Chapter 6 Simple Pricing

Chapter 6 – Summary of main points Aggregate demand or market demand is the total number of units that will be purchased by a group of consumers at a given price. Pricing is an extent decision. Reduce price (increase quantity) if MR > MC. Increase price (reduce quantity) if MR < MC. The optimal price is where MR = MC. Price elasticity of demand, e = (% change in quantity demanded) ÷ (% change in price) Estimated price elasticity = [(Q1 - Q2)/(Q1 + Q2)] ÷ [(P1 - P2)/(P1 + P2)] is used to estimate demand from a price and quantity change. If |e| > 1, demand is elastic; if |e| < 1, demand is inelastic. %ΔRevenue ≈ %ΔPrice + %ΔQuantity Elastic Demand (|e| > 1): Quantity changes more than price. Inelastic Demand (|e| < 1): Quantity changes less than price.

Chapter 6 – Summary (cont.) MR > MC implies that (P - MC)/P > 1/|e|; in words, if the actual markup is bigger than the desired markup, reduce price Equivalently, sell more Four factors make demand more elastic: Products with close substitutes (or distant complements) have more elastic demand. Demand for brands is more elastic than industry demand. In the long run, demand becomes more elastic. As price increases, demand becomes more elastic. Income elasticity, cross-price elasticity, and advertising elasticity are measures of how changes in these other factors affect demand. It is possible to use elasticity to forecast changes in demand: %ΔQuantity ≈ (factor elasticity)*(%ΔFactor). Stay-even analysis can be used to determine the volume required to offset a change in costs or prices, which is how businesses use marginal analysis.

Introductory anecdote: Hot Wheels Mattel: introduced Hot Wheels in 1968, kept price below $1.00 for 40 years, even as production costs rose Finally tested a price increase, experienced profits increase of 20% Why? Profit=(P-C)xQ Businesses tend to focus on C and Q, neglect P In many instances, companies can make money by simply raising prices

Background: consumer surplus and demand curves First Law of Demand - consumers demand (purchase) more as price falls, assuming other factors are held constant. Consumers make consumption decisions using marginal analysis, consume more if marginal value > price But, the marginal value of consuming each subsequent unit diminishes the more you consume. Consumer surplus = value to consumer - price paid Definition: Demand curves are functions that relate the price of a product to the quantity demanded by consumers

Background: consumer surplus and demand curves (cont.) Pizza consumer Values first slice at $5, next at $4 . . . fifth at $1 Note that if pizza slice price is $3, consumer will purchase 3 slices NEED TO REPLACE CHART WITH NEW GRAPHICS.

Background: aggregate demand Aggregate Demand: the buying behavior of a group of consumers; a total of all the individual demand curves. To construct demand, sort by value. Discussion: Why do aggregate demand curves slope downward? Role of heterogeneity? How to estimate? REPLACE WITH BETTER GRAPHIC

Pricing trade-off Pricing is an extent decision Profit= Revenue - Cost Demand curves turn pricing decisions into quantity decisions: “what price should I charge?” is equivalent to “how much should I sell?” Fundamental tradeoff: Lower price sell more, but earn less on each unit sold Higher price sell less, but earn more on each unit sold Tradeoff created by downward sloping demand

Marginal analysis of pricing Marginal analysis finds the profit increasing solution to the pricing tradeoff. It tells you only whether to raise or lower price, not . Definition: marginal revenue (MR) is change in total revenue from selling extra unit. If MR>0, then total revenue will increase if you sell one more. If MR>MC, then total profits will increase if you sell one more. Proposition: Profits are maximized when MR = MC

Example: finding the optimal price Start from the top If MR > MC, reduce price (sell one more unit) Continue until the next price cut (additional sale) until MR<MC REPLACE WITH BETTER GAPHIC

How do we estimate MR? Price elasticity is a factor in calculating MR. Definition: price elasticity of demand (e) (%change in quantity demanded)  (%change in price) If |e| is less than one, demand is said to be inelastic. If |e| is greater than one, demand is said to be elastic. NEED BETTER GRAPHIC

Estimating elasticities Definition: Arc (price) elasticity= [(q1-q2)/(q1+q2)]  [(p1-p2)/(p1+p2)]. Discussion: Why, when price changes from $10 to $8, does quantity changes from 1 to 2? Example: On a promotion week for Vlasic, the price of Vlasic pickles dropped by 25% and quantity increased by 300%. Is the price elasticity of demand -12? HINT: could something other than price be changing? Note that in many examples, the arc price formula is not used for simplicity Answer: In the Vlasic example, price of Heinz is coming off promotion and the Vlasic price is being advertised in the newspaper, in store coupons, and end of aisle displays.

Estimating elasticities (cont.) 3-Liter Coke Promotion (Instituted to meet Wal-Mart promotion) Compute price elasticity of 3 liter coke; cross price elasticity of 2 liter coke with respect to 3 liter price; Extra credit: aggregate elasticity of demand for 2 and 3 liter coke. (compute change in price index and change in liters consumed. REPLACE WITH BETTER GRAPHIC

Intuition: MR and price elasticity Revenue and price elasticity are related. %Rev ≈ %P + %Q Elasticity tells you the size of |%P| relative to |%Q| If demand is elastic If P↑ then Rev↓ If P↓ then Rev↑ If demand is inelastic If P↑ then Rev↑ If P↓ then Rev↓ Discussion: In 1980, Marion Barry, mayor of the District of Columbia, raised the sales tax on gasoline sold in the District by 6%. What happened to gas sales and availability of gas? Why? ANSWER to question: tax revenue declined by 40% because demand for gasoline in the district of columbia is very price elastic.

Formula: elasticity and MR Proposition: MR = P(1-1/|e|) If |e|>1, MR>0. If |e|<1, MR<0. Discussion: If demand for Nike sneakers is inelastic, should Nike raise or lower price? Discussion: If demand for Nike sneakers is elastic, should Nike raise or lower price?

Elasticity and pricing MR>MC is equivalent to P(1-1/|e|)>MC P>MC/(1-1/|e|) (P-MC)/P>1/|e| Discussion: e= –2, p=$10, mc= $8, should you raise prices? Discussion: mark-up of 3-liter Coke is 2.7%. Should you raise the price? Discussion: Sales people MR>0 vs. marketing MR>MC.

What makes demand more elastic? Products with close substitutes have elastic demand. Demand for an individual brand is more elastic than industry aggregate demand. Products with many complements have less elastic demand.

Describing demand with price elasticity First law of demand: e < 0 ( as price goes up, quantity goes down). Discussion: Do all demand curves slope downward? Second law of demand: in the long run, |e| increases. Discussion: Give an example of the second law of demand.

Describing demand (cont.) Third law of demand: as price increases, demand curves become more price elastic, |e| increases. Discussion: Give an example of the third law of demand. REPLACE WITH BETTER GRAPHIC

Other elasticities Inferior (neg.) vs. normal (pos). Definition: income elasticity measures the change in demand arising from a change in income (%change in quantity demanded)  (%change in income) Inferior (neg.) vs. normal (pos). Definition: cross-price elasticity of good one with respect to the price of good two (%change in quantity of good one)  (%change in price of good two) Substitute (pos.) vs. complement (neg.). Definition: advertising elasticity; a change in demand arising form a change in advertising (%change in quantity)  (%change in advertising) . Discussion: The income elasticity of demand for WSJ is 0.50. Real income grew by 3.5% in the United States. Estimate WSJ demand

Stay-even analysis Stay-even analysis tells you how many sales you need when changing price to maintain the same profit level Q1 = Q0*(P0-VC0)/(P1-VC0) When combined with information about the elasticity of demand, the analysis gives a quick answer to the question of whether or not changing price makes sense. To see the effect of a variety of potential price changes, we can draw a stay-even curve that shows the required quantities at a variety of price levels. Derivation of formula Profit0 = P0*Q0 – VC0*Q0 – FC0 Profit1 = P1*Q1 – VC0*Q1 – FC0 Set equal and solve for Q1

Stay-even curve example Note that if demand is elastic, price cuts increase revenue When demand is inelastic, price increases will increase revenue REPLACE WITH BETTER GRAPHIC

Extra: quick and dirty estimators Linear Demand Curve Formula, e= p / (pmax-p) Discussion: How high would the price of the brand have to go before you would switch to another brand of running shoes? Discussion: How high would the price of all running shoes have to go before you should switch to a different type of shoe?

Extra: market share formula Proposition: The individual brand demand elasticity is approximately equal to the industry elasticity divided by the brand share. Discussion: Suppose that the elasticity of demand for running shoes is –0.4 and the market share of a Saucony brand running shoe is 20%. What is the price elasticity of demand for Saucony running shoes? Proposition: Demand for aggregate categories is less-elastic than demand for the individual brands in aggregate.

Alternate introductory anecdote In 1994, the peso devalued by 40% in Mexico Interest rates and unemployment shot up Overall economy slowed dramatically and consumer income fell Concurrently, demand for Sara Lee hot dogs declined This surprised managers because they thought demand would hold steady, or even increase, since hot dogs were more of a consumer staple than a luxury item. Surveys revealed the decline was mostly confined to premium hot dogs And, consumers were using creative substitutes Lower priced brands did take off but were priced too low. Failure to understand demand and to price accordingly was costly Substitution to cat food mixed with eggs and rolled up in a tortilla.