Law of demand and demand elasticity

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Law of demand and demand elasticity

  1. 1. Law of Demand  Other things equal, the quantity demanded of a good falls when the price of good rises . Elasticity A measure of the responsiveness of quantity demanded or quantity supplied to one of its determinants. Price Elasticity of Demand A measure of how much the quantity demanded of a good responds to a change in the price of that good, computed as the percentage change in quantity demanded divided by the percentage change in price.
  2. 2. Question Suppose that your demand schedule for compact discs is as follows: Price QUANTITY DEMANDED QUANTITY DEMANDED $ (INCOME = $10,000) (INCOME = $12,000) 8 40 50 10 32 45 12 24 30 14 16 20 16 8 12
  3. 3. a. Use the midpoint method to calculate your price elasticity of demand as the price of compact discs increases from $8 to $10 if (i) your income is $10000 and (ii) your income is $ 12000. b. Calculate your income elasticity of demand as your income increases from $10,000 to $12000 if (i) the price is $12 (ii) the price is $16.
  4. 4. Solution a(i). The price of compact discs increase from $8 to $10, (i) if our income is $10,000; According to the midpoint method, (Q2 - Q1)/[( Q2 + Q1)/2] Price elasticity of demand = (P2 - P1)/[( P2 + P1)/2] P1 = 8 P2 = 10 Q1 = 40 Q2 = 32 Price QUANTITY DEMANDED QUANTITY DEMANDED $ (INCOME = $10,000) (INCOME = $12,000) 8 40 50 10 32 45
  5. 5. So, (32 -40)/ [ (32+ 40/2] Price elasticity of demand = (10 - 8)/[( 10 + 8)/2] -8/ 72/2 Price elasticity of demand = -8/36 = 2/18/2 -2/9 = 2/9 2/9 Price elasticity of demand = -1 Our price elasticity of demand is equal 1 So, our price elasticity of demand is unit elastic demand.
  6. 6. Price P1 = 8 , Q1 = 40 – total revenue = p1 x Q1 = 8x40 = 320 P2= 10,Q2 = 32 – total revenue = P2 x Q2 = 10x32 = 320 -in unit elastic demand(Ed=1) , a change in the price does not affect total revenue. p2 p1 Demand curve q2 q1 Quantity
  7. 7. a(ii). The price of compact discs increase from $8 to $10, (ii) if our income is $12,000; According to the midpoint method, (Q2 - Q1)/[( Q2 + Q1)/2] Price elasticity of demand = (P2 - P1)/[( P2 + P1)/2] P1 = P2 = 8 10 Q1 = 50 Q2 = 45 Price QUANTITY DEMANDED QUANTITY DEMANDED $ (INCOME = $10,000) (INCOME = $12,000) 8 40 50 10 32 45
  8. 8. So, (45 -50)/ ( 45+ 50/2] Price elasticity of demand = (10 - 8)/[( 10 + 8)/2] -5/ 95/2 Price elasticity of demand = -5x 2/95 = 2/18/2 -2/19 = 2/9 2/9 2 = 19 9 x 2 Price elasticity of demand = 9/19 = 0.47 Our price elasticity of demand is smaller than 1 So, Our price elasticity of demand is inelastic demand.
  9. 9. Price P1 = 8 , Q1 = 50 – total revenue = p1 x Q1 = 8x50 = 400 P2= 10,Q2 = 45 – total revenue = P2 x Q2 = 10x32 = 450 -in inelastic demand (Ed < 1) , a price increase rises total revenue and a price decrease reduces total revenue. p2 p1 Demand curve q2 q1 Quantity
  10. 10. b. Calculate your income elasticity of demand as your income increases from $10,000 to $12000 if (i) the price is $12 (ii) the price is $16. Our income elasticity of demand is as our income increases from $ 10,000 to $ 12000 if (i) the price is $ 12 According to the equation i. Percentage change in quantity demanded Income elasticity of demanded = Percentage change in income Price QUANTITY DEMANDED QUANTITY DEMANDED $ (INCOME = $10,000) (INCOME = $12,000) 12 24 30
  11. 11. Point A: Income = 10,000 Point B: Income = 12,000 Quantity Demanded = 24 Quantity Demanded = 30 Going to Point A to Point B, the income rises by 20 percent because 12000-10000/10000 x 100 = 20 and the quantity demanded also rise 25 percent because 30-24/24 x 100 = 25 25 Income elasticity of demanded = 5 = 20 = 1.25 4 As our income increases from $ 10,000 to $ 12000 if (i) the price is $ 12 , our income elasticity of demand is 1.25 and so it is positive income elasticity and we conclude that is normal good.
  12. 12. ii. Our income elasticity of demand is as our income increases from $ 10,000 to $ 12000 if (ii) the price is $ 16 According to the equation Percentage change in quantity demanded Income elasticity of demanded = Percentage change in income Price QUANTITY DEMANDED QUANTITY DEMANDED $ (INCOME = $10,000) (INCOME = $12,000) 16 8 12
  13. 13. Point A: Point B: Income = 10,000 Income = 12,000 Quantity Demanded = 8 Quantity Demanded = 12 Going to Point A to Point B, the income rises by 20 percent because 12000-10000/10000 x 100 = 20 and the quantity demanded also rise 50 percent because 12-8/12 x 100 = 33 50 Income elasticity of demanded = 10 = 20 = 2.5 4 As our income increases from $ 10,000 to $ 12000 if (ii) the price is $ 16 , our income elasticity of demand is 2.5 and so it is positive income elasticity and we conclude that is normal good.

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