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MEASUREMENTAND INTERPRETATION
OF ELASTICITIES
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Discussion TopicsOwn price elasticity of demandIncome elasticity of demandCross price elasticity of demandOther general propertiesApplicability of demand elasticities
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Key Concepts Covered…
Own price elasticity = %Qbeef for a given %Pbeef
Income elasticity = %Qbeef for a given %IncomeCross price elasticity = %Qbeef for a given %Pchicken
Arc elasticity = range along the demand curvePoint elasticity = point on the demand curve
Price flexibility = reciprocal of own price elasticity
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Own Price Elasticity
of Demand
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Own Price Elasticity of DemandOwn price
elasticity of
demand
Percentage change in quantity Percentage change in price
=
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Arc Elasticity Approach
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Own Price Elasticity of DemandOwn price elasticity
of demandPercentage change in quantity Percentage change in price
=
where:P = (Pa + Pb) 2; Q = (Qa + Qb) 2; Q = (Qa – Qb); and P = (Pa – Pb)
Arc elasticity
Own price elasticity
of demand= [QP] x [PQ]
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The subscript “a” here againstands for “after” while “b”stands for “before”
Equation 5.3
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Own Price Elasticity of DemandPercentage change in quantity Percentage change in price
=
where:P = (Pa + Pb) 2; Q = (Qa + Qb) 2; Q = (Qa – Qb); and P = (Pa – Pb)
Arc elasticity
= [QP] x [PQ]
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The subscript “a” here againstands for “after” while “b”stands for “before”
The “bar” over the P andQ variables indicates anaverage or midpoint.
Own price elasticity
of demand=
Own price elasticity
of demand
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Own Price Elasticity of DemandPercentage change in quantity Percentage change in price
=
where:P = (Pa + Pb) 2; Q = (Qa + Qb) 2; Q = (Qa – Qb); and P = (Pa – Pb)
= [QP] x [PQ]
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The subscript “a” here againstands for “after” while “b”stands for “before”
Specific rangeon curve
PbPa
QbQa
Arc elasticity
Own price elasticity
of demand
Own price elasticity
of demand
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Interpreting the Own Price Elasticity of Demand
If elasticity coefficient is:
Demand is said to be:
% in quantity is:
Greater than 1.0 ElasticGreater than % in price
Equal to 1.0 Unitary elasticSame as %
in price
Less than 1.0 InelasticLess than %
in price
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Demand Curves Come in a Variety of Shapes
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Demand Curves Come in a Variety of Shapes
Perfectly inelastic
Perfectly elastic
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Demand Curves Come in a Variety of Shapes
Inelastic
Elastic
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Demand Curves Come in a Variety of Shapes
Inelastic where %Q < % P
Elastic where %Q > % P
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Unitary Elastic where %Q = % P
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Example of arc own-price elasticity of demand
Unitary elasticity…a one for one exchange
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Inelastic demand
Elastic demand
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Pb
Pa
Qb Qa
Price
Quantity
Elastic Demand Curve
0
Cut in price Brings about a larger
increase in the quantity demanded
c
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Pb
Pa
Qb Qa
Price
Quantity
What happened toproducer revenue?
What happened to consumer surplus?
0
c
Elastic Demand Curve
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Pb
Pa
Qb Qa
Price
Quantity
Producer revenueincreases since %Pis less that %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
a
b
0
c
Elastic Demand Curve
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Pb
Pa
Qb Qa
Price
Quantity
Producer revenueincreases since %Pis less that %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
a
b
0
c
Elastic Demand Curve
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Pb
Pa
Qb Qa
Price
Quantity
Producer revenueincreases since %Pis less that %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
a
b
0
c
Elastic Demand Curve
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Revenue ImplicationsOwn-price elasticity is:
Cutting the price will:
Increasing the price will:
Elastic Increase revenue Decrease revenue
Unitary elastic Not change revenue
Not change revenue
Inelastic Decrease revenue Increase revenue
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Pb
Pa
Qb Qa
Price
Quantity
Consumer surplusbefore the price cutwas area Pbca.
a
b
0
c
Elastic Demand Curve
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Pb
Pa
Qb Qa
Price
Quantity
Consumer surplusafter the price cut isArea Pacb.
a
b
0
c
Elastic Demand Curve
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Pb
Pa
Qb Qa
Price
Quantity
So the gain inconsumer surplusafter the price cut isarea PaPbab.
a
b
0
c
Elastic Demand Curve
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Pb
Pa
Qb Qa
Price
Quantity
Cut in price
Brings about a smallerincrease in the quantitydemanded
Elastic Demand Curve
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Pb
Pa
Qb Qa
Price
Quantity
What happened toproducer revenue?
What happened to consumer surplus?
Elastic Demand Curve
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Pb
Pa
Qb Qa
Price
Quantity
Producer revenuefalls since %P isgreater than %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
a
b
0
Elastic Demand Curve
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Pb
Pa
Qb Qa
Price
Quantity
Producer revenuefalls since %P isgreater than %Q.
Revenue before thechange was 0PbaQb.Revenue after thechange was 0PabQa.
a
b
0
Elastic Demand Curve
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Pb
Pa
Qb Qa
Price
Quantity
Consumer surplusincreased by areaPaPbab
a
b
0
Elastic Demand Curve
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Revenue ImplicationsOwn-price elasticity is:
Cutting the price will:
Increasing the price will:
Elastic Increase revenue
Decrease revenue
Unitary elastic Not change revenue
Not change revenue
Inelastic Decrease revenue
Increase revenue
Characteristic of agriculture Page 81
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Retail Own Price Elasticities
• Beef = -.6166• Cheese = -.3319• Bananas = -.4002• Milk = -.2588• Carrots = -.0388
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InterpretationLet’s take rice as an example, which has an own price elasticity of - 0.1467. This suggests that if the price of rice drops by 10%, for example, the quantity of rice demanded will only increase by 1.467%.
P
Q
10% drop
1.467% increase
Rice producerRevenue?
Consumer surplus?
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Example1. The Dixie Chicken sells 1,500 Burger platters per
month at $3.50 each. The own price elasticity for this platter is estimated to be –1.30. If the Chicken increases the price of the platter by 70 cents:
a. How many platters will the chicken sell?__________
b. The Chicken’s revenue will change by $__________
c. Consumers will be ____________ off as a result of this price change.
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The answer…1. The Dixie Chicken sells 1,500 Burger platters per month at
$3.50 each. The own price elasticity for this platter is estimated to be –1.30. If the Chicken increases the price of the platter by 70 cents:
a. How many platters will the chicken sell?__1,110____
Solution:-1.30 = %Q%P-1.30= %Q[20%]%Q=(-1.30 × 20) = –26%So the new quantity of burger platters is 1,110, or (1-.26) ×1,500, or .74 ×1,500
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The answer…1. The Dixie Chicken sells 1,500 Burger platters per
month at $3.50 each. The own price elasticity for this platter is estimated to be –1.30. If the Chicken increases the price of the platter by 70 cents:
a. How many platters will the chicken sell?__1,110____
b. The Chicken’s revenue will change by $__-$588___Solution:Current revenue = 1,500 × $3.50 = $5,250 per monthNew revenue = 1,110 × $4.20 = $4,662 per monthSo revenue decreases by $588 per month, or $4,662minus $5,250
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The answer…1. The Dixie Chicken sells 1,500 Burger platters per
month at $3.50 each. The own price elasticity for this platter is estimated to be –1.30. If the Chicken increases the price of the platter by 70 cents:
a. How many platters will the chicken sell?__1,110____
b. The Chicken’s revenue will change by $__-$588___
c. Consumers will be __worse___ off as a result of this price change.
Why? Because price increased.
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Income Elasticity
of Demand
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Income Elasticity of DemandIncome
elasticity of demand
Percentage change in quantity
Percentage change in income=
where:
I = (Ia + Ib) 2 Q = (Qa + Qb) 2 Q = (Qa – Qb) I = (Ia – Ib)
= [QI] x [IQ]
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Indicates potential changes or shifts in the demand curve asconsumer income (I)changes….
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Interpreting the Income Elasticity of Demand
If the income elasticity is equal to:
The good is classified as:
Greater than 1.0 A luxury and a normal good
Less than 1.0 but greater than 0.0
A necessity and a normal good
Less than 0.0 An inferior good!
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Some Examples
CommodityOwn Price elasticity
Income elasticity
Beef and veal -0.6166 0.4549Chicken -0.5308 .3645Cheese -0.3319 0.5927Rice -0.1467 -0.3664Lettuce -0.1371 0.2344Tomatoes -0.5584 0.4619Fruit juice -0.5612 1.1254Grapes -1.3780 0.4407Nonfood items -0.9875 1.1773
ElasticPage 99
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Some ExamplesCommodity
Own Price elasticity
Income elasticity
Beef -0.6166 0.4549Chicken -0.5308 .3645Cheese -0.3319 0.5927Rice -0.1467 -0.3664Lettuce -0.1371 0.2344Tomatoes -0.5584 0.4619Fruit juice -0.5612 1.1254Grapes -1.3780 0.4407Nonfood items -0.9875 1.1773
Inferior goodElastic
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Some ExamplesCommodity
Own Price elasticity
Income elasticity
Beef -0.6166 0.4549Chicken -0.5308 .3645Cheese -0.3319 0.5927Rice -0.1467 -0.3664Lettuce -0.1371 0.2344Tomatoes -0.5584 0.4619Fruit juice -0.5612 1.1254Grapes -1.3780 0.4407Nonfood items -0.9875 1.1773
Inferior good Luxury goodElastic
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ExampleAssume the government cuts taxes, thereby increasing disposable income by 5%. The income elasticity for chicken is .3645.
a. What impact would this tax cut have upon the demand for chicken?
b. Is chicken a normal good or an inferior good? Why?
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The Answer1. Assume the government cuts taxes, thereby increasing
disposable income (I) by 5%. The income elasticity for chicken is .3645.
a. What impact would this tax cut have upon the demand for chicken?Solution:.3645 = %QChicken % I.3654 = %QChicken 5 %QChicken = .3645 5 = + 1.8225%
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The Answer1. Assume the government cuts taxes, thereby
increasing disposable income by 5%. The income elasticity for chicken is .3645.
a. What impact would this tax cut have upon the demand for chicken? _____+ 1.8225%___
b. Is chicken a normal good or an inferior good? Why?
Chicken is a normal good but not a luxury since the income elasticity is > 0 but < 1.0
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Cross Price Elasticity
of Demand
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Cross Price Elasticity of DemandCross Price elasticity of
demand
Percentage change in quantity
Percentage change in another price=
where:
PT = (PTa + PTb) 2
QH = (QHa + QHb) 2
QH = (QHa – QHb)PT = (PTa – PTb)
= [QHPT] × [PTQH]
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Indicates potential changes or shifts in the demand curve asthe price of othergoods change…
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Interpreting the Cross Price Elasticity of Demand
If the cross price elasticity is equal to:
The good is classified as:
Positive Substitutes
Negative Complements
Zero Independent
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Some ExamplesItem Prego Ragu Hunt’s
Prego -2.5502 .8103 .3918
Ragu .5100 -2.0610 .1381
Hunt’s 1.0293 .5349 -2.7541
Values in red alongthe diagonal are ownprice elasticities…
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Some ExamplesItem Prego Ragu Hunt’s
Prego -2.5502 .8103 .3918
Ragu .5100 -2.0610 .1381
Hunt’s 1.0293 .5349 -2.7541
Values off the diagonal are all positive, indicating these products are substitutes as prices change…
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Some ExamplesItem Prego Ragu Hunt’s
Prego -2.5502 .8103 .3918
Ragu .5100 -2.0610 .1381
Hunt’s 1.0293 .5349 -2.7541
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An increase in the price ofRagu Spaghetti Sauce has a bigger impact on Hunt’sSpaghetti Sauce than viceversa.
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Some ExamplesItem Prego Ragu Hunt’s
Prego -2.5502 .8103 .3918
Ragu .5100 -2.0610 .1381
Hunt’s 1.0293 .5349 -2.7541
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A 10% increase in the price ofRagu Spaghetti Sauce increasesthe demand for Hunt’s Spaghetti Sauce by 5.349%…..
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Some ExamplesItem Prego Ragu Hunt’s
Prego -2.5502 .8103 .3918
Ragu .5100 -2.0610 .1381
Hunt’s 1.0293 .5349 -2.7541
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But…a 10% increase in the price ofHunt’s Spaghetti Sauce increasesthe demand for Ragu Spaghetti Sauce by only 1.381%…..
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Example1. The cross-price elasticity for hamburger demand
with respect to the price of hamburger buns is equal to –0.60.
a. If the price of hamburger buns rises by 5 percent,
what impact will that have on hamburger consumption?
b. What is the demand relationship between these products?
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The Answer1. The cross-price elasticity for hamburger demand
with respect to the price of hamburger buns is equal to –0.60.
a. If the price of hamburger buns rises by 5%, what
impact will that have on hamburger consumption? ____ - 3% ______
Solution:-.60 = %QH %PHB
-.60 = %QH 3 %QH = 3 (-.60) = – 3%
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The Answer1. The cross-price elasticity for hamburger demand
with respect to the price of hamburger buns is equal to –0.60.
a. If the price of hamburger buns rises by 5%, what
impact will that have on hamburger consumption? ___ - 3% _____
b. What is the demand relationship between these products?
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The Answer1. The cross-price elasticity for hamburger demand
with respect to the price of hamburger buns is equal to –0.60.
a. If the price of hamburger buns rises by 5%, what
impact will that have on hamburger consumption? ___ - 3% _____
b. What is the demand relationship between these products?
These two products are complements as evidenced by the negative sign on this cross-price elasticity.
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Another Example
2. Assume that a retailer sells 1,000 six-packs of Pepsi per day at a price of $3.00 per six-pack. Also assume the cross-price elasticity for Pepsi with respect to the price of Coca Cola is 0.70.
a. If the price of Coca Cola rises by 5 percent, what
impact will that have on Pepsi consumption?
b. What is the demand relationship between these products?
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The Answer2. Assume that a retailer sells 1,000 six-packs of
Pepsi per day at a price of $3.00 per six-pack. Also assume the cross-price elasticity for Pepsi with respect to the price of Coca Cola is 0.70.
a. If the price of Coca Cola rises by 5 percent, what
impact will that have on Pepsi consumption?
Solution:.70 = %QPepsi %PCoke
.70 = %QPepsi 5 %QPepsi=5*.7=3.5%New quantity sold = 1,000 1.035 = 1,035New value of sales = 1,035 $3.00 = $3,105
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The Answer2. Assume that a retailer sells 1,000 six-packs of
Pepsi per day at a price of $3.00 per six-pack. Also assume the cross-price elasticity for Pepsi with respect to the price of Coca Cola is 0.70.
a. If the price of Coca Cola rises by 5 percent, what
impact will that have on Pepsi consumption? __35 six-packs or $105 per day__
b. What is the demand relationship between these products?
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The Answer2. Assume that a retailer sells 1,000 six-packs of
Pepsi per day at a price of $3.00 per six-pack. Also assume the cross-price elasticity for Pepsi with respect to the price of Coca Cola is 0.70.
a. If the price of Coca Cola rises by 5 percent, what
impact will that have on Pepsi consumption? __35 six-packs or $105 per day__
b. What is the demand relationship between these products?
The products are substitutes as evidenced by the positive sign on this cross-price elasticity!
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Price Flexibilityof Demand
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Price Flexibility
We earlier said that the price flexibility is the reciprocal of the own-price elasticity. If the calculated elasticty is - 0.25, then the flexibility would be - 4.0.
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Price FlexibilityWe earlier said that the price flexibility is the reciprocal of the own-price elasticity. If the calculated elasticty is - 0.25, then the flexibility would be - 4.0.
This is a useful concept to producers when forming expectations for the current year. If the USDA projects an additional 2% of supply will likely come on the market, then producers know the price will likely drop by 8%, or:
%Price = - 4.0 x %Quantity = - 4.0 x (+2%) = - 8%
If supply increases by 2%, price would fall by 8%!
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We earlier said that the price flexibility is the reciprocal of the own-price elasticity. If the calculated elasticty is - 0.25, then the flexibility would be - 4.0.
This is a useful concept to producers when forming expectations for the current year. If the USDA projects an additional 2% of supply will likely come on the market, then producers know the price will likely drop by 8%, or:
%Price = - 4.0 x %Quantity = - 4.0 x (+2%) = - 8%
If supply increases by 2%, price would fall by 8%!
Note: make sure you use the negative sign for both the elasticity and the flexibility.
Price Flexibility
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Revenue ImplicationsOwn-price elasticity is:
Increase in supply will:
Decrease in supply will:
Elastic Increase revenue
Decrease revenue
Unitary elastic Not change revenue
Not change revenue
Inelastic Decrease revenue
Increase revenue
Characteristic of agriculture Page 81
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Short run effects Long run effects
Over time, consumers respond ingreater numbers. This is referredto as a recognition lag…
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Changing Price Response Over Time
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Pb
Pa
Qb Qa
Price
Quantity
Ag’s Inelastic Demand Curve
A small increase in supplywill cause the price of Agproducts to fall sharply.
This situation explains why majorprogram crops receivesubsidies from the federalgovernment.
a
b
0
Increase insupply
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Pb
Pa
Qb Qa
Price
Quantity
Inelastic Demand Curve
While subsidies increase thecosts of governmentprograms and hencebudget deficits, rememberconsumers benefit fromcheaper food costs.
a
b
0
Pb
Pa
Qb Qa
Price
a
b
0
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In Summary…Know how to interpret all three
elasticities
Know how to interpret a price flexibility
Understand revenue implications for producers if prices are cut (raised)
Understand the welfare implications for consumers if prices are cut (raised)
Know what causes movement along versus shifts the demand curve
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Chapter 6 starts a series of chapters that culminates in a market supply curve for food and fiber products….