PowerPoint Slides © Michael R. Ward, UTA 2014

Some Theory BackgroundEcon 5313

• Lots of formulas and math with this chapter. Trust me, there is a payoff

• Demand curves slope downward• For two reasons:

• People value the first unit more than the second, etc.• Different people value the product differently

DemandEcon 5313

Q

P • A Typical Demand “Curve”

• Purely hypothetical

MR from DemandEcon 5313

P Q Revenue MR MC Profit$7.00 1$6.00 2$5.00 3$4.00 4$3.00 5$2.00 6$1.00 7

• Very simple demand curve• Calculate Revenues

MR from DemandEcon 5313

P Q Revenue MR MC Profit$7.00 1 $7.00$6.00 2 $12.00$5.00 3 $15.00$4.00 4 $16.00$3.00 5 $15.00$2.00 6 $12.00$1.00 7 $7.00

• Multiply price (P) times quantity (Q)• Rises then falls

MR from DemandEcon 5313

P Q Revenue MR MC Profit$7.00 1 $7.00$6.00 2 $12.00 $5.00$5.00 3 $15.00 $3.00$4.00 4 $16.00 $1.00$3.00 5 $15.00 -$1.00$2.00 6 $12.00 -$3.00$1.00 7 $7.00 -$5.00

• MR is the change in revenue from selling another unit• Falls fast

MR from DemandEcon 5313

P Q Revenue MR MC Profit$7.00 1 $7.00 $1.50$6.00 2 $12.00 $5.00 $1.50$5.00 3 $15.00 $3.00 $1.50$4.00 4 $16.00 $1.00 $1.50$3.00 5 $15.00 -$1.00 $1.50$2.00 6 $12.00 -$3.00 $1.50$1.00 7 $7.00 -$5.00 $1.50

• Compare MR to a constant MC of $1.50• How many to produce?

MR from DemandEcon 5313

P Q Revenue MR MC Profit$7.00 1 $7.00 $1.50 $5.50$6.00 2 $12.00 $5.00 $1.50 $9.00$5.00 3 $15.00 $3.00 $1.50 $10.50$4.00 4 $16.00 $1.00 $1.50 $10.00$3.00 5 $15.00 -$1.00 $1.50 $7.50$2.00 6 $12.00 -$3.00 $1.50 $3.00$1.00 7 $7.00 -$5.00 $1.50 -$3.50

• For 1, 2, & 3, MR > MC so profits rise• For 4+, MR < MC so profits fall

Why Does MR Fall So Fast?Econ 5313

P*

Q

P

Q*

• Current price P* yields quantity Q*

• What does the blue area represent?

• What happens when we reduce the price a bit?

Why Does MR Fall So Fast?Econ 5313

Q

P• Reduce price

means you sell more units.

• Revenue increases by the green area.

• But reduced price means less revenue on each unit.

• Revenue decreases by red area.

• Net effect is “Marginal Revenue”

Why Does MR Fall So Fast?Econ 5313

• Another hypothetical: Suppose you want to sell one more unit. How much does your revenue go up?

• To sell that one more unit, you have to reduce the price just a smidgeon. So it earns you something just less than the current price.

• But, if you lower the price by even a smidgeon, you earn slightly less on each unit you would have sold before. This decrease in revenue is also “marginal” to your decision to sell another unit.

Why Does MR Fall So Fast?Econ 5313

• So there are two effects:• Gain P-smidgeon on one more unit.• Lose smidgeon×Q on all “infra-marginal” units.

• Both effects make MR < P because of these smidgeons.• But how about the cotton farmer example from last time?

• He had MR = P• There he pretty much could sell as much as he wanted without

reducing his price by even a smidgeon• This means he does not lose any revenue on “infra-marginal”

sales• But this is the extreme case

Why Does MR Fall So Fast?Econ 5313

• You want to set MR = MC.• But you have P > MR.• So do you want to find the spot on the demand curve

where P = MC?• No!• Revenue = P×Q• Cost = MC×Q + FC• Profit = Revenue – Cost = P×Q – MC×Q - FC = -FC < 0

• Need P > MR = MC just to break even• How much greater?• Depends on flatness or steepness of demand

Why Does MR Fall So Fast?Econ 5313

Q

P • If demand is flatter, reducing price increases quantity more

• Revenue increases by more

• MR is bigger

Why Does MR Fall So Fast?Econ 5313

Q

P • If demand is steeper, reducing price increases quantity less

• Revenue increases by less

• MR is smaller

Taxes imply Price IncreasesEcon 5313

• In 1980, Mayor Marion Berry raised the tax on gasoline in Washington, DC by 6%.

• What do you think happened to gas tax revenue?

ElasticityEcon 5313

• We measure flatness or steepness with elasticity• Why not slope?• How do you measure elasticity?• Definition: Arc (price) elasticity:

• e = [(q1-q2)/(q1+q2)] [(p1-p2)/(p1+p2)]

• Need two points on a demand curve (1 and 2)

Elasticity ExperimentEcon 5313

• Form groups of 4-5 with neighbors• You have five dollars that you can spend on each of four

items. You must spend all you “income.” Make your choices under “Individual Quantities.” There will be three treatments and all three are completely different and unrelated.

• First Treatment: Income = $5, Price(Coke) = $1, Price(Fritos) = $1, Price(Snickers Bar) = $1, Price(Granola Bar) = $1

Elasticity ExperimentEcon 5313

• You have five dollars that you can spend on each of four items. You must spend all you “income.” Make your choices under “Individual Quantities.”

• First Treatment: Income = $5, Price(Coke) = $1, Price(Fritos) = $1, Price(Snickers Bar) = $2, Price(Granola Bar) = $1

Elasticity ExperimentEcon 5313

• You have five dollars that you can spend on each of four items. You must spend all you “income.” Make your choices under “Individual Quantities.”

• First Treatment: Income = $5, Price(Coke) = $1, Price(Fritos) = $1, Price(Snickers Bar) = $3, Price(Granola Bar) = $1

Elasticity ExperimentEcon 5313

• In your group, calculate the quantity demanded for each good and each treatment.

• What is the elasticity of demand for a snickers bar for your group when the price increased from $1 to $2?

• e = [(q1-q2)/(q1+q2)] [(p1-p2)/(p1+p2)]• What is the elasticity of demand for a snickers bar when

the price increased from $2 to $3?• Report group totals to me• For the market, what are the demand elasticities?• For the market, what are the cross-price elasticities with

granola?

The Ugly MathEcon 5313

• Proposition: MR = P(1-1/|e|)• Proof(ish)

• MR = DRev/DQ• ≈ (DQP+DPQ)/DQ • = P(DQ/DQ)+(DPQ/PDQ) • = P[1+(DP/DQ)(Q/P)] • = P[1+(DP/P)/(DQ/Q)]• = P[1+%DP/%DQ]• = P(1+1/e)• MR = P(1-1/|e|)

• So, with cotton example, e → neg. infinity and MR → P

Elastic and InelasticEcon 5313

• If the demand for Nike sneakers is inelastic (|e|<1), should Nike raise or lower price?• Implies MR < 0

• If the demand for Amana ovens is elastic (|e|>1), should Amana raise or lower price?• Implies MR > 0 but we do not know relative to MC

Actual versus Desired MarkupEcon 5313

• Need to know if MR > MC • But, MR = P(1-1/|e|)• So need to know if P(1-1/|e|) > MC• But this is P-P/|e| > MC• Or, P-MC > P/|e|• Or, (P-MC)/P > 1/|e|• Or, actual markup > desired markup

• actual markup = (P-MC)/P • desired markup = 1/|e|

Using ElasticitiesEcon 5313

• Example: e= –2, p=$10, mc= $8, should you raise prices?• Actual is (10-8)/10 = 0.2• Desired is 1/|-2| = 0.5• Actual < Desired• Do you know how much to raise price?

• Example: Markup in 3-liter coke is 2.7%, should you raise price?• This is (P-MC)/P = 0.027• It would be correct only if 1/|e| = 0.027• We would need e = -37• Realistic value for e?• Other reasons?

What makes demand elastic?Econ 5313

• More complements make demand less elastic• Ex iPod and iTunes

• Products with close substitutes are more elastic• Ex iPhone and Android phones

• Demand for an individual brand is more elastic than industry aggregate demand • More close substitutes

• Products with smaller shares often have lower margins• More likely to be “fringe” competitors

Brand versus Industry ElasticitiesEcon 5313

• The individual brand demand elasticity is approximately equal to the industry elasticity divided by the brand share • First approximation e(brand) = e(market)/share(brand)

• Helpful because we are more likely to know industry elasticity than individual product elasticity

• Discussion: Suppose that the elasticity of demand for running shoes is –0.4 and the market share of a Nike brand running shoe is 20%.

• What is the price elasticity of demand for Nike running shoes?

Linear Rule of ThumbEcon 5313

• Marketing Dept. estimates linear demand for you. (i.e., p = pmax - a×q)

• Linear Demand Curve Formula, e= p / (pmax -p)• Alternatively, e= p / (a×q)

Laws of DemandEcon 5313

• First law of demand: e < 0 ( as price goes up, quantity goes down)• Do all demand curves slope downward?

• Second law of demand: in the long run, |e| increases• Why does time matter?

• A bank experimented with increasing ATM fees. After a month they saw a slight drop in usage but this was more than offset by the higher fees. Should they decide to keep the higher fees at the end of the month?

Laws of DemandEcon 5313

• Third law of demand: as price increases, demand curves become more price elastic, |e| increases• Why would this be the case?

• Give an example of the third law of demand• True in the Snickers experiment?

Other ElasticitiesEcon 5313

• Own-price elasticity of demand is the most important elasticity. But there are others.

• Income elasticity• Cross-price elasticity• Advertising elasticity• These are usually used in forecasting exercises

• We are moving into a new area with 50% higher income. If the income elasticity is 0.8, how will sales be affected?

• Our competitor raised his price 10%. If the cross-price elasticity is 2, how will our sales be affected?

• Our advertising budget doubled. If the advertising elasticity is 0.5, how will our sales be affected?

Stay-even AnalysisEcon 5313

• Stay-even analysis tells you how many sales you need when changing price to maintain the same profit level

• Q1×(P1-MC) - FC = Q0×(P0-MC) - FC

• Q1 = Q0×(P0-MC)/(P1-MC)

• You know Q0, P0 and MC and are considering P1. Just how many units would you have to sell to “stay even?”

• Calculate Q1 • Is this “reasonable” given general notions about demand?• When combined with more general information about the

elasticity of demand, the analysis gives a quick answer to the question of whether or not changing price makes sense.

Music Survey DataEcon 5313

• Similar to what you might get from Marketing Dept.• How to use?

From the Blog• Chapter 6• Uber Pricing• Turkeys are cheaper at Thanksgiving• Market Research on Meth• Estimating Demand Functions• Smart Parking Meters

Econ 5313

Main Points• Demand is the number of units bought at different prices• Pricing is an extent decision:

• MR > MC => increase Q and visa versa

• Elasticity = [(q1-q2)/(q1+q2)] [(p1-p2)/(p1+p2)]• MR>MC (P-MC)/P > 1/|e|

• Compare “actual” markup to “desired” markup

• Factors that affect elasticity: • Substitutes (More elastic with more close substitutes)• Complements (Less elastic with more close complements)• Product breadth (Industry versus Brand)• Time (More elastic as time elapses)• Price level (More elastic as price rises)

Econ 5313

Main Points• Other elasticities can be used for forecasting

• Income, cross-price, advertising• %DQuantity = Factor elasticity × %DFactor

• Stay-even analysis can be used to determine Q necessary for a price change• %DQuantity = %DPrice / (%DPrice + margin)• Is predicted quantity loss less than stay-even quantity?

Econ 5313