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Economic Analysis for Business Session V: Elasticity and its Application-1I

Economic Analysis for Business Session V: Elasticity and its Application-1I. Instructor Sandeep Basnyat 9841892281 Sandeep_basnyat@yahoo.com. 0. APPLICATION: Does Drug Interdiction Increase or Decrease Drug-Related Crime?.

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Economic Analysis for Business Session V: Elasticity and its Application-1I

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  1. Economic Analysis for BusinessSession V: Elasticity and its Application-1I InstructorSandeep Basnyat 9841892281 Sandeep_basnyat@yahoo.com

  2. 0 APPLICATION: Does Drug Interdiction Increase or Decrease Drug-Related Crime? • One side effect of illegal drug use is crime: Users often turn to crime to finance their habit. • We examine two policies designed to reduce illegal drug use and see what effects they have on drug-related crime. • For simplicity, we assume the total dollar value of drug-related crime equals total expenditure on drugs. • Demand for illegal drugs is inelastic, due to addiction issues. CHAPTER 5 ELASTICITY AND ITS APPLICATION

  3. new value of drug-related crime Price of Drugs S2 D1 S1 P2 initial value of drug-related crime P1 Quantity of Drugs Q1 Q2 0 Policy 1: Interdiction Interdiction reduces the supply of drugs. Since demand for drugs is inelastic, P rises propor-tionally more than Q falls. Result: an increase in total spending on drugs, and in drug-related crime CHAPTER 5 ELASTICITY AND ITS APPLICATION

  4. new value of drug-related crime Price of Drugs D2 D1 S initial value of drug-related crime P1 P2 Quantity of Drugs Q2 Q1 0 Policy 2: Education Education reduces the demand for drugs. P and Q fall. Result:A decrease in total spending on drugs, and in drug-related crime. CHAPTER 5 ELASTICITY AND ITS APPLICATION

  5. Percent change in Qd Income elasticity of demand = Percent change in income Income Elasticity of Demand • The income elasticity of demand measures the response of Qd to a change in consumer income. CHAPTER 5 ELASTICITY AND ITS APPLICATION

  6. Calculating Income Elasticity of Demand • Arc Elasticity: • where Y stands for income. • Example • If a 1% increase in income results in a 3% decrease in quantity demanded, the income elasticity of demand is x = -3%/1% = -3.

  7. Numerical Example a) Suppose the demand for an automobile as a function of income per capita is given by: Q = 50,000 + 5I What is the income elasticity of demand when per capita income increases from $10,000 to $11,000?

  8. Numerical Example a) Suppose the demand for an automobile as a function of income per capita is given by: Q = 50,000 + 5I What is the income elasticity of demand when per capita income increases from $10,000 to $11,000? Solution: When I1 = 10,000 Q1 = 100,000 When I2 = 11,000, Q2 = 105,000 Percentage Change in Q = 4.88 Percentage Change in I = 9.52 Income Elasticity of Demand = 4.88 / 9.52 = 0.512

  9. Numerical Example-Point Income Elasticity b) Suppose the demand for an automobile as a function of income per capita is given by: Q = 50,000 + 5I What is the income elasticity of demand at the income level of $10,500?

  10. Numerical Example b) Suppose the demand for an automobile as a function of income per capita is given by: Q = 50,000 + 5I What is the income elasticity of demand at the income level of $10,500? Solution: When I = 10,500; Q = 102,500 dQ / dI = b = 5 Income Elasticity of Demand = b x (P/Q) = 5 x (10500 / 102500) E = 0.512

  11. Necessities, Inferior goods and luxuries • Elasticity measurement as: • E < 0 : Inferior goods (negative) • 0 < E ≤ 1 : Normal goods or necessities • E > 1 : Luxuries • An increase in income causes an increase in demand for a normal good and luxuries. • An increase in income causes a decrease in demand for inferior goods. CHAPTER 5 ELASTICITY AND ITS APPLICATION

  12. % change in Qd for good 1 Cross-price elast. of demand = % change in price of good 2 Cross Price Elasticity of Demand • The cross-price elasticity of demand measures the response of demand for one good to changes in the price of another good. • For substitutes, cross-price elasticity > 0 (positive)E.g., an increase in price of goat meat causes an increase in demand for chicken. • For complements, cross-price elasticity < 0 (Negative)E.g., an increase in price of computers causes decrease in demand for software. CHAPTER 5 ELASTICITY AND ITS APPLICATION

  13. Calculating Cross Price Elasticity of Demand • Arc Elasticity, • where Po stands for price of another good. • Example • If a 1% increase in the price of a related good results in a 3% decrease in quantity demanded, the cross-price elasticity of demand is = -3%/1% = -3.

  14. Numerical Example Demand for a publisher’s book is given as: Qx = 12,000 – 5,000Px + 5I + 500Pc • Px = Price of the book = $5 • I = Income per capita = $10,000 • Pc = Price of the books from competing publishers = $6 • Find Price elasticity of demand for the book. What effect a price increase would have on total revenues? • Find income elasticity of demand for the book. Find if the book is inferior good, normal good or luxury. • Assess the probable impact on demand for the book if competing publishers raise their prices. Are the books substitute for each other or complements?

  15. Numerical Example 1) a) Find Price elasticity of demand for the book. b) What effect a price increase would have on total revenues? Solution: a) Substituting the values of Iand Pc Qx = 12,000 – 5,000Px + 5(10000) + 500(6) Or, Qx = 65,000 – 5,000Px When Px= $5 (given), Qx= 40,000 Now, dQx/dPx = b = - 5000 Therefore, E p = -5000 x (5 / 40000) = - 0.625 b) Since, the demand for the book is inelastic, an increase in the price of the book would increase total revenue.

  16. Numerical Example Demand for a publisher’s book is given as: Qx = 12,000 – 5,000Px + 5I + 500Pc • Px = Price of the book = $5 • I = Income per capita = $10,000 • Pc = Price of the books from competing publishers = $6 • Find Price elasticity of demand for the book. What effect a price increase would have on total revenues? • Find income elasticity of demand for the book. Find if the book is inferior good, normal good or luxury. • Assess the probable impact on demand for the book if competing publishers raise their prices. Are the books substitute for each other or complements? DONE

  17. Numerical Example 2) a) Find income elasticity of demand for the book. b) Find if the book is inferior good, normal good or luxury. Solution: a) Substituting the values of Pxand Pc Qx = 12,000 – 5,000(5) + 5I + 500(6) Or, Qx = - 10,000 + 5I When I= $10000 (given), Qx= 40,000 Now, dQx/dI = b = 5 Therefore, E I = 5 x (10000 / 40000) = 1.25 b) Since, the E I > 1 for the book, the book is luxury.

  18. Numerical Example Demand for a publisher’s book is given as: Qx = 12,000 – 5,000Px + 5I + 500Pc • Px = Price of the book = $5 • I = Income per capita = $10,000 • Pc = Price of the books from competing publishers = $6 • Find Price elasticity of demand for the book. What effect a price increase would have on total revenues? • Find income elasticity of demand for the book. Find if the book is inferior good, normal good or luxury. • Assess the probable impact on demand for the book if competing publishers raise their prices. Are the books substitute for each other or complements? DONE DONE

  19. Numerical Example 3) a) Assess the probable impact on demand for the book if competing publishers raise their prices. b) Are the books substitute for each other or complements? Solution: a) Substituting the values of Pxand I Qx = 12,000 – 5,000(5) + 5(10000) + 500Pc Or, Qx = 37,000 + 500Pc When Pc = $6 (given), Qx= 40,000 Now, dQx/dPc = b = 500 Therefore, Cross price elasticity of demand for the book E c = 500 x (6 / 40000) = 0.075 1% increase in competitor’s book price will increase the demand for the book by 0.075% b) Since, the E C > 0 for the book, the book is substitute to competing producer’s book.

  20. Basic Concept on Marginal Effects Consider a simple linear equation for a demand curve: Q =180 -2p ………………………….……(i) When p = 5; Q = 180 - 2 x 5 = 170 P = 6; Q = 168 P = 7; Q = 166 For every 1 unit increase in the p, Q decreases by 2 units. So, -2 = Marginal effect of Price on Quantity Similarly for multivariate equation: Q = a + bP + cI ‘c’ is the Marginal Effect of Income on quantity. For the inverse demand function of equation (i) above, P = 90 - 0.5Q Q is the marginal effect of quantity on price.

  21. Numerical Applications of Marginal Effects PK Corp estimates that its demand function is as follows: Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P* Where; Q = quantity demanded per month P=price of the product A=firm’s advertising expenditure per month Y=per capita disposable income P *=price of BJ Corp a) During the next five years, per capita disposable income is expected to increase by $2,500. What effect will this have on the firm’s sales?

  22. Numerical Applications of Marginal Effects • PK Corp estimates that its demand function is as follows: • Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P* • During the next five years, per capita disposable income is expected to increase by £2,500. What effect will this have on the firm’s sales? • Solution: • For 1 unit increase I Y; Q increases by 2.8 unit • For 2500 units increase in Y; Q increases by 2500 x 2.8 units. • Therefore, Increase in sales = 7000 units.

  23. Numerical Applications of Marginal Effects PK Corp estimates that its demand function is as follows: Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P* b) What is the relationship between the products of PK and BJ??

  24. Numerical Applications of Marginal Effects PK Corp estimates that its demand function is as follows: Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P* b) What is the relationship between the products of PK and BJ?? Solution: For 1 unit increase Price of BJ (P*); Quantity of PK (Q) decreases by 1.2 units Therefore Cross price elasticity of Demand is negative (<0) Hence, both companies are producing complementary products.

  25. Numerical Applications of Marginal Effects PK Corp estimates that its demand function is as follows: Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P* c) PK intends to charge $15 and spend $10,000 per month on promotion, while it believes per capita income will be $12,000 and BJ’s price will be $3, calculate the income elasticity of demand. What does this tell you about the nature of PK’s product?

  26. Numerical Applications of Marginal Effects PK Corp estimates that its demand function is as follows: Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P* c) PK intends to charge $15 and spend $10,000 per month on promotion, while it believes per capita income will be $12,000 and BJ’s price will be $3, calculate the income elasticity of demand. What does this tell you about the nature of PK’s product? Solution: YED = 2.8 x (12000 / 41665.4) = 0.806 PK is selling normal goods.

  27. Numerical Applications of Marginal Effects PK Corp estimates that its demand function is as follows: Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P* d) What effect would an increase in advertising of $1000 have on profitability, if each additional unit costs $10 to produce?

  28. Numerical Applications of Marginal Effects PK Corp estimates that its demand function is as follows: Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P* d) What effect would an increase in advertising of $1000 have on profitability, if each additional unit costs $10 to produce? Solution: If Increase in A = 1; Increase in Q = 0.8 = 800 units; Increase in R = 800 x 15 = $12,000 Increase in Costs = 800 x 10 + advertisement (A)$1000= $9,000 Thus every additional $1,000 spent on advertising increases profit by $3,000.

  29. Basic Concepts on Power form Elasticity Recall the basic non-linear (power form) function: Q = Pα Here, Price Elasticity of Demand = α Eg. If, Q = P2 PED = 2 Meaning: for 1 % increase in the P, Q decreases by 2%. Analysis can be extended to a multivariate functions: Q= aPb Ac Yd P0e Here, P = price of the good A = Advertisement expenditure Y = Income level of the people PO = Price of other goods.

  30. Basic Concepts on Power form Elasticity Consider a non-linear demand function: Q = 9.83P-1.2A2.5Y1.6P01.4 Here, P = price of the good =$60 A = Advertisement expenditure = $120,000 Y = Income level of the people = $28,000 P0 = Price of other goods = $45 Find the equation for the demand curve.

  31. Basic Concepts on Power form Elasticity Consider a non-linear demand function: Q = 9.83P-1.2A2.5Y1.6P0-1.4 Here, P = price of the good =$60 A = Advertisement expenditure = $120,000 Y = Income level of the people = $28,000 P0 = Price of other goods = $45 Find the equation for the demand curve. Solution: Q = 9.83P-1.2(120000)2.5(28000)1.6(45)-1.4 Q = 3100718641762767839.13P-1.2

  32. Percentage change in Qs Price elasticity of supply = Percentage change in P 0 Price Elasticity of Supply • Price elasticity of supply measures how much Qs responds to a change in P. • Loosely speaking, it measures the price-sensitivity of sellers’ supply. • Again, use the midpoint method to compute the percentage changes. CHAPTER 5 ELASTICITY AND ITS APPLICATION

  33. P S Percentage change in Qs Price elasticity of supply = P2 Percentage change in P P1 Q Q1 Q2 16% = 2.0 8% 0 Price Elasticity of Supply Price elasticity of supply equals Example: P rises by 8% Q rises by 16% CHAPTER 5 ELASTICITY AND ITS APPLICATION

  34. 0 The Variety of Supply Curves • Economists classify supply curves according to their elasticity. • The slope of the supply curve is closely related to price elasticity of supply. • Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity. • The next 5 slides present the different classifications, from least to most elastic. CHAPTER 5 ELASTICITY AND ITS APPLICATION

  35. % change in Q Price elasticity of supply = = % change in P P S P2 Q 0 “Perfectly inelastic” (one extreme) 0% = 0 10% S curve: vertical Sellers’ price sensitivity: P1 0 P rises by 10% Elasticity: Q1 0 Q changes by 0% CHAPTER 5 ELASTICITY AND ITS APPLICATION

  36. % change in Q Price elasticity of supply = = % change in P P S P2 Q Q2 0 “Inelastic” < 10% < 1 10% S curve: relatively steep Sellers’ price sensitivity: P1 relatively low P rises by 10% Elasticity: Q1 < 1 Q rises less than 10% CHAPTER 5 ELASTICITY AND ITS APPLICATION

  37. % change in Q Price elasticity of supply = = % change in P P S P2 Q Q2 0 “Unit elastic” 10% = 1 10% S curve: intermediate slope Sellers’ price sensitivity: P1 intermediate P rises by 10% Elasticity: Q1 = 1 Q rises by 10% CHAPTER 5 ELASTICITY AND ITS APPLICATION

  38. % change in Q Price elasticity of supply = = % change in P P S P2 Q Q2 0 “Elastic” > 10% > 1 10% S curve: relatively flat Sellers’ price sensitivity: P1 relatively high P rises by 10% Elasticity: Q1 > 1 Q rises more than 10% CHAPTER 5 ELASTICITY AND ITS APPLICATION

  39. % change in Q Price elasticity of supply = = % change in P P S Q Q2 Q1 0 “Perfectly elastic” (the other extreme) any % = infinity 0% S curve: horizontal P1 P2 = Sellers’ price sensitivity: extreme P changes by 0% Elasticity: infinity Q changes by any % CHAPTER 5 ELASTICITY AND ITS APPLICATION

  40. The Determinants of Supply Elasticity • The more easily sellers can change the quantity they produce, the greater the price elasticity of supply. • Example: Supply of King’s Way property is harder to vary and thus less elastic than supply of new cars. • For many goods, price elasticity of supply is greater in the long run than in the short run, because firms can build new factories, or new firms may be able to enter the market. CHAPTER 5 ELASTICITY AND ITS APPLICATION

  41. ACTIVE LEARNING 3: Elasticity and changes in equilibrium • The supply of beachfront property is inelastic. The supply of new cars is elastic. • Suppose population growth causes demand for both goods to double (at each price, Qd doubles). • For which product will P change the most? • For which product will Q change the most? 41

  42. P S D1 D2 B P2 P1 A Q Q1 Q2 ACTIVE LEARNING 3: Answers Beachfront property (inelastic supply): When supply is inelastic, an increase in demand has a bigger impact on price than on quantity. 42

  43. P D1 D2 S B P2 A P1 Q Q2 Q1 ACTIVE LEARNING 3: Answers New cars(elastic supply): When supply is elastic, an increase in demand has a bigger impact on quantity than on price. 43

  44. P S $15 12 4 $3 Q 100 200 500 525 0 How the Price Elasticity of Supply Can Vary Supply often becomes less elastic as Q rises, due to capacity limits. elasticity < 1 elasticity > 1 CHAPTER 5 ELASTICITY AND ITS APPLICATION

  45. Thank you

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