ECONOMICS
poorva
cm06_elasticity-tax-crossprices.pptxMicroeconomics
SUMMER SESSION
July 1, 2019
Summary (our story thus far)
June 19 – syllabus, introduction, and economic concepts
June 20 – supply, demand, market equilibrium
June 24 - shortage, surplus, market analysis
June 25 – price controls, CS & PS, math of markets
June 26 – demand elasticity, and along straight line demand curve
Outline for today
Other types of elasticity
Cross-price elasticity of demand
Substitutes and complements
Income elasticity
Elasticity matrix
Supply elasticity
Who pays the tax?
Demand elasticity, supply elasticity, and tax burden
Some math
Microeconomics
CROSS PRICE ELASTICITY, INCOME ELASTICITY, AND SUPPLY ELASTICITY
Cross Price Elasticity
Recall: Demand & Prices of Related Goods
Substitutes
Two goods that satisfy similar needs or desires. If two goods are substitutes, then demand for one rises as the price of the other rises (or the demand for one falls as the price of the other falls).
Complements
Two goods that are used jointly in consumption. If two goods are complements, then demand for one rises as the price of the other falls (or the demand for one falls as the price of the other rises).
Substitutes and complements
A good is considered a substitute if, when the price of good X increases, the quantity demanded of good Y increases. (direct/positive relationship)
↑PX ↑QY
Coke and Pepsi; beef and chicken; butter and margarine; tea and coffee
A good is considered a complement if, when the price of good X increases, the quantity demanded of good Y decreases. (inverse/negative relationship)
↑PX ↓QY
Strawberries and cream; bananas and pudding mix; printer and ink cartridges
Apples and Peaches Substitutes or Complements?
Apples and Peaches
Apples and Peaches are Substitutes
Cross Price Elasticity of Substitutes
Apples and Peaches are Substitutes
↑PAPPLES ↑QPEACHES
Cross Price Elasticity of Substitutes
Apples and Peaches are Substitutes
↑PAPPLES ↑QPEACHES
Midpoint Method:
Let i = Apples
Let j = Peaches
Substitutes: Elastic and Inelastic
Elastic Substitutes
↑Pi ↑Qj
εij > 0
| εij | > 1
Inelastic Substitutes
↑Pi ↑Qj
εij > 0
| εij | < 1
Apples and Peaches: Inelastic Substitutes
Suppose that when the price of apples increases 10%, the quantity demanded of peaches increases 5.46%.
Substitutes and complements
A good is considered a substitute if, when the price of good X increases, the quantity demanded of good Y increases. (direct/positive relationship)
↑PX ↑QY
Coke and Pepsi; beef and chicken; butter and margarine; tea and coffee
A good is considered a complement if, when the price of good X increases, the quantity demanded of good Y decreases. (inverse/negative relationship)
↑PX ↓QY
Strawberries and cream; bananas and pudding mix; printer and ink cartridges; apples and strawberries
Apples and Strawberries
Cross Price Elasticity of Complements
Apples and Strawberries are Complements
↑PAPPLES ↓QSTRAWBERRIES
Apples & Strawberries: Elastic Complements
Suppose that when the price of apples increases 10%, the quantity demanded of strawberries decreases 12.5%.
Complements: Elastic and Inelastic
Elastic Complements
↑Pi ↓Qj
εij < 0
| εij | > 1
Inelastic Complements
↑Pi ↓Qj
εij < 0
| εij | < 1
Summary of Cross Price Elasticities
Substitutes
Complements
Empirical Evidence
Research shows that…
Apples and peaches: substitutes
Apples and strawberries: complements
Peaches and strawberries: substitutes
Elasticities are not symmetric
Cross-Price Elasticity Matrix
| Pi \ Qj | APPLE | PEACH | STRAWBERRY |
| APPLE | -0.450 | +0.546 | -1.253 |
| PEACH | +0.157 | -0.952 | +0.433 |
| STRAWBERRY | -0.206 | +0.249 | -0.449 |
From: Henneberry et al. (1999) Consumer Safety Concerns and Fresh Produce Consumption. Table 5 Hicksian Demand Elasticities. J Ag Res 24:98.
URL: http://ageconsearch.umn.edu/bitstream/30865/1/24010098.pdf
Income Elasticity
Recall: Demand & Income
Normal Good: increased income increased demand
Normal Good: decreased income decreased demand
Inferior Good: increased income decreased demand
Inferior Good: decreased income increased demand
INCOME elasticity
Income elasticity of demand
Measures the responsiveness of the quantity demanded for one good, when the income of buyers changes
Income Elasticity Exercise (1 of 3)
When median household income in Allentown rose from $3,300 to $3,900 per month, economists found that the quantity demanded of beef filet mignon rose from 6 pounds per month to 12 pounds per month. Based on this information, the calculated income elasticity is ----- which suggests that for consumers in Allentown beef is -----.
a. 0.50; a luxury
b. -0.18; an inferior good
c. +0.25; a necessity use the midpoint method
d. +4.0; a luxury
Income Elasticity Exercise (2 of 3)
When median household income in Allentown rose from $3,300 to $3,900 per month, economists found that the quantity demanded of beef filet mignon rose from 6 pounds per month to 12 pounds per month. Based on this information, the calculated income elasticity is ----- which suggests that for consumers in Allentown beef is -----.
a. 0.50; a luxury
b. -0.18; an inferior good
c. +0.25; a necessity
d. +4.0; a luxury
Income Elasticity Exercise (3 of 3)
In Allentown, filet mignon is a luxury!
Supply Elasticity
Elasticity of Supply
ELASTIC SUPPLY (ε > 1)
The percentage change in the quantity supplied is greater than the percentage change in the price.
PERFECTLY ELASTIC (ε = ∞)
Horizontal supply curve
INELASTIC SUPPLY (ε < 1)
The percentage change in the quantity supplied is less than the percentage change in the price.
UNIT ELASTIC SUPPLY (ε = 1)
PERFECTLY INELASTIC (ε = 0)
Vertical supply curve
Which supply curve appears more elastic?
Which supply curve appears more elastic?
RELATIVELY FLATTER RELATIVELY MORE ELASTIC
ELASTIC SUPPLY
Changes in demand can be met without large price changes.
Spare production capacity – such as during recessions
High stocks of raw materials and high inventories of finished products.
Easy factor substitution – inputs are easily configured for production of related goods (printing press: magazines vs books)
Time – long run supply is more elastic than short run supply (e.g., housing market)
INELASTIC SUPPLY
Changes in demand lead to large price changes
Production at or near capacity so unable to easily increase output
Scarcity of raw materials; low inventories of finished goods
Factor substitution inhibited - inputs not as mobile
Short run supply is less elastic when compared to the long run
Summary
Own Price Elasticity
Cross Price Elasticity
Substitute
Elastic substitute
Inelastic substitute
Complement
Elastic complement
Inelastic complement
Income Elasticity
Inferior good
Normal good
Necessity
Luxury
Supply Elasticity
More Examples and Exercises
Substitutes
Recall: if the price of a substitute good increases, then demand for a related good increases because buyers substitute one for the other, ceteris paribus.
India Pale Ale vs. India Rye Lager
Suppose the price of Imperial Pale Ale increases from $6/pint to $7/pint.
The quantity demanded falls from 4 pints to 3 pints. (this is the Law of Demand)
Substitute goods
CROSS PRICE ELASTICITY
where i is the good for which the price changed, and j is the substitute good
SIGN MATTERS!
CROSS PRICE ELASTICITY
IPA price increases
IRL demand increases
Qd of IRL at every price increases
εij = 4.3 > 0
SUBSTITUTE
ELASTIC
complements
Recall: if the price of a good increases, then demand for a complementary good falls
India Pale Ale vs. French Fries
Suppose the price of Imperial Pale Ale increases from $6/pint to $7/pint.
The quantity demanded falls from 4 pints to 3 pints (Law of Demand)
COMPLEMENT goods
CROSS PRICE ELASTICITY
where i is the good for which the price changed, and j is the substitute good
CROSS PRICE ELASTICITY
IPA price increases
FF demand decreases
Qd of FF at every price decreases
Complementary Good
Cross-price inelastic
Your turn
The price of good X increased from $12/unit to $18/unit.
The quantity demanded of good Y increased from 22 units to 24 units.
Using the midpoint method, calculate the cross price elasticity, and state whether the two goods are substitutes or complements, and whether the cross price elasticity is elastic, or inelastic.
The two goods are SUBSTITUTES and the cross price elasticity is INELASTIC
Exercise 2
The price of good X fell from $100/unit to $50/unit.
The quantity demanded of good Y increased from 20 units to 60 units.
Using the midpoint method, calculate the cross price elasticity, and state whether the two goods are substitutes or complements, and whether the cross price elasticity is elastic, or inelastic.
The two goods are COMPLEMENTS and the cross price elasticity is ELASTIC
Elasticity Matrix with Statistics
Who pays the tax?
Initially a market is in equilibrium, then the government imposes a tax on sales of this good. What effect will this have on the market’s equilibrium price and quantity?
Initially a market is in equilibrium, then the government imposes a tax on sales of this good. What effect will this have on the market’s equilibrium price and quantity?
Does this change affect demand or supply?
Initially a market is in equilibrium, then the government imposes a tax on sales of this good.
Supply Decreases:
shifts supply curve leftward
higher equilibrium price
lower equilibrium quantity
Initially a market is in equilibrium, then the government imposes a tax on sales of this good.
Supply falls
Price rises
Quantity falls
But who pays the tax?
A tax is represented as a left shift of the supply curve.
The tax is equal to the vertical difference from the original supply curve to the new supply curve.
The tax is equal to the vertical difference from the original supply curve to the new supply curve.
Buyers pay the new equilibrium price,
yet…. P2-P1 < TAX
So the buyers are not paying the full tax
Numerical Example
In equilibrium
P* = 170 Q* = 4
Now suppose a tax of $100 per unit…
Suppose the government imposes a $100 tax per unit sold.
New equilibrium price
$190
New equilibrium quantity
2 units
Before the tax
P* = 170 Q* = 4
After the tax
P* = 190 Q* = 2
But who paid the tax?
Before the tax
P* = 170 Q* = 4
After the tax
P* = 190 Q* = 2
Sellers apply the entire tax to the good, and pass the tax along to the buyer:
New price sellers would like to receive is $170 + $100 = $270/unit.
But the tax shifts the supply curve back so that the equilibrium price is higher $190…this does not cover the full tax!
Buyers pay (190-170) = $20 of the tax.
Sellers receive $190, and transfer $100 to the government ($20 of which came from buyers), which means that:
Sellers pay the remainder = $80 of the tax
Supply decreases such that the vertical distance equals the tax.
Buyers pay a tax that is equal to the difference in the old and new equilibrium prices.
Sellers pay the remainder.
Extreme conditions
What is required for buyers to pay the full tax?
What is required for sellers to pay the full tax?
Buyers PAY THE FULL TAX
Buyers PAY THE FULL TAX
SELLERS PAY THE FULL TAX
SELLERS PAY THE FULL TAX
Summary
A tax shifts supply leftward
The shift is such that the vertical distance from the old supply curve to the new supply curve is equal to the per unit tax
The equilibrium price rises (except in special cases)
The tax may be paid by buyers, the sellers, or both.
The Math of Taxes
Demand:
P = 12 – 2QD
Supply:
P = 4 + ½QS
Tax:
$2 per unit
The Math of Taxes
Demand:
P = 12 – 2QD
Supply:
P = 4 + ½QS
Tax:
$2 per unit
The Math of Taxes
Demand:
P = 12 – 2QD
Supply:
P = 4 + ½QS
P* = 5.6, Q* = 3.2
Supply with $2 Tax:
(tax = intercept shift)
P = 4+2 + ½ QS
The Math of Taxes
Demand:
P = 12 – 2QD
Supply:
P = 4 + ½QS
P* = 5.6, Q* = 3.2
Supply with $2 Tax:
P = 6 + ½ QS
P* = 7.2, Q* = 2.4
The Math of Taxes
Demand:
P = 12 – 2QD
Supply:
P = 4 + ½QS
P* = 5.6, Q* = 3.2
Supply with $2 Tax:
P = 6 + ½ QS
P* = 7.2, Q* = 2.4
Ideally, the sellers would like the buyers to pay the full tax at $2 per unit.
That is, $5.60 + $2.00 = $7.60
Yet buyers paid $7.20
So sellers pay $0.40 (7.60-7.20)
Total Revenue = $7.20 x 2.4
= $17.28
Tax Revenue
$2 x 2.4 = $4.80
Net Revenue = $12.48
Summary
Other types of elasticity
Cross-price elasticity of demand
Substitutes and complements
Income elasticity
Elasticity matrix
Supply elasticity
Who pays the tax?
Demand elasticity
Supply elasticity
