Finance 30210: Managerial Economics Competitive Pricing Techniques
Once production decisions have been made, a firm can be represented by it’s cost function Total costs of production are a function of quantity produced MC For pricing decisions, we focus on marginal cost $1.50 56 An increase in production from 55 to 56 increased total costs by $1.50
We will be assuming that pricing decisions are being made to maximize current period profits Total Costs (note that total costs here are economic costs. That is, we have already included a reasonable rate of return on invested capital given the risk in the industry) Profits Total Revenues equal price times quantity
As with any economic decision, profit maximization involves evaluating every potential sale at the margin How do my costs change if I increase my sales by 1? (Marginal Costs) How do my profits change if I increase my sales by 1? How do my revenues change if I increase my sales by 1? (Marginal Revenues)
As with any economic decision, profit maximization involves evaluating every potential sale at the margin MC MR=MC: Profits are Maximized Producer Surplus MR Q* MR>MC: Profits are increasing MR>MC: Profits are Decreasing Profit = Producer Surplus – Fixed Costs
Recall that in a perfectly competitive world, price equals marginal revenue Firm Level Market Dollars Dollars Supply MC P* MR P* Producer Surplus Producer Surplus Demand 0 Q 0 Q* The prevailing price (treated as a constant by each firm) becomes that firms marginal revenue The market determines the equilibrium price
Recall the characteristics we laid out for a competitive market #1: Many buyers and sellers – no individual buyer/firm has any real market power #2: Homogeneous products – no variation in product across firms #3: No barriers to entry – it’s costless for new firms to enter the marketplace #4: Perfect information – prices and quality of products are assumed to be known to all producers/consumers Can you think of situations where all these assumptions hold?
When making pricing decisions, you need to be aware of what your market structure is Market Structure Spectrum Monopoly Perfect Competition The market is supplied by many producers – each with zero market share One Producer With 100% market share Firm Level Demand DOES NOT equal industry demand Firm Level Demand EQUALS industry demand
Measuring Market Structure – Concentration Ratios Suppose that we have the following three industries… • Industry B • 22 Firms in the industry • The two largest firms have 20% market share each • The remaining 20 Firms have 3% market share each • Industry C • 8 Firms in the industry • The 4 largest firms have 15% market share each • The remaining 4 Firms have 10% market share each • Industry A • 10 Firms in the industry, each with an equal 10% market share Which industry is the most competitive? Which is the least?
Let’s plot out the three industries and take a look… Cumulative Market Share 100 80 60 40 20 # of Firms 0 0 1 2 3 4 5 6 7 8 9 10 22
Concentration ratios look at the cumulative market share of the N largest firms Cumulative Market Share 100 80 60 40 20 # of Firms 0 0 1 2 3 4 5 6 7 8 9 10 22 20 40 80 100 100 40 46 58 64 100 30 60 100 100 100
Concentration Ratios in US manufacturing; 1947 - 1997 Concentration Ratios in US by Industry Aggregate manufacturing in the US hasn’t really changed since WWII Concentration ratios vary significantly by industry!!
Measuring Market Structure: The Herfindahl-Hirschman Index (HHI) = Market share of firm i HHI = 2,000
The HHI index penalizes a small number of total firms Cumulative Market Share 100 A 80 HHI = 500 B HHI = 1,000 40 20 0 0 1 2 3 4 5 6 7 10 20
The HHI index also penalizes an unequal distribution of firms Cumulative Market Share 100 80 HHI = 500 HHI = 555 A 40 B 20 0 0 1 2 3 4 5 6 7 10 20
= Market share of firm i Cumulative Market Share 100 80 60 40 20 # of Firms 0 0 1 2 3 4 5 6 7 8 9 10 22
In a monopolized market, the single firm in the market faces the industry demand curve Individual Market Dollars Dollars MC Producer Surplus P MR Demand 0 0 Q Q The single firm in the market has profit maximized based off of where MR = MC Given the chosen quantity, industry demand determines price
In a world where firms have market power, they control their level of sales by setting their price. Suppose that you have the following demand curve (A relationship between price and quantity): Your listed price Total Sales For example: If you were to set a price of $20, you can expect 60 sales
We could also talk about inverse demand (a relationship between quantity and price): Your target for sales A price that will hit that target For example: If you wanted to make 40 sales, you could set a $30 price
Either way, if we know price and total sales, we can calculate revenues Total Revenues = Price*Quantity Total Revenues =($30)(40) = $1200 Can we increase revenues past $1200 and, if so, how?
Either way, if we know price and total sales, we can calculate revenues Total Revenues =($35)(30) = $1050 Total Revenues =($25)(50) = $1250 Turns out lowering price was the right thing to do to raise revenues.
Initially, you have chosen a price (P) to charge and are making Q sales. Total Revenues = PQ D Suppose that you want to increase your sales. What do you need to do?
Your demand curve will tell you how much you need to lower your price to reach one more customer This area represents the revenues that you lose because you have to lower your price to existing customers This area represents the revenues that you gain from attracting a new customer D
Your demand curve will tell you how much you need to lower your price to reach one more customer Revenues =($30)(40) = $1200 • $29.50 From additional sale • $20 loss from lowering price • $9.50 increase in revenues ($.50)(40) =$20 Revenues =($29.50)(41) = $1209.50 ($29.50)(1) =$29.50 D
An elasticity of demand that is greater than 1 in absolute value indicates that lowering price will increase revenues .80% -1.70% 2.5% Total Revenues =($30)(40) = $1200 Total Revenues =($29.50)(41) = $1209.5 % Change in revenues = .80%
An elasticity of demand that is less than 1 in absolute value indicates that raising price will increase revenues 3.75% 5.00% -1.25% % Change in revenues = 3 .75% Total Revenues =($10.50)(79) = $829.50 Total Revenues =($10)(80) = $800
Revenues are maximized when the elasticity of demand equals -1 Elasticity is less than -1: raise price Elasticity is greater than -1: lower price Quantity = 50 Price =$25 Elasticity = -1 Max Revenues Quantity = 50 Price =$25 Revenues = $1,250
Because you must lower your price to existing customers to attract new customers, marginal revenue will always be less than price Q = 40 P = $30 Revenues = ($30)(40) = $1200 Q = 41 P = $29.50 Revenues = ($29.50)(41) = $1209.50 P = $30 Marginal Revenues = $9.50 MR = $9.50
Note that because we have ignored the cost side, we are assuming marginal costs are equal to zero! Revenues = $1250 P = $25 P MR = MC = $0 MR
Now, let’s bring in the cost side. For simplicity, lets assume that you face a constant marginal cost equal to $20 per unit. Continuing on down…
A profit maximizing price sets marginal revenue equal to marginal cost. Marginal revenue is the change in total revenue (i.e. the slope) Slope = 20 Profits = $450
A profit maximizing price sets marginal revenue equal to marginal cost Price = $35 Quantity = 30 Elasticity = -2.36 P = $35 Profit = ($35-$20)*30 = $450
A profit maximizing strategy equates marginal revenues with marginal costs… Marginal Revenue D Firm’s will be charging a markup over marginal cost where the markup is related to the elasticity of demand
A profit maximizing price sets marginal revenue equal to marginal cost Price = $35 Quantity = 30 Elasticity = -2.36 P = $35 Profit = ($35-$20)*30 = $450 This is not a coincidence. A monopoly sets a markup that is inversely proportional to the elasticity of demand!
Markups for Selected Industries Suppose that we assumed the automobile industry were monopolized… So, a 1% increase in automobile prices will lower sales by 2.3%
Perfectly competitive firms face demand curves that are perfectly elastic (infinite elasticity. Hence, the markup (and profits) are zero) Industry Firm Level D D Note: Industry elasticities in competitive industries are always less than 1 (industry profits could be increased by raising price!)
Is it possible to attract new customers without lowering your price to everybody? Loss from charging existing customers a lower price Gain from attracting new customers You need to be able to identify customer types and prevent resale!! D
Let’s suppose that Notre dame has identified three different consumer types for Notre Dame football tickets. Further, assume that Notre Dame has a marginal cost of $20 per ticket. Dollars Alumni $120 Faculty $80 If Notre Dame had to set one uniform price to everybody, what price would it set? Students $40 0 40,000 70,000 80,000
Let’s suppose that Notre dame has identified three different consumer types for Notre Dame football tickets. Further, assume that Notre Dame has a marginal cost of $20 per ticket. Dollars Alumni $120 Faculty $80 Students $40 $20 MC 0 40,000 70,000 80,000
Now, suppose that Notre Dame can set up differential pricing. • Pricing Schedule • Regular Price: $120 • Faculty/Staff: $80 • Student: $40 Dollars Alumni $120 Faculty $80 Students $40 $20 MC What would Notre Dame need to do to accomplish this? 0 40,000 70,000 80,000
Example: DVD codes are a digital rights management technique that allows film distributors to control content, release date, and price according to region. DVD coding allows for distributors to price discriminate by region.
Suppose that you are the pricing for the DVD release of Avatar Your marginal costs are constant at $4and you have the following demand curves: US Sales European Sales + Total Sales
Here is what our aggregate demand looks like Price At a price above $24, Europeans aren’t buying. You only have the American market $36 At a price below $24, we now have both markets. $24 + Quantity 3
Option #1: We could charge a common price to everyone… Solve for inverse demand Price $36 Calculate total revenues Equate marginal revenues to marginal costs $24 $17 $4 Quantity 3 6.5
Option #2: Why don’t we just charge them different prices? America Europe Price Price $36 $80,000 $24 $20 $14 $4 $4 Quantity Quantity 4 2.5
Why is movie theatre popcorn so expensive? Dollars General Public $15 This would be an easy price discrimination problem… Senior Citizens $8 • Pricing Schedule • Regular Price: $15 • Senior Citizens: $8 0 200 300
Now, suppose that the identities are unknown? How can the theatre extract more money out of the avid moviegoer? Dollars Avid Moviegoer $15 Occasional Moviegoer As long as the total price (popcorn + ticket) is $15 or less, avid moviegoers will still go $8 0 200 300 Which pricing option would you choose?
Suppose that Disneyworld knows something about the average consumer’s demand for amusement park rides. Disneyworld has a constant marginal cost of $.02per ride Dollars .50 Demand 0 50
As a first pass, we could solve for a profit maximizing price per ride Dollars .51 Profit = $24.01 .02 MC Demand 0 49 MR