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**office hours: 3:45PM to 4:45PM tuesday LUMS C85**

ECON 100 Tutorial: Week 8 office hours: 3:45PM to 4:45PM tuesday LUMS C85

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Question 1 Match each of the three types of price discrimination to the following definitions: (a) When a firm charges a consumer so much for the first so many units purchased, a different price for the next so many units purchased and so on. (ii) Second-degree price discrimination (b) When a firm divides consumers into different groups and charges a different price to each group, but the same price to all the consumers within a group. (iii) Third-degree price discrimination (c) When a firm charges each consumer for each unit the maximum price the consumer is willing to pay for that unit. (i) First-degree price discrimination Mankiw (2nd Ed.) pgs

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Question 2 Under what circumstances can a monopolist practice price discrimination? Illustrate your answer with appropriate examples. Firms must be price setters, not price takers There must be no possibility for resale between segments Consumers must have different price elasticities in separate markets This will ensure that optimal price is different in the different markets Examples: Discounts to the elderly for entry to theatres, meals in restaurants and travel on buses and rail Different prices for kids and adults for sporting and other attractions Gender pricing in some bars/clubs EuroRail pass for student travel - compared to standard fares for business users Length of stay in airline tickets Mankiw (2nd Ed.) pgs

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Question 3(a) In the diagram above what is the price and quantity if there is perfect competition? P = £12 and Q = 8 units In a perfectly competitive market, there are zero profits , so firms choose to produce where AC = AR. Mankiw (2nd Ed.) pgs For an individual firm in a competitive market, the demand curve is flat. AR = Price for all quantities. At the market level, if 4 units were being produced, then there would be positive profits. If there are positive profits, then the entry condition says that other firms will enter. This will cause more units to be produced until there are zero profits. This is why for a market, the equilibrium condition is where AC = AR, i.e. where Supply = Demand.

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Question 3(b) and (c) (b) If the firm could act as a monopolist selling at a single price what would be the equilibrium price and output? P = £15, Q = 4 units (c) What would supernormal profit be at this position? Profit = (P – AC)Q = (£15 – £12) × 4 = £12 Mankiw (2nd Ed.) Figures 15.5 and 15.6

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Question 3(d) and (e) (d) If the monopolist could sell to each customer according to their willingness to pay, what would their revenue be? Shade in this area on the diagram. TR =(£12 × 8) + 0.5(£8 × 8 ) TR = £128 (e) What name is given to this practice First degree price discrimination Mankiw (2nd Ed.) Figure 15.10

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Question 3(f) Is this (first degree price discrimination) better for society than selling at a single monopoly price? Briefly explain. Some consumers are better off because they receive the good at prices below the single monopoly price of £15, though others are worse off because they have paid in excess of £15. The monopolist has captured the consumer surplus of these consumers because it has worked out their willingness to pay for this good. Overall, a successful first-degree price discrimination strategy is equivalent to a perfectly competitive outcome except that the monopolist captures the entire consumer surplus shown by triangle ABC. Mankiw (2nd Ed.) pgs , Figure 15.10 For an economist, consumer surplus and producer surplus have equal value to society. In that context, successful first-degree price discrimination would be just as good as a perfectly competitive market because the sum of CS and PS in a perfectly competitive market equals PS in a successful first-degree price discrimination scenario. Both of these are then better than a monopoly market, where some amount of deadweight loss and CS + PS is less than in the other two scenarios.

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**Question 4 Define natural monopoly.**

A natural monopoly is characterized by falling AC in the relevant industry output range. This makes production cheaper for one firm than for two or more firms. Mankiw (2nd Ed.) pgs and 330 Figure 15.2 The relevant industry output range is roughly the range in output between what an individual firm would produce in a competitive market and what is produced by the entire market.

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Question 4(a) Use a diagram to explain the equilibrium position if there is a single monopoly producer. A monopoly has optimal production where MR=MC, at Qm and sets price where Qm crosses AR, at Pm, so profit will be the blue-shaded rectangle. From Caroline’s lecture slides

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Question 4(b) Use the diagram to explain why a duopoly industry structure will be inefficient. At any level of total production, in a duopoly, the cost to each firm will be higher and the profit for each firm will be lower than the cost and profit for a monopoly producing at that same total level of production. From Caroline’s lecture slides For more on duopolies:

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**Question 4(c) MC Pricing is when Price is set where D=MC.**

If MC < AC, a monopolist would want some sort of subsidy to keep prices at this level. AC Pricing is when Price is set where D=AC. At this price level, a monopolist will earn zero profit because P=AC, making this a more sustainable solution than MC Pricing. Show on the diagram the equilibria when MC and AC pricing policies are adopted, indicating any profits/losses that are obtained. From Caroline’s lecture slides

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Question 5 A single firm delivers all the water to a set of households in an area – in total Q units. Suppose costs consist of fixed costs, F, and a constant MC of m per unit, so total cost is given by C = F + mQ. If an entrant would have the same costs does the incumbent firm have a natural monopoly? If each firm delivers to half of the households, then each firm would have costs equal to C = F + mQ/2, So then, the combined costs of two firms would be: 2F + mQ The combined costs of the two firms is greater than the costs under the monopoly (C = F + mQ) – so it's a natural monopoly

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Question 6(a) Allergan is the monopoly producer of Botox, a wrinkle treatment - well, it was originally a successful treatment for an eye condition that led to blindness and they noticed that wrinkles disappeared! A vial of Botox costs $25 to produce and this MC is constant. Beauty technicians buy vials at a price of $400 each. Sales revenue is $400m. This tells us: MC = $25, P = $400, Total Revenue = PQ, so Q = TR/P Q = $400 mil./$400, so Q = 1 (where Q is in millions) What is the price elasticity of demand? Note: for a monopolist, (P-MC)/P=-1/.

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Question 6(a) We know: MC = $25, P = $400, Total Revenue = PQ, so Q = TR/P Q = $400 mil./$400, so Q = 1 million What is the price elasticity of demand? We are told that for a monopolist, (P-MC)/P=-1/. We can re-arrange to solve for : = - P/(P-MC) = -400/(400-25) =

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Question 6(b) Note that the firm is a profit maximiser and sets MR = MC. Assuming that demand is linear, then work out the equation of the inverse demand curve and the corresponding MR curve. We know that if inverse demand is linear, it will be in y=mx+c form (slope-intercept). So, our inverse demand curve will be P = a + bQ, where a and b are the intercept and slope, respectively. From the previous slide, we know the following: MC = $25, P = $400, Q = 1 and = We can use our equation for elasticity to solve for a and b to get our inverse demand equation.

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From the previous slide, we know the following: MC = $25, P = $400, Q = 1 million and = And we know that our inverse demand curve will be in the form P = a + bQ First, we’re going to re-arrange the inverse demand curve, solving for Q: P = a + bQ -bQ = a – P Q = (a – P)/(-b) so, 𝑄= 𝑃−𝑎 𝑏 , which we can re-write as 𝑄= 𝑃 𝑏 − 𝑎 𝑏 If we take the derivative with respect to P, we get: 𝑑𝑄 𝑑𝑃 = 1/b We know that our equation for elasticity is: 𝜀= 𝑑𝑄 𝑑𝑃 ∙ 𝑃 𝑄 We can plug in 𝑑𝑄 𝑑𝑃 , P, Q, and 𝜀, into the elasticity equation, in order to solve for b: 𝜀= 𝑑𝑄 𝑑𝑃 ∙ 𝑃 𝑄 𝜀= 1 𝑏 ∙ 𝑃 𝑄 −1.067= 1 𝑏 ∙ b = −1.067 b = -375

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**Question 6(b) ctd. From the previous slide, we know the following:**

MC = $25, P = $400, Q = 1 and = We also know that our inverse demand curve will be in the form P = a + bQ and b = -375 Now, we can plug b back into our inverse demand function, plug in P and Q, and solve to get a. P = a + bQ 400 = a * 1 Solving for a, we get: a = = 775. So the inverse demand curve is P = 775 – 375 Q.

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**Question 6(b) ctd. From the previous slide, we know the following:**

MC = $25, P = $400, Q = 1 and = And the inverse demand curve is P = 775 – 375 Q. To find MR, it helps to know about the relationship between MR and AR for a monopolist firm. (Note: AR is the inverse demand curve) MR has twice the slope of AR. The Y-intercept is the same for both. From this, we can write our MR curve as: MR = 775 – 750Q

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Question 6(c) Work out the CS, profits and DWL. To find these, we first need to find the profit maximising P & Q. From part B, we have MC=25 and MR = 775 – 750 Q To find profit-maximizing Q, we’ll set MC = MR: 775 – 750 Q = 25 Q = 1 From part B, we have P = 775 – 375Q We can plug Q in and solve for P: P = 775 – 375(1) P = 400

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Question 6(c) ctd. Once we find P and Q, we can solve for CS, profits, and DWL. CS = area A CS = ½ (1m)( ) CS = $187m profits = area B profits = (1m)(400-25) profits =$375m minus an FC DWL = area C DWL = ½ (2m-1m)(400-25) DWL = $187m

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Question 6(d) If Allergan could perfectly price discriminate what would happen to profits? Profits would be the entire area of the triangle under the demand curve, above MC: A+B+C= $750m

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**Some notes on study skills**

If you are having questions about lecture slides, visit Ian or Caroline during their office hours – they are there to answer questions about their material. Don’t put it off – ask right away. Also, if you weren’t pleased with your marks on the exam or with the way that you prepared for the exam, then get help with your study skills. your faculty student learning advisor (Most of you will be in either FASS or Management School) and let them know what your concerns are or what you need help with. Faculty Student Learning Advisors: 1.) Faculty of Arts & Social Sciences - Joanne Wood Web: https://modules.lancs.ac.uk/course/view.php?id=283 2.) Faculty of Sciences & Technology and Faculty of Health & Medicine - Robert Blake Web: https://modules.lancs.ac.uk/course/view.php?id=282 3.) Management School - Gill Burgess and Sharon McCulloch Web: https://modules.lancs.ac.uk/course/view.php?id=281 Don’t put it off for the week before Exam 2!

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