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Unit 4.

Unit 4. Quantitative Demand Analysis (as functions of output level) (Ch. 3, 8). Revenue Concepts and Output Relationships. Graphical. Mathematical  Revenue Concept = f(q). D Curves Facing Individual Firms. Case #1: P = a – bX  ‘imperfect’ competition

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Unit 4.

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  1. Unit 4. Quantitative Demand Analysis (as functions of output level) (Ch. 3, 8)

  2. Revenue Concepts and Output Relationships • Graphical Mathematical  Revenue Concept = f(q)

  3. D Curves Facing Individual Firms • Case #1: P = a – bX  ‘imperfect’ competition * firm has some control over P (P maker)  significant portion of mkt supply  firm output influences mkt supply * heterogeneous products * difficult mkt entry (& exit) * imperfect info

  4. D Curves Facing Individual Firms • Case #2: P = a  ‘perfect’ competition * firm has no control over P (P taker)  insignificant portion of mkt supply  firm output does not impact mkt supply * homogenous products * easy mkt entry (& exit) * perfect info

  5. Revenue Concepts

  6. Market & Firm D (Perfect Competition)

  7. Revenue ConceptsP = a

  8. Revenue ConceptsP=a-bQ

  9. TR Max • P-Taking firm • No TR max as TR keeps increasing with Q • P-Setting firm • Max TR where MR = 0  P =a/2

  10. Question • If a firm wants to increase its dollar sales of a product, should it P or P?

  11. Quote of the Day • “Students of Economics need to be taught, in business, sometimes you should raise your price, and sometimes you should lower your price.” CEO of Casey’s

  12. Business managers often want to know: • If a D factor affecting sales of their product changes by a given %, what will be the corresponding % impact on Q sold of their product. = “Elasticity of Demand”

  13. Elasticity of D Definition (Meaning) • = A measure of responsiveness of D to changes in a factor that influences D • Two components • Magnitude of change (number) • Direction of change (sign) • = The number shows the magnitude of how much D will change due to a 1% change in a D factor • The sign shows whether the D factor and D are changing in the same or opposite directions +  same direction -  opposite direction

  14. Elasticities of Demand •  EQ,F = %Qdx/% F = %Q/%F where, Qdx = the quantity demanded of X F = a factor that affects Qdx Notes: sign > 0  Qdx & F, ‘directly’ related sign < 0  Qdx & F, ‘indirectly’ related number > 1  %Qdx>%F

  15. Elasticity Calculation

  16. Types of Elasticities

  17. Elasticity Value Meanings (e.g.) • E0 = -2  for each 1% Px,Qd for X will  by 2% in opposite direction • EC = +1/2  for each 1% PY,Qd for X will  by 1/2% in same direction • EI = +.1  for each 1% I,Qd for X will  by .1% in same direction

  18. Own Price Elasticity of Demand • Negative according to the ‘law of demand’

  19. Perfectly Elastic & Inelastic Demand

  20. E0 Calculation E0 = EX,Px

  21. E0 and Linear D (P = a – bx) Px E0 a/2 > a/2 < a/2

  22. Example of Linear Demand • Qd = 10 – 2P • Own-Price Elasticity: (-2)P/Q • If P=1, Q=8 (since 10 – 2 = 8) • Own price elasticity at P=1, Q=8: (-2)(1)/8 = -0.25

  23. Factors Affecting Own Price Elasticity • Available Substitutes • The more substitutes available for the good, the more elastic the demand. • Time • Demand tends to be more inelastic in the short term than in the long term. • Time allows consumers to seek out available substitutes. • Expenditure Share • Goods that comprise a small share of consumer’s budgets tend to be more inelastic than goods for which consumers spend a large portion of their incomes.

  24. Uses of E0 • Calculate % change in P needed to bring about desired % change in Q sold • Calculate % change in Q sold that will result from a given % change in P • Calculate magnitude of change in TR that will result from a given % change in P

  25. Example 1: Pricing and Cash Flows • According to an FTC Report by Michael Wad, AT&T’s own price elasticity of demand for long distance services is –8.64. • AT&T needs to boost revenues in order to meet it’s marketing goals. • To accomplish this goal, should AT&T raise or lower it’s price?

  26. Example 2: Quantifying the Change • If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T?

  27. Answer • Calls would increase by 25.92 percent!

  28. Own-Price Elasticity and Total Revenue • Elastic • Increase (a decrease) in price leads to a decrease (an increase) in total revenue. • Inelastic • Increase (a decrease) in price leads to an increase (a decrease) in total revenue. • Unitary • Total revenue is maximized at the point where demand is unitary elastic.

  29. Change in TR (math) TR1 = P1Q1 TR2 = P2Q2 = (P1+P)(Q1+Q) = P1Q1+PQ1+QP1+PQ TR = TR2 – TR1 = PQ1+QP1+PQ = PQ1+QP1 (PQ  0 for small P and small Q)

  30. Change in TR Due to Q (i.e. MR) NOTE: MR = 0 if E is unitary > 0 if E is elastic < 0 if E is inelastic

  31. Change in TR and E0

  32. Quantifying the Change inTR • = ($100 mil) (1 – 8.64) (-.03) • = (100 mil) (-7.64) (-.03) • = $ + 22.92 mil.

  33. Cross Price Elasticity of Demand + Substitutes - Complements

  34. Example 3: Impact of a change in a competitor’s price • According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is 9.06. • If MCI and other competitors reduced their prices by 4%, what would happen to the demand for AT&T services?

  35. Answer • AT&T’s demand would fall by 36.24 percent!

  36. Income Elasticity + Normal Good - Inferior Good

  37. Demand Functions • Mathematical representations of demand curves • Example: • X and Y are substitutes (coefficient of PY is positive) • X is an inferior good (coefficient of M is negative)

  38. Elasticity Calculation

  39. Specific Demand Functions • Linear Demand Own Price Cross Price Income Elasticity Elasticity Elasticity

  40. EX,Px Calculation Given D Function Equation • X = 10 – 2Px + 3PY – 2M = 10 – 2Px + 3(4) – 2(1)  X = 20 – 2PX  Px = 10 - .5X

  41. EX,Px at PX = 4 ?

  42. EX,I Calculation Given D Equation • X = 10 – 2PX + 3PY – 2I = 10 – 2(1) + 3(4) – 2I X = 20 – 2I

  43. EX,I at I = 2 ?

  44. Log-Linear Demand • Own Price Elasticity: X • Cross Price Elasticity: Y • Income Elasticity: M

  45. Summary • Elasticities are tools you can use to quantify the impact of changes in prices, income, and advertising on sales and revenues. • Given market or survey data, regression analysis can be used to estimate: • Demand functions • Elasticities • A host of other things, including cost functions • Managers can quantify the impact of changes in prices, income, advertising, etc.

  46. Use of Elasticities • Pricing • Managing cash flows • Impact of changes in competitors’ prices • Impact of economic booms and recessions • Impact of advertising campaigns • And lots more!

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