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

ECON 100 Tutorial: Week 7 office hours: 3:45PM to 4:45PM tuesday LUMS C85

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Question 1 From the list of points below select those which distinguish a monopolistically competitive industry from a perfectly competitive industry. There are no barriers to the entry of new firms into the market. Firms in the industry produce differentiated products. The industry is characterised by a mass of sellers, each with a small market share. A downward sloping demand curve means the firm has some control over the product's price. In the long run only normal profits will be earned. Advertising plays a key role in bringing the product to the attention of the consumer.

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Question 1 From the list of points below select those which distinguish a monopolistically competitive industry from a perfectly competitive industry. There are no barriers to the entry of new firms into the market Perfectly competitive Firms in the industry produce differentiated products Monopolistically competitive The industry is characterised by a mass of sellers, each with a small market share. Perfectly competitive A downward sloping demand curve means the firm has some control over the product's price. Monopolistically competitive In the long run only normal profits will be earned Perfectly competitive Advertising plays a key role in bringing the product to the attention of the consumer Monopolistically competitive See Mankiw. Pg and Figure 15.3

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Question 2 Draw a diagram depicting a firm in a monopolistically competitive market that is making profits. Use diagrams to show what happens to this firm in the long run as new firms enter the industry.

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**A firm under monopolistic competition is similar to a monopoly in the short run**

Firm is in equilibrium -- Q is where MR = MC But AR>AC, so the firm earns a profit (PXYZ rectangle) But unlike in a monopoly, other firms may enter the market in the long run. This lowers price and reduces market share Demand (AR) will shift to the left as entry increases until it is just tangent to the AC curve The long run demand curve will be more inelastic than the short run demand curve Firm is in equilibrium -- Q is where MR=MC Industry is in equilibrium, so AR = AC Thus, in the long‐run, the competition brought about by the entry of new firms will cause each firm in a monopolistically competitive market to earn normal profits, just like a perfectly competitive firm. Question 2 Solution. The difference between the short‐run and the long‐run in a monopolistically competitive market is that in the long‐run new firms can enter the market, which is especially likely if firms are earning positive economic profits in the short‐run. New firms will be attracted to these profit opportunities and will choose to enter the market in the long‐run. In contrast to a monopolistic market, no barriers to entry exist in a monopolistically competitive market; hence, it is quite easy for new firms to enter the market in the long‐run. The entry of new firms leads to an increase in the supply of differentiated products, which causes the firm's market demand curve to shift to the left. As entry into the market increases, the firm's demand curve will continue shifting to the left until it is just tangent to the average total cost curve at the profit maximizing level of output. At this point, the firm's economic profits are zero, and there is no longer any incentive for new firms to enter the market. Thus, in the long‐run, the competition brought about by the entry of new firms will cause each firm in a monopolistically competitive market to earn normal profits, just like a perfectly competitive firm.

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Question 3 Draw the average revenue and marginal revenue curves for a monopolist. Why does the marginal revenue curve lie below the average revenue curve for a monopolist? Note: Because the monopoly’s price equals its average revenue, the demand curve is also the average revenue curve. See Mankiw pg and Figure 15.4 Note: If AR is linear (i.e. in Y=mX+c form, or in our case, P = mQ+c), then MR will have a slope that is two times the slope of AR. To show that this holds true for any linear AR: We can write the AR curve as P = mQ+c. We know that TR = AR(Q), so then we can write TR as 𝑇𝑅=𝑚 𝑄 2 +𝑐𝑄. MR is the derivative of TR, so taking the derivative of 𝑇𝑅=𝑚 𝑄 2 +𝑐𝑄, we get 𝑀𝑅=2𝑚𝑄+𝑐. So, we can see that the slope of MR is two times the slope of AR.

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Question 3 (ctd.) See Mankiw pg and Figure 15.4

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Question 4 Marginal revenue is the addition to total revenue as a result of the sale of one extra unit of output. Given this definition, explain how marginal revenue can be negative. Marginal revenue is negative when the price effect on revenue is greater than the output effect. This means that when the firm produces an additional unit of output, the price falls by enough to cause the firm’s total revenue to decline, even though the firm is actually selling more units. See Mankiw pg. 315 – 316 and Figure 15.4 and Table 15.1

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Question 5(a) Describe the Sylos Postulate using diagrams where appropriate. Sylos Postulate: Potential entrants behave as though they expected existing firms to adopt the policy most unfavorable to them, namely, the policy of maintaining output while reducing the price (or accepting reductions) to the extent required to enforce such an output policy (Modigliani, 1958: 217) If a monopolistic incumbent firm maintains its pre-entry output level, then the addition of the new entrant’s production would result in a market with an increased quantity of the product – and thus a lower market clearing price. At this low price, both firms would be losing money, deterring new entry into the market. Whether the entry deterrence is effective or not depends on the credibility of the threats and commitments of the incumbent firm. From Lecture slides This question introduces us to the idea of a firm’s strategies and other firms having best response functions to the firm’s strategy. The monopolist has an idea of other firm’s best response function looks like and may wish to set its strategy so that other firm’s best response is to remain outside the market. In this case, for the Sylos postulate to be effective, the other firm must perceive the monopolist’s threat (the lowered price) as credible. Strategies, best response functions and credible threats are concepts that we will look at in more detail when we cover game theory (Week 9 Tutorial). Whether the entry deterrence is effective or not depends on the credibility of the threats and commitments of the incumbent firm. The effectiveness of entry deterrence can be studied by game theory.

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Question 5(b) Suggest a firm/industry that you believe may use a limit pricing strategy. In a situation with no potential new entrants, a monopolist sets price where MC=MR to maximize profits. This price may be well above the monopolist’s ATC. If potential entrants are present, the monopolist may have a lower cost curve than potential entrants. Rather than maximizing profits, the monopolist now may wish to set a price to deter new entry. Limit pricing strategy: When a monopolist sets prices equal to the Average Total Cost that potential entrants may face, in order to prevent new firms from joining the market.

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**(a) What is the maximum-profit output**

(a) What is the maximum-profit output? 200 units (where MC = MR) (b) What is the maximum-profit price? £60 (given by AR curve at 200 units) (c) What is the total revenue at this price and output? TR = (AR)(Q) TR = £60 200 units TR = £12,000 (d) What is the total cost at this price and output? TC = (AC)(Q) TC = £30 200 units = £6,000 (e) What is the level of profit at this price and output? π = TR – TC π = £12,000 - £6,000 π = £6000 Question 6 See Mankiw pg and Figures 15.5 and 15.6. Note: we generally use P for price, so often π (the Greek letter, pi) is used to denote profit.

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Question 6 (f) If the monopolist were ordered to produce 300 units, what would be the market price? £50 (where AR curve = Q) (g) How much profit would now be made? π = TR – TC π = (AR – AC)Q π = (£50 - £35) 300 π =£15 300 π =£4500

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**Question 6 π = TR – TC π = (AR – AC)Q π = (£70 - £60) 100**

(h) If the monopolist were faced with the same demand, but average costs were constant at £60 per unit, what output would maximise profit? 100 units (where AC = MC = MR = £60) What would be the price now? £70 (given by AR curve at 100 units) (j) How much profit would now be made? π = TR – TC π = (AR – AC)Q π = (£70 - £60) 100 π = £10 100 π = £1000

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Question 6 (k) Assume now that the monopolist decides not to maximise profits, but instead sets a price of £40. How much will now be sold? 400 units (given by AR curve) (l) What is the marginal revenue at this output? MR = 0 (m) What does the answer to (l) indicate about total revenue at a price of £40? Total Revenue is Maximised When MR = 0, TR is no longer increasing, so it has reached a maximum point. (Note MR is the derivative of TR)

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Question 6 (n) What is the price elasticity of demand at a price of £40? Hint: You do not need to do a calculation to work this out: think about the relationship between MR and TR. When P = £40, Unit elastic (When Q<400, MR>0, elastic When Q>400, MR<0, inelastic When Q=400, unit elastic because MR=0) We know from previous weeks that: If a good has elastic demand, then an increase in quantity will lead to an increase in revenue. Likewise, if for some good an increase in quantity leads to an increase in revenue, then that good’s demand is elastic. If a good has inelastic demand, then an increase in quantity will lead to a decrease in revenue. Likewise, if for some good an increase in quantity leads to a decrease in revenue, then that good’s demand is inelastic. Following this pattern, if a good has unit elastic demand, then an increase in quantity will lead to no change in revenue. Likewise, if for some good an increase in quantity leads to no change in revenue, then the goods demand is unit elastic, elasticity is -1.

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**When 0< 𝐸 𝐷 <1, demand is inelastic, and MR<0.**

We can write down the relationship between MR and elasticity of demand as a formula: 𝑀𝑅=𝑃 (1− 1 𝐸 𝐷 ) What this means is that: When 1< 𝐸 𝐷 <∞ , then demand is elastic, and the formula implies MR > 0. When 𝐸 𝐷 = 1, demand is unit elastic, and the formula implies that MR = 0. When 0< 𝐸 𝐷 <1, demand is inelastic, and MR<0. Ian’s lecture slides also discus the relationship between MR and 𝐸 𝐷 . Note, I am keeping with the convention of dropping negative signs for elasticity. If you do not drop the negative sign for elasticity of demand, then your equation should be 𝑀𝑅=𝑃 ( 𝐸 𝐷 ). For a further look at this topic:

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Question 7 When the iPad was introduced Apple engineers reckoned that the MC was about $200 and the fixed costs were about $2 billion. Apple’s econometricians estimated that the inverse demand function was P = Q where Q is in millions - although at the time they were working in the dark. Its hard to figure out what the demand curve was likely to be for what was effectively a new product in the market. In fact they relied on information from selling their old “Newton” touchpad (never a big seller and now a museum piece) and estimates of the price differentials associated with the various features of the iPad that could be found on other machines. Apple was effectively a monopolist in the sale of high end tablets at this time – there have been many entrants since of course, but Apple retains a strong cost advantage.

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Question 7(a) When the iPad was introduced Apple engineers reckoned that the MC was about $200 and the fixed costs were about $2 billion. Apple’s econometricians estimated that the inverse demand function was P = Q where Q is in millions - although at the time they were working in the dark. What was the AC function? AC = TC/Q AC = (FC + VC)/Q We know: FC = $2bil and VC = MC * Q TC = $2bil + $200 * Q AC = $2bil/Q + $200 How to show that VC = MC * Q: 𝑑𝑇𝐶 𝑑𝑄 = 𝑑(𝐹𝐶+𝑉𝐶) 𝑑𝑄 = 𝑑𝐹𝐶 𝑑𝑄 + 𝑑𝑉𝐶 𝑑𝑄 =0+ 𝑑𝑉𝐶 𝑑𝑄 , so then MC= 𝑑𝑉𝐶 𝑑𝑄 If MC is constant, (say MC = c), then TC must be linear (TC = cQ + k). In fact cQ is VC and k is FC. Ian’s solution: Answer: AC= /Q; The inverse demand curve IS the AR curve for a monopolist so total revenue is R = PQ =800Q – 10 Q2 and so (using the rule for finding a slope) MR = 800 – 20 Q. Note that the MR curve of a monopolist is the same as the AR curve EXCEPT it has twice the slope – I cannot find a statement in MT to this effect, although its clear from Fig 15.4 that its true. If you know this relationship between AR and MR then you wouldn’t have to use the slope rule to find MR – you could just take the AR formula and double the slope.

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Question 7(a) ctd. When the iPad was introduced Apple engineers reckoned that the MC was about $200 and the fixed costs were about $2 billion. Apple’s econometricians estimated that the inverse demand function was P = Q where Q is in millions - although at the time they were working in the dark. Assuming that Apple maximised profits, what was MR? Average revenue is the demand curve for a monopolist (both give price received for a given quantity), so AR = 800 – 10 Q. TR = AR*Q TR = 800Q – 10Q2 MR = 𝑑𝑇𝑅 𝑑𝑄 (Note: MR is the derivative, or slope, of TR) MR = 800 – 20Q

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Question 7(b) Use Excel to draw the AC, MC, Demand and MR curves (over the range of Q from 0 to 40). Suggested Solution: Instead of finding the slope using the rule you could draw AR (ie the demand curve) in Excel and then use excel to calculate the change in R when output changes by 1 unit) and then plot this against Q.

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Question 7(c) What was the profit maximising P and Q? MR = MC 800 – 20Q = Q = -600 Q = 30 At Q = 30, the demand function (P = 800 – 10 Q) gives: P = 800 – 10 * 30 P = 800 – 300 P = $500 Ian’s solution: MR=MC implies that 800 – 20Q = 200 , so Q = 30 (million). Hence P=500. Which is why they charged $499! Profit was (P-AC)Q = (500-( /Q))Q = $7 billion – that was a good year for Apple stock!

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Question 7(c) ctd. What was its level of profit? Profit = (P – AC) * Q Since AC = $2bil/Q + $200, Profit = P*Q – AC*Q = P*Q – ($2bil/Q + $200)*Q P = $500, so : = $500*Q – $2bil – $200*Q = $300*Q – $2bil Q = 30 million, so: = $300*30mil – $2bil = $9bil – $2bil = $7 billion Ian’s solution: MR=MC implies that 800 – 20Q = 200 , so Q = 30 (million). Hence P=500. Which is why they charged $499! Profit was (P-AC)Q = (500-( /Q))Q = $7 billion – that was a good year for Apple stock!

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Question 8(a) Suppose a monopolist sells in two countries, 1 and 2, and can prevent resale. MC=20 The inverse demand equations are: p1=100-Q1 and p2=100-2Q2. What does he charge in each country? We want to find where MR = MC. We are given MC and the inverse demand equations. We know that MR is the derivative (or the slope) of TR. So, we can solve this in three steps: 1) We can plug the inverse demand equations for each country into the equation for Total Revenue: TR = P*Q 2) Once we have TR, we can take the derivative to get MR, set that equal to MC and solve for Quantity. 3) Once we have Quantity, we can plug it in to our inverse demand equation and solve for the price that the monopolist will charge in each country.

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Question 8(a) In both countries: MC=20 The inverse demand equations are: p1=100-Q1 and p2=100-2Q2. Step 1) We plug the inverse demand equations for each country into the equation for Total Revenue: TR = P*Q Country 1: TR1 = p1Q1 TR1 = (100-Q1)Q1 TR1 = 100Q1 - Q12

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**Question 8(a) We are given: MC=20 p1=100-Q1 p2=100-2Q2**

Step 2) We have TR, so we will take the derivative of TR, which is MR; then we’ll set that equal to MC and solve for Quantity. Country 1: TR1 = 100Q1 - Q12 MR1=100-2Q1 Set MR = MC 100-2Q1 = 20 Solving for Q1: Q1 = -80 Q1=40 Step 3) We found how much will be produced in Country 1. To find the price that will be charged, we will plug Q1=40 into our inverse demand equation: p1=100-40 p1= 60

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**Question 8(a) So P1=60 and P2=60.**

Given: MC= p1=100-Q1 and p2=100-2Q2 We use the same methods for Country 2: Step 1) We plug the inverse demand equations for each country into the equation for Total Revenue: TR = P*Q TR2 = p2Q2 TR2 = (100-2Q2)Q2 TR1 = 100Q2 - 2Q22 Step 2) We have TR, so we will take the derivative, which is MR; then we’ll set that equal to MC and solve for Quantity. TR2 = 100Q2 - 2Q22 MR2=100-4Q2 Set MR = MC 100-4Q2 = 20 Solving for Q1: Q2 = -80 Q2=20 Step 3) This how much will be produced in Country 2. To find the price that will be charged, we will plug Q2=20 into our inverse demand equation: p2=100-2Q2 p2=100-40 p2= 60 So P1=60 and P2=60.

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Question 8(b) Does it price discriminate or not? Why/Why not? In this case P1 = P2 = 60, so the firm does NOT discriminate – even though it could. In this case, it doesn't because its optimal not to do so. Note that the two demand curves differ in their slopes but not their intercepts. Price discrimination is possible when the monopolist can prevent resale and it is profitable when different consumers have different elasticities. In this case, the first is true, but at optimal P and Q, the two countries have the same elasticity. So, Price discrimination, while possible, is not profitable and therefore will not occur. Ian notes the following in his suggested solution: Note that the monopolist prices in each market such that the elasticities are equal. Since a monopolist choose a price such that (P-MC)/P=-1/ (sometimes called the Lerner index) and MC is the same in both markets and the elasticity is the same, then the P must be the same.

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