# ECON 101 Tutorial Week 2: Demand Elasticity Calculation

This tutorial focuses on solving for the price elasticity of demand of good A using a given demand function, and analyzing the elasticity status.

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## About ECON 101 Tutorial Week 2: Demand Elasticity Calculation

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1. ECON 101 Tutorial: Week 2 Shane Murphy s.murphy5@lancaster.ac.uk Office Hours: Monday 3:00-4:00 LUMS C86

2. Outline Substitute Lecturer Next Week Roll Call Class Rep Problems Discussion

3. Class Rep

4. Exercise Consider the following demand function: Q A =100- 8P A +0.5P B +2Y, where Q A is the quantity demanded of good A, P A is the price of good A, P B is the price of good B and Y is the income. a) If P A =7, P B =12 and Y=4.5 calculate the price elasticity of demand of good A. Is the demand elastic or inelastic? First, let us solve for Q A Q A = 100 - 8P A + 0.5P B + 2Y = 100 8 (7) + 0.5 (12) + 2 (4.5) = 100 56 + 6 + 9 = 59

5. Exercise Consider the following demand function: Q A =100- 8P A +0.5P B +2Y, where Q A is the quantity demanded of good A, P A is the price of good A, P B is the price of good B and Y is the income. a) If P A =7, P B =12 and Y=4.5 calculate the price elasticity of demand of good A. Is the demand elastic or inelastic?

6. Exercise a) If P A =7, P B =12, Y=4.5 and Q A = 59, and Q A =100- 8P A +0.5P B +2Y calculate the price elasticity of demand of good A. Is the demand elastic or inelastic? Ped = dQ A /dP A * P A /Q A dQ A /dP A = -8 ped = dQ A /dP A * P A /Q A = -8 * 7/59 = -56/59 By convention, we write ped = 56/59 (positive) Elasticity of Demand is Inelastic (ped<1)

7. Exercise b) If P A =7, P B =12, Y=4.5 and Q A = 59, and Q A =100- 8P A +0.5P B +2Y calculate the calculate the income elasticity. What kind of good is A? (Normal/Inferior? If normal then necessity or luxury?) ied = dQ A /dY * Y/Q A dQ A /dY = 2 ied = dQ A /dY * Y/Q A = 2 * 4.5/59 = 9/59 This is a normal good (ied>0) This is a necessity (0

8. Exercise c) If P A =7, P B =12, Y=4.5 and Q A = 59, and Q A =100- 8P A +0.5P B +2Y calculate the cross price elasticity. What kind of goods are A and B? (Complements or substitutes?) cped = dQ A /dP B * P B /Q A dQ A /dP B = 0.5 cped = dQ A /dP B * P B /Q A = 0.5 * 12/59 = 6/59 These goods are substitutes (cped > 0)

9. Exercise 5 Suppose that your demand Schedule for DVDs is as follows: a) Use the midpoint method to calculate your price elasticity of demand as the price of DVDs increases from 8 to 10 for income of 10,000 and income of 12,000. Income of 10,000: ped = [(Q A Q B )/([Q A + Q B ]/2)/[(P A P B )/([P A + P B ]/2) = [(40 32)/([40 + 32]/2)/[(8 10)/([8 + 10]/2) = (8/36)/(-2/9) = -4/4 = -1 Price Quantity Demanded (Y = 10,000) Quantity Demanded (Y = 12,000) 8 40 50 10 32 45 12 24 30 14 16 20 16 8 12

10. Exercise 5 Suppose that your demand Schedule for DVDs is as follows: a) Use the midpoint method to calculate your price elasticity of demand as the price of DVDs increases from 8 to 10 for income of 10,000 and income of 12,000. Income of 12,000: ped = [(Q A Q B )/([Q A + Q B ]/2)/[(P A P B )/([P A + P B ]/2) = [(50 45)/([50 + 45]/2)/[(8 10)/([8 + 10]/2) = (5/47.5)/(-2/9) = -45/95 = -0.47 Price Quantity Demanded (Y = 10,000) Quantity Demanded (Y = 12,000) 8 40 50 10 32 45 12 24 30 14 16 20 16 8 12

11. Exercise 5 Suppose that your demand Schedule for DVDs is as follows: b) Use the midpoint method to calculate your income elasticity of demand as your income increases from 10,000 to 12,000 for price of 12 and price of 16. Price of 12: ied = [(Q A Q B )/([Q A + Q B ]/2)/[(Y A Y B )/([Y A + Y B ]/2) = [(24 30)/([24 + 30]/2)/ [(10,000 12,000)/([10 ,000+ 12,000]/2) = (-6/27)/(-2/11) = 66/54 = 1.22 Price Quantity Demanded (Y = 10,000) Quantity Demanded (Y = 12,000) 8 40 50 10 32 45 12 24 30 14 16 20 16 8 12

12. Exercise 5 Suppose that your demand Schedule for DVDs is as follows: b) Use the midpoint method to calculate your income elasticity of demand as your income increases from 10,000 to 12,000 for price of 12 and price of 16. Price of 16: ied = [(Q A Q B )/([Q A + Q B ]/2)/[(Y A Y B )/([Y A + Y B ]/2) = [(8 12)/([8 + 12]/2)/ [(10,000 12,000)/([10 ,000+ 12,000]/2) = (-4/10)/(-2/11) = 44/20 = 2.2 Price Quantity Demanded (Y = 10,000) Quantity Demanded (Y = 12,000) 8 40 50 10 32 45 12 24 30 14 16 20 16 8 12

13. Exercise 7 Consider public policy aimed at smoking a) Studies indicate the ped for cigarettes is about 0.4. If a packed of cigarettes is currently priced at 6 and the government wants to reduce smoking by 20%, by how much should it increase the price? b) If the government permanently increases the price of cigarettes, will the policy have a larger effect on smoking one year from now or five years from now? c) Studies also find that teenagers have a higher price elasticity of demand for cigarettes than do adults. Why might this be true? a) ped = % change in Q/% change in P 0.4 = -0.2/% change in P % change in P = -0.2/0.4 = -1/2 price should increase by 50 percent (4 using the midpoint method) b) Goods tend to be more elastic over longer time horizons, so the policy will have a smaller effect in the short run than the long run

14. Exercise 7 Consider public policy aimed at smoking a) Studies indicate the ped for cigarettes is about 0.4. If a packed of cigarettes is currently priced at 6 and the government wants to reduce smoking by 20%, by how much should it increase the price? b) If the government permanently increases the price of cigarettes, will the policy have a larger effect on smoking one year from now or five years from now? c) Studies also find that teenagers have a higher price elasticity of demand for cigarettes than do adults. Why might this be true? c) ped might be a function of income as income increases, elasticity falls ped might be a function of age as people get older, they are less flexible, and have more inelastic demand functions ped might be a function of the experiences of the consumer Older smokers might be more addicted and less elastic to price changes Older smokers might have a taste for fewer substitutes for smoking