ECN 453: Pricing and Monopoly PDF

ECN 453: Pricing and Monopoly Nicholas Vreugdenhil 1 / 34 Optimal pricing for a monopolist - Today we will discuss optimal pricing for a monopolist. - The ‘optimal price’ is the price which maximizes profit. - Why is this useful? - Policymake...

ECN 453: Pricing and Monopoly Nicholas Vreugdenhil 1 / 34 Optimal pricing for a monopolist - Today we will discuss optimal pricing for a monopolist. - The ‘optimal price’ is the price which maximizes profit. - Why is this useful? - Policymakers: understand how the monopolist is reducing welfare (due to its pricing) - Firm strategy: Suppose you are working as an economist in a firm that is launching a new product. How should you set prices for this new product to maximize profits? - (Most of what we will see today is review from your previous courses) 2 / 34 Plan 1. Pricing: example using a table 2. Pricing: MR=MC 3. Pricing: elasticities 4. Welfare costs of monopoly pricing and regulation 3 / 34 Plan 1. Pricing: example using a table 2. Pricing: MR=MC 3. Pricing: elasticities 4. Welfare costs of monopoly pricing and regulation 4 / 34 Pricing: example using a table - Question: - You are working as an economist in a firm and you know demand and total cost in the table below for a new product. - How should you set optimal prices (prices that maximize profit)? (In this example you can only sell whole numbers of the product.) price demand TR MR TC MC profit 6 0 4.5 5 1 5 4 2 5.5 3 3 6 2 4 6.5 1 5 7 5 / 34 Pricing: example using a table - Question: - You are working as an economist in a firm and you know demand and total cost in the table below for a new product. - How should you set optimal prices (prices that maximize profit)? (In this example you can only sell whole numbers of the product.) price demand TR MR TC MC profit 6 0 0 - 4.5 - -4.5 5 1 5 5 5 0.5 0 4 2 8 3 5.5 0.5 2.5 3 3 9 1 6 0.5 3 2 4 8 -1 6.5 0.5 1.5 1 5 5 -3 7 0.5 -2 - Idea: Keep raising prices so long as MR ≥ MC. 6 / 34 1. Pricing: example using a table 2. Pricing: MR=MC 3. Pricing: elasticities 4. Welfare costs of monopoly pricing and regulation 7 / 34 Pricing: MR=MC - In the previous example we could only sell whole numbers of the product. - When we can sell fractions of the product (which we usually assume) then the optimal price will occur when: MR = MC - This is a very important formula. - I will now apply the formula to solve for a monopolist’s optimal price. - (This should be a review from your previous courses) 8 / 34 Pricing: MR=MC: monopoly example - Question: - Suppose a monopolist faces the demand curve q = 2 − 15 p and has constant marginal cost of 5. What is the optimal price? 9 / 34 Pricing: MR=MC: monopoly example - Question: - Suppose a monopolist faces the demand curve q = 2 − 15 p and has constant marginal cost of 5. What is the optimal price? - Solution: - Compute MR from the demand curve using the ‘double the slope’ rule: MR = 10-10q - Next, use MR=MC to find the optimal quantity: 10 − 10q = |{z} 5 | {z } MR MC - Rearranging, get the optimal quantity: q ∗ = 0.5. - Finally, plug in q ∗ = 0.5 to the demand curve to get the optimal price: p ∗ = 10 − 5 × 0.5 = 7.5 9 / 34 Pricing: MR=MC: algorithm - Lets reiterate those steps again - follow this algorithm to find the optimal price for a monopolist given demand and marginal cost. 1. Get MR from the demand curve. (Use the ’double the slope’ trick if demand is linear.) 2. Use MR=MC; solve for the optimal quantity 3. Plug the optimal quantity back into the demand curve to get the optimal price - I’ll now repeat these steps using a graphical analysis. 10 / 34 Pricing: MR=MC: graph price MC D quantity 11 / 34 Pricing: MR=MC: graph 1. get MR from demand price MC MR D quantity 12 / 34 Pricing: MR=MC: 2. Use MR=MC; get q ∗ price MC MR D q∗ quantity 13 / 34 Pricing: MR=MC: 3. Get p ∗ from the demand curve. price Optimal price/quantity p∗ MC MR D q∗ quantity 14 / 34 Plan 1. Pricing: example using a table 2. Pricing: MR=MC 3. Pricing: elasticities 4. Welfare costs of monopoly pricing and regulation 15 / 34 Elasticity rule - There is a relationship between the optimal price and demand elasticity. - This is known as the elasticity rule: p − MC −1 = p e |{z} | {z } Margin Inverse elasticity - Note: divide by price on the left-hand-side not cost. - Equivalently we can isolate the price on the left-hand-side: MC p= 1 + 1e 16 / 34 Elasticity rule: math (optional) - The elasticity rule comes from MR = MC. Let’s unpack the math. 17 / 34 Elasticity rule: math (optional) - The elasticity rule comes from MR = MC. Let’s unpack the math. - If the inverse demand curve is p = P (q ) then total revenue is: TR = pq = P (q )q - Marginal revenue is then (applying the product rule): dTR dP (q )q MR = = = p + P 0 (q )q dq dq - Now, setting MR = MC: p + P 0 (q )q = MC dq p - Rearranging and applying e = dp q : p − MC q −1 = −P 0 (q ) = p p e 17 / 34  p −MC −1 Elasticity rule: p = e - Let’s check this rule holds for the example where we used MR = MC. - Before, we showed that given demand p = 10 − 5q and MC = 5, the optimal price is p ∗ = 7.5 and optimal quantity is q ∗ = 0.5. 18 / 34  p −MC −1 Elasticity rule: p = e - Let’s check this rule holds for the example where we used MR = MC. - Before, we showed that given demand p = 10 − 5q and MC = 5, the optimal price is p ∗ = 7.5 and optimal quantity is q ∗ = 0.5. p −MC 7.5−5 - Left-hand-side of the elasticity rule is: p = 7.5 = 1/3 - Right-hand-side of the elasticity rule requires computing the elasticity. First, rearrange demand so that q = 2 − 15 p. Then, the elasticity is: dq p 1 7.5 e= =− × = −3 dp q 5 0.5 - So, right-hand-side = −1 = −1 = 1/3 = left-hand-side e −3 - So, the elasticity rule works! 18 / 34 Using the elasticity rule - Why is the elasticity rule a useful way to think about optimal prices? - It turns out it is really useful for real-world empirical applications. Why? 19 / 34 Using the elasticity rule - Why is the elasticity rule a useful way to think about optimal prices? - It turns out it is really useful for real-world empirical applications. Why? - For example, suppose you are working as an economist in a firm and you are trying to optimally price a product. - Typically, you will know the MC. You can (using econometric methods which outside the scope of this course) find the demand elasticity. - Then just plug MC and demand elasticity into the elasticity rule to get the optimal price. 19 / 34 Plan 1. Pricing: example using a table 2. Pricing: MR=MC 3. Pricing: elasticities 4. Welfare costs of monopoly pricing and regulation 20 / 34 Welfare costs of monopoly pricing price B Monopolist’s price/quantity. pm A C Competitive ppc D MC qm qpc quantity 21 / 34 Welfare costs of monopoly pricing price - Here’s the diagram from before with the competitive price/quantity (this is where MC=D and is denoted by qpc , ppc - Area A: Producer surplus (equal to total B profit if fixed costs=0) Monopolist’s price/quantity. pm - Area B: Consumer surplus - Monopoly sets price ‘too high’ and A C quantity ‘too low’ compared to the Competitive ppc D MC competitive case. This causes a dead-weight-loss: Area C qm qpc quantity 21 / 34 Welfare costs of monopoly pricing: summary - Competition would result in prices that maximize total surplus - Monopolist sets prices ‘optimally’ (i.e. optimal for itself) and maximizes profit - The monopolist ends up setting a price ‘too high’ and a quantity ‘too low’ compared to competition. - The difference in total surplus between a monopolist and competition is called the dead-weight-loss. - Monopoly is an example of a market failure. 22 / 34 Regulating monopolies - How can we correct the market failure of a monopoly and increase total surplus/reduce dead-weight-loss? - One option: break up the monopoly into smaller firms that compete with each other. - This is an example of antitrust policy (policies that correct market failure due to a lack of competition) 23 / 34 Regulating monopolies: case study of Facebook vs FTC - Background: - In 2012 Facebook acquired Instagram - In 2014 Facebook acquired Whatsapp 24 / 34 Regulating monopolies: case study of Facebook vs FTC - In 2020 the Federal Trade Commission (FTC) sued Facebook. - FTC was seeking to (amongst other things) require divestiture (the forced sale) of Whatsapp and Instagram. - FTC alleged “Facebook has engaged in a systematic strategy [of acquisitions]... to eliminate threats to its monopoly” - FTC: “Facebook’s actions to entrench and maintain its monopoly deny consumers the benefits of competition.” 25 / 34 Regulating monopolies: case study of Facebook vs FTC - Outcome: Court dismissed the FTC’s complaint in June 2021. - Court stated that FTC did not prove that Facebook was a monopoly. - In addition, court argued that FTC waited too long to challenge the acquisitions. - The court allowed Facebook to refile at a future date with more evidence that Facebook is a monopoly. 26 / 34 Regulating monopolies: other examples of breaking up a monopoly - Standard Oil: enormous oil company run by John D. Rockefeller. - Standard Oil was broken up into companies including Chevron, ExxonMobil, and Amoco at the start of the 20th century. - AT&T: Broken up into many smaller firms in 1984 - There are many other examples of monopoly breakups, as well as attempted breakups (e.g. Microsoft in 2001) - That said, as we will see in Part 3 of the course, much of antitrust policy is focused on preventing new monopolies. 27 / 34 Regulating monopolies: marginal and average cost pricing - Sometimes it is not possible to break up the monopoly into smaller firms. - Examples: a power plant, a bridge - These are known as ‘natural monopolies’ - How should we regulate these monopolies? 28 / 34 Regulating monopolies: marginal cost pricing - One possibility for regulation: marginal cost pricing - Idea: force the monopolist to set p = MC - This is the perfect competition price and so there will be no dead-weight-loss. - But there is an issue. Suppose that the monopolist has a cost function of C (q ) = F + cq where F is a fixed cost and c is the constant marginal cost. 29 / 34 Regulating monopolies: marginal cost pricing - One possibility for regulation: marginal cost pricing - Idea: force the monopolist to set p = MC - This is the perfect competition price and so there will be no dead-weight-loss. - But there is an issue. Suppose that the monopolist has a cost function of C (q ) = F + cq where F is a fixed cost and c is the constant marginal cost. - Then, the monopolists profit will be: Profit = TR − TC = pq − F − cq - Since p = MC = c, the monopolists profit will be −F i.e. negative! - Clearly, this firm would shutdown under regulation because profit is negative. To prevent firm shutdown, a possibility is to also give the firm a government subsidy of F. 29 / 34 Regulating monopolies: average cost pricing - Another possibility for regulation: average cost pricing - Idea: force the monopolist to set p = AC. This is the price consistent with the monopolist making zero profits: - If Profit = 0 then, equivalently, TR = TC. - Since TR = pq, TR = TC is equivalent to pq = TC. - Rearranging: p = TC /q = AC 30 / 34 Regulating monopolies: average cost pricing - Essentially, average cost pricing allows the monopolist to exercise its monopoly power only to cover its fixed costs. - So, a government subsidy is no longer necessary. - Average cost pricing is commonly used to regulate privately owned power plants in the US and many other countries and in this context it is called ‘rate of return regulation’. - We will now see average cost pricing on the previous monopoly graph. 31 / 34 Regulating monopolies: average cost pricing price Monopolist’s price/quantity. pm Av cost pricing pac AC Competitive ppc MR D MC qm qac qpc quantity - Diagram from before with average cost pricing (quantity = qac , price = pac ) 32 / 34 Summary of key points* - Know the optimal price occurs at MR = MC (where ‘optimal price’ means the profit maximizing price) - Know the steps to solve for the monopolist’s optimal price and compute the dead-weight-loss, graphically and using math - Know the elasticity rule - Know three potential solutions to monopoly market failure (and how to apply them): 1. divestment 2. marginal cost pricing 3. average cost pricing. *To clarify, all the material in the slides, problem sets, etc is assessable unless stated otherwise, but I hope this summary might be a useful place to start when studying the material. 33 / 34 References - Monopoly graph based on: https://github.com/EconoTodd/LaTeX_code/blob/master/naturalmonopoly 34 / 34