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) (Point) price elasticity = (1/slope)*(P /Q) is used to estimate price elasticity of demand at a point on the demand curve. 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.

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 (this comes from the law of diminishing returns) – if you are really thirsty the first bottle of water will give you a lot more satisfaction than the second etc. Consumer surplus = value to consumer - price paid. (think back to the example in Chapter 1 and 2 about the bottle of water in the vending machine

Definition: Demand curves are functions that relate the price of a product to the quantity demanded by consumers Think of yourself as a consumer. How would you respond to increases in price – would you want to consume more or less. Similarly how would you respond to decreases in price – would you want to consume more or less. Also think of your capacity to consume – in terms of your budget: an increase in prices would restrict your ability to consume more, while a decrease in prices would enhance your ability to consume more. Thus consumer demand depends on an individuals willingness and ability to consume products Thus as prices increase quantity demanded will decrease and vice-versa.

Background: consumer surplus and demand curves (cont.) Hot dog consumer Values first dog at $5, next at $4... fifth at $1 Consumers choose their consumption to maximize their surplus Note that if hot dogs price is $3, consumer will purchase 3 hot dogs

Background: aggregate demand Aggregate Demand: the buying behavior of a group of consumers; a total of all the individual demand curves. Example: Discussion: Why do aggregate demand curves slope downward? Role of heterogeneity? How to estimate?

Pricing trade-off Pricing is an extent decision i.e. you want to change prices as long as the MR from the price change is at least as large as the MC. 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

Extent Decision 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

To calculate MR, we took the change in TR between two rows, and divided by the change in Quantity between two rows (which is 1 in this example) The MC is fixed at 1.50 Should we produce the first unit ? MR is $7, MC is $1.50 so by producing 1 unit we add $5.50 to profits. Produce 2 ? MR = $5 > MC = $1.50, thus by producing 2 units you will add $3.50 to total profits. Similarly we should produce the third unit. What about 4: MR = 1 < MC = 1.50 thus we will subtract 0.50 from profits if we produce 4 units Thus the optimal quantity is 3 units

How do we estimate MR? Doing what we did in the previous two slides step by step is a painstaking affair. Can we make it easier? Yes – by estimating 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. Numerator < Denominator, since TR = PxQ, Price will have a larger effect on TR change than Q, so TR will follow P If |e| is greater than one, demand is said to be elastic. Denominator < Numerator, Q will have a larger effect on TR change than P. Thus TR will follow Q.

Estimating elasticities (cont.) Why is elasticity important. Think of the difference in consumption behavior between gasoline and plasma TVs. An increase in price doesn’t necessary lead to a much lower consumption of gasoline because we have to use our cars. However an increase in price of TVs will lead to substantial decrease in consumption. Gasoline is a necessity and plasma tv is a luxury. Elasticity measures the difference in a quantifiable way. Calculation of (point) elasticity: e = (1/slope)*(P/Q) Example: Suppose P=13-.5Q, value of slope =.5, for Q=10, P=$8, value of elasticity = 1.6 To Increase TR If Demand is elastic, Reduce P, so Q increases and TR Increases If Demand is inelastic, Increase P so TR increases.

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?

Formula: elasticity and MR The following formula can be used to estimate MR that will help us simplify the extent decision making process 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 How do we further simplify our extent decision making? MR>MC is equivalent to P(1-1/|e|)>MC or P-(P/|e|) >MC or (P-MC)>(P/|e|) or (P-MC)/P>1/|e| or Actual Markup (which is the definition of the left hand side) is greater than Optimal Markup (which is the right hand side)

If actual markup > optimal markup it means that MR>MC, so reduce prices and sell more; and vice versa. Logically speaking, if Actual Markup is greater than the Optimal Markup that means you are charging too high a price (for profit maximization) and hence you need to lower your prices; and vice versa if Actual Markup is Less than Optimal Markup (increase prices) Thus for optimal pricing (profit maximization) or for MR = MC it has to be true that the actual markup = optimal markup or (P- MC)/P=1/|e| Discussion: e= –2, p=$10, mc= $8, should you raise or reduce prices? How do we solve this problem ? Remember, the value of elasticity is 2, so plug in the values of P and MC in the actual markup formula and the value of e in the optimal markup formula i.e. Actual Markup is (10-8)/10 = 0.2 Optimal Markup is ½ =0.5 Thus, Actual Markup < Optimal Markup so Increase Prices.

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.

Other elasticities 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 Real income grew by 3.5% in the United States. Estimate WSJ demand

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