Q1
TR
TR is a maximum
TR
TR = PQ, so the maximum TR is therectangle 0Q1 EP1
0
E
elastic
price risesP2
Q2
(P2
Q2)
is less
than (P1 Q1) Loss inTR whenP
+TR
As price rises into the elastic rangethe TR will decrease. Notice that in this range the slope of demandis negative, the slope of TR ispositive
Price andTR move in opposite directions
Fall '97Economics 205Principles of
MicroeconomicsSlide 23
P
Q/ut
D
inelastic
TR
at the midpoint, ep = -1
0
EP1
Q1
TR is a maximum
TR = P1 Q1
[Maximum]
TRWhen price elasticity of demand isinelastic
A price decrease
P0
Q0
results in a smaller PQ [TR]
will result ina decrease in TR [PQ]. notice thatboth TR and Demand have a negative slope in the inelastic range of the demand function.Price and TR “move in the samedirection.”
A price decrease will reduceTR; a price increase will increase TR. Note that this information is usefulbut does not provide information about profits!
Fall '97Economics 205Principles of
MicroeconomicsSlide 24
“Own” Price Elasticity of Demand
· ep is a measure of the responsiveness of buyers to changes in the price of the good.
· ep will be negative because the demand function is
negatively sloped.· A linear demand function will have unitary elasticity at
its “midpoint.” AT THIS POINT TR IS A MAXIMUM!· A linear demand function will be more “elastic” at
higher prices and tends to be more “inelastic” in the lower price ranges
Fall '97Economics 205Principles of
MicroeconomicsSlide 26
Inelastic ep
· When ep< 1 [less than 1] the demand is “inelastic”· The %Q< %Pbuyers are not
very responsive to changes in price.· An increase in the price of the good
results in an increase in total revenue [TR], a decrease in the price decreases TR. Price and TR move in the same direction
Fall '97Economics 205Principles of
MicroeconomicsSlide 27
P
Q/ut
D1
D1 is a “perfectly elastic”demand function.
ep % Q
% P
For an infinitesimally smallchange in price, Q changes by infinity.
= undefined
perfectly elasticep = undefined
.
Buyers are very responsive to price changes. An infinitely small change in pricechanges Q by infinity.
D2
perfectlyinelastic
ep = 0
D2 is a “perfectly inelastic” demand function, no matter howmuch the price changes the same amount is bought. Buyersare not responsive to price changes! ep = 0, perfectly inelastic.
0
P 0= 0
.
As the demand function becomes more horizontal, [buyers are more responsiveto price changes],ep approaches infinity.
De
Fall '97Economics 205Principles of
MicroeconomicsSlide 28
Examples
· Goods that are relatively price elastic· lamb, restaurant meals, china/glassware,
jewelry, air travel [LR], new cars, Fords· in the long run, eptends to be greater
· Goods that are relatively price inelastic· electricity, gasoline, eggs, medical care,
shoes, milk· in the short run, eptends to be less
Fall '97Economics 205Principles of
MicroeconomicsSlide 29
Income Elasticity[normal goods]
ey % Qx
% Y[Where Y = income]
Income elasticity is a measure of the change in demand [a “shift” of the demand function] that is “caused” by a change in income.
.
Q/ut
P
D
At a price of P1 , the quantity demandedgiven the demand D is Q1 .
P1
Q1
D is the demand function when the income is Y1 .
For a “normal good” an increasein income to Y2 will “shift” thedemand to the right. This is anincrease in demand to D2.
Due to increase in income,
demandincreases
D2
The increase in income, Y, increases demand to D2. The increase in demand results in a larger quantity being purchased at the
same Price [P1]..
Q2
% Y > 0; % Q> 0; therefore,
ey >0 [it is positive]
Fall '97Economics 205Principles of
MicroeconomicsSlide 30
Income Elasticity [continued. . .][normal goods]
ey % Qx
% Y
Q/ut
P
D1
A decrease in income is associated with a decrease inthe demand for a normal good.
At income Y1, the demand D1 representsthe relationship between P and Q. At a price [P1] the quantity [Q1] is demanded.
P1
Q1
For a decrease in income [-Y],the demand decreases; i.e. shiftsto the left,
A decrease in income, decreasesdemand
D2
at the price [P1 ], a smaller Q2 will be purchased.
Q2
% Y < 0 [negative]; % Q < 0 [negative];
so, ep > 0 [ positive]
For either an increase or decrease in income
the ep is positive. A positive relationship [positive correlation] between Y and Qis evidence of a normal good.
Fall '97Economics 205Principles of
MicroeconomicsSlide 31
When income elasticity is positive, the good is considered a “normalgood.” An increase in income is correlated with an increase in the demand function.
ey % Qx
% Y
ey % Qx
% Y + % Y
+ % Qx+ ey
A decrease in income is associated with a decrease in the demand function.
- % Y
- % Qx
+ ey
For both increases and decreases in income, ey is positive
.
The greater the value of ey, the more responsive buyersare to a change in their incomes.
When the value of ey is greater than 1, it is called a “superior good.”
.
The |% Qx| is greater than the |% Y|.Buyers are very responsive to changes inincome. Sometimes “superior goods” arecalled “luxury goods.”
Fall '97Economics 205Principles of
MicroeconomicsSlide 32
ey % Qx
% Y
D1
Income Elasticity[inferior goods]
There is another classification of goods where changes in income shift the demand function in the “opposite” direction.
An increase in income [+Y] reduces demand.
Q/ut
P
P1
Q1
decreasesdemand
D2
Q2
+Y
- %Qx
-%Qx
-ey =
.
An increase in income reduces the amount that individualsare willing to buy at each priceof the good. Income elasticity
is negative: - ey
The greater the absolute valueof - ey, the more responsive buyersare to changes in income
.
Fall '97Economics 205Principles of
MicroeconomicsSlide 33
D1
Income Elasticity[inferior goods]
A decrease in income [-Y] increases demand.
Q/ut
P
P1
Q1
D2
Q2
ey % Qx
% Y-Y
+%Qx
Decreases in income increase the demand for inferior goods.
+%Qx - ey
.
A decrease in income [-Y] results in an increase in demand,the income elasticity of demand is negative
.
For both increases and decreases in income the income elasticity is negativefor inferior goods. The greater the
absolute value of ey, the more responsivebuyers are to changes in income
Fall '97Economics 205Principles of
MicroeconomicsSlide 34
Income Elasticity
· Income elasticity [ey] is a measure of the effect of an income change on demand. [Can be calculated as point or arc.]
· ey > 0, [positive] is a normal or superior good an increase in income increases demand, a decrease in income decreases demand.· 0 < ey < 1 is a normal good
· 1 < ey is a superior good
· ey < 0, [negative] is an inferior good
Fall '97Economics 205Principles of
MicroeconomicsSlide 35
Examples of ey
· normal goods, [0 < ey < 1 ], (between 0 and 1) · coffee, beef, Coca-Cola, food, Physicians’
services, hamburgers, . . .
· Superior goods, [ ey > 1], (greater than 1)
· movie tickets, foreign travel, wine, new cars, . . .
· Inferior goods, [ey < 0], (negative)
· flour, lard, beans, rolled oats, . . .
Fall '97Economics 205Principles of
MicroeconomicsSlide 36
Cross-Price Elasticity
· Cross-price elasticity [exy] is a measure of how responsive the demand for a good is to changes in the prices of related goods.
· Given a change in the price of good Y [Py ], what is the effect on the demand for good X [Qy ]?
· exy is defined as:
xyx
y
eQP
%
%
Fall '97Economics 205Principles of
MicroeconomicsSlide 37
Cross-price elasticity of demand , [exy][substitutes]
.
When the price of pork increases, it will tend to increase the demand for beef. People will substitute beef, which is relatively cheaper, forpork, which is relatively more expensive.
pork/ut
[pri
ce o
f pork
]
Pp
Dp
When pork is $1.50, Qp porkis purchased.
1.50
Db
beef/ut
[pri
ce o
f beef]
Pb
Qp
When beef is $2, Qb beefis purchased.
2
Qb
price of pork increases
2
The quantity demanded of pork decreases.
Qp’
-Qp
at Pb = $2 more beef will be bought to substitute for the smaller
quantity of pork.
increase demand
Db’
Qb’
for an increase
in Ppork, demand forbeef increases
Fall '97Economics 205Principles of
MicroeconomicsSlide 38
Cross-price elasticity
· In the case of beef and pork· the ebp is not the same as epb
· ebp is the % change in the demand for beef with respect to a % change in the price of pork
· epb is the % change in the demand for pork with respect to a % change in the price of beef
· beef may not be a good substitute for pork · pork may not be a good substitute for beef
Fall '97Economics 205Principles of
MicroeconomicsSlide 39
Cross-price elasticity of demand , [exy][substitutes]
The cross elasticity of the demand for beef with respect to the
price of pork, ebeef-pork or ebp can be calculated:
ebp =% Q of beef
%P of pork
An increase in the price of pork,
+ Pp
“causes” an increase in the demand for beef.
+ Qb+ebppositive
cross elasticity is positive
ebp =% Q of beef
%P of pork
A decrease in the price of pork,
- Pp
“causes” a decrease in the demand for beef.
- Qb+ebppositive
If goods are substitutes, exy will be positive. The greater the coefficient, the more likely they are good substitutes.
Fall '97Economics 205Principles of
MicroeconomicsSlide 40
Cross-price elasticity of demand , [exy][compliments]
colour books
Pc
crayons
Pc
Dp
a decrease in the price of crayons,
P1
Q1
$3
2000
Po
Q2
increases the quantity demanded of crayons
as more crayons arepurchased, the demand for colour books increases.
DcDc’
increasedemand
2500
At the sameprice a larger quantity will be bought
ebc =% Q of b
%P of c
-Pc
- Pc
+ Qb
+ Qb- ebcnegative
for compliments, the cross elasticity is negative for priceincrease or decrease.
Fall '97Economics 205Principles of
MicroeconomicsSlide 41
Cross-Price Elasticity
· exy > 0 [positive], suggests substitutes, the higher the coefficient the better the substitute
· exy < 0 [negative], suggests the goods are compliments, the greater the absolute value the more complimentary the goods are
· exy = 0, suggests the goods are not related
· exy can be used to define markets in legal proceedings
Fall '97Economics 205Principles of
MicroeconomicsSlide 42
Elasticity of Supply
· Elasticity of supply is a measure of how responsive sellers are to changes in the price of the good.
· Elasticity of supply [ep] is defined:
seQuantity Supplied
price%
%
Fall '97Economics 205Principles of
MicroeconomicsSlide 43
Q /ut
P
Given a supply function,
supply
at a price [P1], Q1 is produced and offeredfor sale.
P1
Q1
At a higher price [P2],
P2
a largerquantity, Q2, will be producedand offered for sale.
Q2
+P
+Q
The increase in price [ P ], inducesa larger quantity goods [ Q]for sale.
The more responsive sellers are to
P, the greater the absolute value of es.
[The supply function is “flatter”ormore elastic]
Elasticity of supply
es = %Qsupplied
%P
Fall '97Economics 205Principles of
MicroeconomicsSlide 44
Q /ut
PThe supply function is amodel of sellers behavior.
Sellers behavior is influenced by:1. technology
2. prices of inputs3. time for adjustment
market periodshort runlong runvery long run
4. expectations 5. anything that influences costs of production
taxesregulations, . . .
Se
a perfectly elastic supply [es is undefined.]
Sia perfectly inelasticsupply, es = 0
as supply approaches horizontal es
approaches infinity
Fall '97Economics 205Principles of
MicroeconomicsSlide 45
Elasticity
· Price elasticity of demand [measures a move on a demand function caused by change in price/arc or point]· elastic, inelastic or unitary elasticity
· income elasticity [measures a shift of a demand function associated with a change in income]· superior, normal, and inferior
· cross elasticity· measure the shift of a demand function for a good
associated with the change in the price of a related good · [compliment/substitute]
· price elasticity of supply [measures move on a supply curve]