Unit 4. Quantitative Demand Analysis (as functions of output level)

Inventory Sale Zebco management has expressed a desire to reduce its current inventory of fishing reels by 10%. What price change is most likely to achieve this goal?

Katrina Impact? In August 2005, Hurricane Katrina basically shut down the production of oil in the southern Gulf coast area, which produces about 10% of the crude oil consumed in the U.S. Transport Inc. is a trucking company that ships products all over the U.S. with a fleet of over 100 trucks. Immediately after Katrina this company is trying to figure out the hurricane’s impact on its short-term and long-term fuel costs. What are reasonable projections?

Expected Bid Price The FCC has announced plans to auction off a license for the right to sell wireless communication products and services in a market with a population of 15 million. Tellcomm management is considering submitting a bid on the license. Previous bids have averaged $80 million for markets averaging 10 million people. Tellcomm’s research department has also observed that previous bids have tended to increase by 1.4% for each 1% increase in population. What is your estimate of the minimum bid that will be required to acquire the new market’s license?

Reebock’s Response to Nike Reebock and Nike compete against each other in the athletic tennis shoe market. Reebock has observed Nike’s decision to decrease its prices by roughly 4%. What is likely to happen to the quantity sales of Reebock shoes if Reebock keeps its prices unchanged? How much will Reebock have to lower its price in order to maintain quantity sales at their previous level?

Let’s Maximize $ Sales The marketing team of Global Concepts has observed total annual sales of $1.104 million for the company when a price of $24 was charged. More recently, the company has had total annual sales of $1.320 million after it had raised its price to $33 for the year. The company’s statistician has just informed the marketing team that the firm’s demand curve has been linear and constant over this time period. If the marketing team would have had all of this information going into each of the previous years, what price should have been charged by the company in order to have maximized the dollar value of total company sales?

Empty Seats, Lost Revenue? Jane is a huge Rod Stewart fan and recently attended one of his concerts. At the concert, she noticed there were a number of empty seats. She concluded the organizers of the concert could have sold more tickets and made more money if they had charged a lower price for the concert. Do you agree or disagree with Jane?

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

‘Unit’ vs % Marginal Analysis Example: P1 = 10, Q1 = 20 P2 = 12, Q2 = 18 Slope: measures the ‘unit’ or ‘absolute’ changes in Y associated with a one unit change in X ΔP/ΔQ = +2/-2 = +1/-1 => A 1 unit change in P is associated with a 1 unit change in Q in the opposite direction Elasticity: measures the % change in Y associated with a 1% change in X Example: %ΔQ/%ΔP = -10/+20 = -.5/1 => A 1% change in P is associated with a .5% change in Q in the opposite direction

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

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

Revenue Concepts Concept/Definition If P = a – bx If P = a 1. TR = Total Revenue = total $ sales to firm = gross income = total $ cost to buyers = Px = (a-bx)x = ax-bx2 = ax 2. AR = Average Revenue = revenue per unit of output = TR/x = (ax-bx2)/x = a – bx = P = ax/x = a 3. MR = Marginal Revenue = additional revenue per unit of additional output = slope of TR curve = TR/x = TR/x = a – 2bx

Market & Firm D (Perfect Competition)

Revenue Concepts P = a

Revenue Concepts P=a-bQ

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

Proof of Max TR (P-Setting Firm) P = a – bQ (b>0) TR = aQ – bQ2 Slope of TR = a-2bQ = MR Max TR => MR = 0 => a-2bQ = 0 => Q = Max TR => P = a-bQ = a – b = a – = = mid pt of D curve

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

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

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”

Calculate the % change in income below Yr Income 1 40,000 2 42,000 % Change: = (income change/orig income) x 100 = (+2,0000/40,000) x 100 = (.05) x 100 = 5%

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

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

Elasticity Calculation

Types of Elasticities Type F E0 = own P PX EC cross P PY EI Income I EA advertising A

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

Summary of demand elasticity values always < 0 ignoring sign: < 1 => inelastic = 1 => unitary > 1 => elastic Ec > 0 => substitutes < 0 => complements E1 > 0 => normal good < 0 => inferior good

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

Perfectly Elastic & Inelastic Demand

Elasticity Calculation Overview = %ΔQ / %ΔF = (∂Q / ∂F) (F/Q) = (slope of Q wrt F) (given values of F&Q)

E0 Calculation E0 = EX,Px

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

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

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.

Managerial Uses of E0 E0 = %ΔQ / %ΔP Can use this 3-variable equation to solve for one variable given the value of the two other variables 1) project %ΔQ due to given %ΔP & E0 => %ΔQ = E0 x %ΔP 2) project %ΔP to be associated with given %ΔQ, given E0 => %ΔP = %ΔQ / E0

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?

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?

Answer Calls would increase by 25.92 percent!

Own-Price Elasticity and Total Revenue 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.

Change in TR (math) (If ↓P) TR1 = P1Q1 TR2 = P2Q2 = (P1+P)(Q1+Q) = P1Q1+PQ1+QP1+PQ TR = TR2 – TR1 = PQ1+QP1+PQ = PQ1+Q (P1+ P) = PQ1+QP2 = lost TR + added TR

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

Change in TR and E0

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

Cross Price Elasticity of Demand + Substitutes - Complements

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?

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

Income Elasticity + Normal Good - Inferior Good

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)

Elasticity Calculation

Specific Demand Functions Linear Demand Own Price Cross Price Income Elasticity Elasticity Elasticity

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

EX,Px at PX = 4 ?

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

EX,I at I = 2 ?

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

E0 & P volatility If E0 is inelastic (=> %ΔQ / %ΔP < 1), => %ΔP > %ΔQ => small changes in Q can result in big changes in P e.g. if E0 = -0.2 => .2% ΔQ => 1% ΔP => 1% ΔQ => 5% ΔP (=> %ΔP is 5 x %ΔQ) => 5% ΔQ => 25% ΔP

When Two or More D Factors Change Combined impact of: 1) 10% ↓PX if E0 = -.4 and 2) 10% ↑I if EI = +.2 %ΔQ due to: 10% ↓ PX = +4% 10% ↑ I = + 2% => combined = +6%

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.