Elasticity and Expenditure

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Elasticity and Expenditure
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Definitions

• Elasticity responsiveness of quantity demanded
  to price.
• Coefficient of elasticity Percent change
  in quantity Percent change in price
• Percent change in Q Change in Q / Q Q2
  - Q1 divided by Q1
• Percent change in P Change in P / P P2
  - P1 divided by P1

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Relationship to expenditure

• ? (PQ) ? P ? Q
• If ? P 3 percent and ? Q -10 , then
  ? (PQ) - 7 or revenue declines
• Coef of elas e ? Q divided by ? P
• hence in the above example
• e 10 / 3 3.33
• The coefficient of elasticity is greater than 1,
  so demand is ELASTIC

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• Problem
• ? Q - 10 , and ? P 4
• a. what is the coefficient of elasticity?
• b. is demand elastic or inelastic?
• c. what is the percent change in consumer
  expenditure?
• See next slide for answersbut not before trying
  to solve the problem

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• Solution
• ? Q - 10 , and ? P 4
• what is the coefficient of elasticity?
• e ? Q / ? P 10 / 4 2.5
• b. is demand elastic or inelastic?
• -- since e gt 1.0, demand is elastic.
• We should expect that consumer expenditure
  will decline with an increase in price.
• c. what is the percent change in consumer
  expenditure?
• Since ? PQ ? P ? Q, we have
• ? PQ 4 - 10 - 6

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• Problem
• ? Q 10 , and ? Revenue 3
• a. what is the percent change in price?
• b. what is the coefficient of elasticity?
• c. is demand elastic or inelastic?
• d. what is the percent change in consumer
  expenditure?
• See next slide for answersbut not before trying
  to solve the problem

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• Solution
• ? Q 10 , and ? Revenue 3
• a. what is the percent change in price?
• Since ? PQ ? P ? Q
• 3 ? P 10
• Price must have fallen by 7 percent
• b. what is the coefficient of elasticity?
• Since e ? Q / ? P 10 / 7 1.43
• c. is demand elastic or inelastic? Elastic demand
  
• a reduction in price leads to an increase in
  revenue
• -- the coefficient of elasticity is greater than
  1.
• d. what is the percent change in consumer
  expenditure?
• The same as the percent change in revenue,
  3

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• Problem
• ? P 10 , and ? Revenue - 3
• a. what is the percent change in quantity?
• b. what is the coefficient of elasticity?
• c. is demand elastic or inelastic?
• d. what is the percent change in consumer
  expenditure?
• See next slide for answersbut not before trying
  to solve the problem

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• Solution
• ? Q 10 , and ? Revenue - 3
• a. what is the percent change in price?
• Since ? PQ ? P ? Q
• - 3 ? P 10
• Price must have fallen by 13 percent
• b. what is the coefficient of elasticity?
• Since e ? Q / ? P 10 / 13
• c. is demand elastic or inelastic? Inelastic
  demand
• a reduction in price leads to a decrease in
  revenue
• -- the coefficient of elasticity is less than 1.
• d. what is the percent change in consumer
  expenditure?
• The same as the percent change in revenue, -
  3

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• Problem
• ? P 10 , and e 2.5
• a. what is the percent change in quantity?
• b. is demand elastic or inelastic?
• c. what is the percent change in consumer
  expenditure?
• See next slide for answersbut not before trying
  to solve the problem

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• Solution
• ? P 10 , and e 2.5
• a. what is the percent change in quantity?
• Since e 2.5 ? Q / ? P ? Q / 10
• We have ? Q - 25 (when price goes up, Q
  down)
• b. is demand elastic or inelastic?
• Since e 2.5, demand is ELASTIC we should
  expect consumer expenditure to decrease when
  price increases.
• c. what is the percent change in consumer
  expenditure?
• Since ? PQ ? P ? Q, we have
• ? PQ 10 - 25 - 15

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• Problem
• ? P 5 , and e 1/4
• a. what is the percent change in quantity?
• b. is demand elastic or inelastic?
• c. what is the percent change in consumer
  expenditure?
• See next slide for answersbut not before trying
  to solve the problem

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• Solution
• ? P 5 , and e ¼
• a. what is the percent change in quantity?
• Since e ¼ ? Q / ? P ? Q / 5
• We have ? Q - 1.25 (when price goes up, Q
  down)
• b. is demand elastic or inelastic?
• Since e ¼ , demand is INELASTIC we should
  expect consumer expenditure to increase when
  price increases.
• c. what is the percent change in consumer
  expenditure?
• Since ? PQ ? P ? Q, we have
• ? PQ 5 - 1.25 3.75

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Calculating elasticity from a table
Price Quantity ? P ? Q Elasticity
1 180
2 160
3 140
4 120
5 100
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Calculating elasticity from a table
Price Quantity ? P ? Q Elasticity
1 180 2 1 / 1 100 20 / 180 11.1 0. 111 (inelastic)
2 160 3 2 / 2 50 20 / 160 12.5 0. 25 (inelastic)
3 140 4 3 / 3 33 20 / 140 14.3 0 . 43 (inelastic)
4 120 5 4 / 4 25 20 / 120 16.7 0. 67 (inelastic)
5 100 6 5 / 5 20 20 / 100 20 1. 00 (unit elastic)
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Elasticity and slope

• The table was derived from the demand equation
• Q 200 - 20 P
• Note that for each dollar price goes up, Q goes
  down by 20 units.
• In mathematical symbolism,
• ? Q / ? P - 20
• This is close to the formula for the coefficient
  of elasticity, but not quite the same. What is
  the difference? Pause for thought

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Elasticity and slope

• Slope ? Q / ? P - 20
• But coefficient of elasticity
• ? Q / Q divided by ? P / P
• The expression for the coefficient of elastictity
  can be rearranged to get
• e ? Q / ? P times P / Q
• Which can be a handy computational rule for
  elasticity AT a point.

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• Problem given the demand equation
• Q 1500 25 P
• What is the coefficient of elasticity at
• P 10 ?
• First note that Q 1500 250 1250,
• So that the coefficient of elasticity is
• e ? Q / ? P times P / Q
• e 25 (10) / 1250 250 / 1250
• e 0. 20

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• Problem given the demand equation
• Q 1500 25 P
• What is the coefficient of elasticity at
• P 50 ?
• First note that Q 1500 1250 250,
• So that the coefficient of elasticity is
• e ? Q / ? P times P / Q
• e 25 (50 / 250) 1250 / 250
• e 5.0