Recall – to obtained the demand curve we varied price, calculated new consumer equilibriums, and then plotted the price and quantity points
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Can we decompose the changes?
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5 6 7 8 Land Units
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Income and Substitution Effects • Consumer equilibrium
M RS
M Uland P land M Ubundle Pbundle
M Uland M Ubundle Pland Pbundle
• Substitution effect – is the change in quantity attributed solely to the change in relative prices Px/Py • Income effect – the change in quantity solely attributed to the effective change in income
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Original equilibrium New budget constraint – leads to a new equilibrium Decompose the total change into income and substitution effects
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Bundle of goods 3 4 5 6 7 8 9 10 11
Land Price Decreases
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5 6 7 8 Land Units
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Income and Substitution Effects Bundle of goods 3 4 5 6 7 8 9 10 11
Draw a budget constraint that is parallel to the new budget constraint but is tangent to the old indifference curve.
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Income that is needed to add / subtract to keep utility constant.
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5 6 7 8 Land Units
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Income and Substitution Effects Bundle of goods 3 4 5 6 7 8 9 10 11
Substitution – movement from original to new point on the same indifference curve, A to B – note red to green budget line a change in relative prices. C A
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B
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Income – movement from old indifference curve and new point to new consumer equilibrium, B to C – note green to black budget line no change in relative prices but change in budget. 9 10
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Income and Substitution Effects Bundle of goods 3 4 5 6 7 8 9 10 11
Bundle substitution ~ 2.5 – 5 = -2.5 loss income ~ 5.5 – 2.5 = +3 gain
C
Land substitution ~ 4 - 2 = 2 gain income ~5.5 – 4 = 1.5 gain
A
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B
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5 6 7 8 Land Units
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Income and Substitution Effects • Substitution effect is always positive for a good whose price has decreased and negative for a good whose price has increased. • Substitution effect will always increase the consumption of the good that is relatively lower priced and decrease the consumption of the relatively higher priced good. • Income effect can be negative or positive.
Substitution Income Effects • •
•
Use points (bundle, land) A (6, 2), B(8, 3.5), and C(5, 5.5) Bundle – Substitution = 8 – 5 = +3 – Income = 6 – 8 = -2 – Total = =+3 + -2 = 1 Land – Substitution = 3.5 – 5.5 = -2 – Income = 2 – 3.5 = -1.5 – Total = -3.5 Important to know why? And how calculated? How to draw the imaginary budget line and what does it do? How much income does it take to keep the same level of utility? Substitution effect is price ratios, how is it represented? See this or other you tube videos https://www.youtube.com/watch?v=E589Nu0fle4
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What Are Elasticities? • Measure of the relationship between two variables Percentage change in y Elasticity =
Percentage change in x
• Elastic vs. inelastic • Arc vs. point
Elasticities of Demand • Own-price elasticity of demand – responsiveness of changes in quantity associated with a change in the goods own price
• Income elasticity of demand – responsiveness of changes in quantity associated with a change in income
• Cross-price elasticity of demand – responsiveness of changes in quantity associated with a change in price of another good
Own-Price Elasticity of Demand Own-price Elasticity =
Percentage change in quantity Percentage change in own price
Own-price elasticity =
=
ΔQ ΔQ P Q = • ΔP ΔP Q P
(QA- QB)/[(QA+ QB)/2] (PA- PB)/[(PA+ PB)/2]
• Interpretation -- 1% increase in price leads to a x% change in quantity purchased over this arc
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Own-Price Elasticity • • • •
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A
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B
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Price
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Consumer bundle B to A Change in quantity 2 to 1 Change in price 9 to 10 What is the own-price elasticity of demand at this arc?
5 4 3 2 1 0 0
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Quantity
Math Details • Recall change in quantity = 2 to 1 and price 9 to 10
% change in quantity (1- 2)/[(1+ 2)/2] - 0.667 = = = -6.33 % change in own price (10 - 9) /[(10 + 9) / 2] 0.105 • or
ΔQ P (1- 2) (10 + 9) / 2 -1 9.5 • = • = • = -6.33 ΔP Q (10 - 9) (1+ 2) / 2 1 1.5 • Interpretation -- 1% increase in price leads to a 6.33% decrease in quantity purchased over this arc
Own-Price Elasticity • Bundles C to D % change in quantity (5 - 6)/[5 + 6)/2] = % change in own price (6 - 5) /[(6 + 5) / 2] - 0.18 = = -1.00 0.18 D Unitary Elasticity -- 1% C increase in price leads to a 1% decrease in quantity purchased over this arc
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Price
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Quantity
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Own-Price Elasticity Interpretation -- 1% increase in price leads to a 0.29% decrease in quantity purchased
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• Bundles E to F % change in quantity % change in price (8 - 9)/[8 9)/2] (3 - 2) /[(3 2) / 2] - 0.117 -0.294 0.40
Price
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F
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E
3 2 1 0 0
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Quantity
Own-Price Elasticity Cont. • Generally elasticities vary over the curve • Negative – law of demand • Linear demand curve - specific
ΔQ P • ΔP Q
Price
Elastic where %Q > % P
Unitary Elastic where %Q = % P Inelastic where %Q < % P
Quantity
Own-Price Elasticity
If value of the elasticity coefficient is Less than -1.0
Demand is said to be
% in quantity is
Elastic
Greater than % in price
Equal to -1.0
Unitary elastic Inelastic
Same as % in price
Greater than -1.0
Less than % in price
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Revenue Implications - Know Own-price elasticity is
Cutting the price will
Increasing the price will
Elastic
Increase revenue
Decrease revenue
Unitary elastic
No change in No change in revenue revenue
Inelastic
Decrease revenue
Increase revenue
Revenue Implications – Why? Unit Elasticity Demand Curve
Brings about the same increase in the quantity demanded – definition of unit elasticity
Price Revenue = price x quantity = consumer expenditures Before change = area PbCQb0
Cut in price
Pb Pa
C D E
After Revenue = area PaDQa0
O
Qb Qa
Quantity
Revenue Implications – Why? Unit Elasticity Demand Curve
Loss in revenue due to price change = Gain in revenue due to quantity change
Price
What about a price increase?
Pb Pa
O
C D E
Qb Qa
Quantity
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Revenue Implications – Why? Inelastic Demand Curve Price Revenue = price x quantity = consumer expenditures Before change = area PbCQb0
Brings about a smaller increase in the quantity demanded – definition of inelastic
Producer revenue falls since %P is greater than %Q.
C
Pb Pa O
E
Revenue before the change was 0PbCQb. Revenue after the change was 0PaDQa.
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Qb Qa
Quantity
Revenue Implications – Why? Inelastic Demand Curve Price Producer revenue falls since the loss is greater than the gain C
Pb Pa O
D E
Qb Qa
Quantity
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Revenue Implications Price
Cut in price
Elastic Demand Curve
Pb Brings about a larger increase in the quantity demanded
Pa
0
Qb
Qa
Quantity
Revenue Implications Price
Elastic Demand Curve C
Pb Pa
D
Producer revenue increases since %P is less that %Q.
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Revenue before the change was 0PbCQb. Revenue after the change was 0PaDQa. 0
Qb
Qa
Quantity
Revenue Implications Price
C
Pb Pa
Producer revenue increases since the gain is Greater than the loss D
E
Elastic Demand Curve 0
Qb
Qa
Quantity
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Question Two bands, the Girl Getters and the Toe Biters, are on tour. They both decide to raise their ticket prices. After one show with higher prices, the Girl Getters discover that their revenue has decreased. The Toe Biters discover that their revenue has increased. Which band is more popular in terms of elasticity? Why? A) Girl Getters B) Toe Biters
Question Two bands, the Girl Getters and the Toe Biters, are on tour. They both decide to raise their ticket prices. After one show with higher prices, the Girl Getters discover that their revenue has decreased. The Toe Biters discover that their revenue has increased. Which band is more popular in terms of elasticity? Why? A) Girl Getters B) Toe Biters
The Toe Biters are the more popular band. The demand curve for their tickets is more inelastic. As they increased their price, their revenue increased. This means that most of their fans continued to purchase their tickets at the higher price. The Girl Getters' revenue decreased, so more people decided not to purchase their tickets at the higher price. This means that the demand curve for their tickets is more elastic.
Relative Elasticities
Price
Perfectly inelastic
Perfectly elastic
Quantity
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Relative Elasticities
Price
Relatively more inelastic
Relatively more elastic Quantity
Long vs. Short-Run •
Demand curves tend to be more elastic (flatter) over time as consumers adjust to changing prices – Why?
Income Elasticity of Demand Income Elasticity of = Demand Income elasticity
=
Percentage change in quantity Percentage change in income =
ΔQ ΔQ I Q = • ΔI ΔI Q I
(QA- QB)/[(QA+ QB)/2] (IA- IB)/[(IA+ IB)/2]
• Interpretation -- 1% increase in income leads to a x% change in quantity purchased over this arc
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Income Elasticity Example • Income and Land – Income change 200 to 400 – Land quantity changes 5 to 9
• What is arc income elasticity of demand?
% change in quantity % change in income (9 - 5)/[9 + 5)/2] = (400 - 200) /[(400 + 200) / 2] 0.66 = = 0.85 0.57
Interpretation?
Interpreting the Income Elasticity of Demand - Know If the income elasticity is
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!
Cross-Price Elasticity of Demand Cross-price Elasticity of = Demand
Percentage change in quantity of good C Percentage change in price D
Cross -price elasticity = ΔQ C ΔQ C PD QC = ΔP = ΔP • Q D D C PD
• Interpretation -- 1% increase in price of good D leads to a x% change in quantity purchased of good C over this arc
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Cross-Price Elasticity Example • Steak quantity and corn price – Corn price change from $20 to $15 / dozen – Steak quantity changes from 2.5 to 2.75 pounds
• What is arc cross-price elasticity of demand for steak? Interpretation? % change in quantity steak = % change in corn price (2.75 - 2.5)/[(2.75 + 2.5)/2] 0.1 = = -0.33 (15 - 20) /[(15 + 20) / 2] - 0.28
Interpreting the Cross Price Elasticity of Demand - Know If the cross price elasticity is
The goods are classified as
Positive
Substitutes
Negative
Complements
Zero
Independent
Stimulus Bill Example • 2009 Stimulus Bill – Included a up to a $1500 tax credit for insulation and energy efficient windows, doors, HVAC units
• What is a tax credit? • Why pass the bill and potential economic effects? - nonpolitical
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Stimulus Bill Insulation •
Assume you have calculated the following elasticities for insulation – – – – –
•
Income elasticity of demand = 1.2 Own-price elasticity = -0.4 Cross price elasticity with lumber = -0.02 Cross price elasticity with energy = 0.09 30% tax bracket – 30% decrease in price caused by the tax credit
What is the effect of the stimulus bill given these elasticities? Recession has decreased incomes by 10%
Stimulus Bill Insulation •
Decrease in insulation sales – recession –
•
–
•
-30% x -0.4 = 12% - increase in insulation sales
Change in lumber sales – stimulus bill –
•
-10% x 1.2 = -12% - decrease in insulation sales
Increase in insulation sales – stimulus bill
-30% x -0.02 = 0.6% - increase in lumber sales
Change in energy use – stimulus bill –
-30% x 0.09 = -2.7% - decrease in energy use
Costs of the Bill • • • • • •
Decrease in tax revenues – insulation tax credit Increase in tax revenues – increase in insulation sales Increase in tax revenues – increase in lumber sales Decrease in tax revenues – decrease in energy use Environmental / other Overall ?
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Revenue Implications – Demand Elasticity and Changes in Supply Own-price elasticity is
Increase in supply will
Decrease in supply will
Elastic
Increase revenue
Decrease revenue
Unitary elastic
No change in No change in revenue revenue
Inelastic
Decrease revenue
Increase revenue
Own-Price Elasticity of Supply • Measures the relationship between change in quantity supplied and a change in price Own-price Elasticity = of Supply
Percentage change in quantity supplied Percentage change in own price
(Q SA - Q SB ) =
(PA - PB )
[(Q SA + Q SB ) / 2] [(PA + PB ) / 2]
Own-Price Elasticity of Supply • Positive – Why? If the elasticity is
Supply is
% in quantity is
Greater than 1.0
Elastic
Greater than % in price
Less than 1.0
Inelastic
Less as % in price
Equal to 1.0
Unitary
Equal to % in price
Equal to 0
Perfectly inelastic
Equal to positive infinity
Perfectly elastic
Zero Vertical supply curve % in price = zero Horizontal supply curve
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Own-Price Elasticity of Supply What is own- price elasticity between points A and B Change in quantity supplied 3 to 4.5 million bushels Change in price $1 to $1.5
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Price
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What is the own-price elasticity of supply for this arc?
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Quantity (millions of bushels)
Math Details • Recall change in quantity = 3 to 4.5 and price 1 to 1.5
% change in quantity % change in own price
( 4.5 - 3)/[(4.5 3)/2] 0.4 1.0 (1.5 - 1) /[(1.5 1) / 2] 0.4 • Interpretation -- 1% increase in price leads to a 1% increase in quantity supplied over this arc
Determinants • Availability of raw materials – Limited availability - less opportunities to respond
• Length and complexity of the production process – Less production time and complexity – more opportunities to respond
• Time to respond – Short vs. long run – long run more able to respond
• Excess capacity – Unused capacity can and will respond quicker
• Inventories – If have inventory can quickly increase supply to market
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Land / Urban Examples Study Gyourko and Voith 1966 - Home sales in PA Barr et al. 2010 – Agricultural Land
Price Demand = ~-1
Income Demand =~1.5
Supply U.S. 0.007 – 0.029 Brazil 0.382-0.895 Brazil pasture land included 0.008-0.245
Sirmans 1978 Inelastic demand for residential sites for all 52 different housing housing areas and for all three time periods markets in the US Pryce 1999 UK housing Elasticities of private house starts smaller in the boom (0.58) than in the slump (1.03) Considerable variation across districts Impact of land release on new house prices more stable over time, and marginally greater in the boom (0.75) than in the slump (0.71).
Use Example
Sources Gyourko and Voith 1966 https://www.lincolninst.edu/pubs/dl/68_GyourkoVoith99a.pdf Barr et al. 2010 http://ageconsearch.umn.edu/bitstream/58047/2/10-WP_505.pdf Sirmans – Price elasticity of derived demand for Urban Residential Land 1978 https://www.ideals.illinois.edu/bitstream/handle/2142/26843/priceelasticityo 462sirm.pdf?sequence=1 Pryce 1999 http://www.gwilympryce.co.uk/housing/Pryce_1999_2SLS_PES_UrbStud.pdf
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Elasticity • We have discussed all types of elasticities. By this point you should be able to pick up new elasticity on your own.
