ECON 100 Tutorial: Week 7

www.lancaster.ac.uk/postgrad/murphys4/s.murphy5@lancaster.ac.uk

Office: LUMS C85

Question 1

a) There are no barriers to the entry of new firms into the market.

b) Firms in the industry produce differentiated products.

c) The industry is characterised by a mass of sellers, each with a small market share.

d) A downward sloping demand curve means the firm has some control over the product's price.

e) In the long run only normal profits will be earned.f) Advertising plays a key role in bringing the product

to the attention of the consumer.

From the list of points below select those which distinguish a monopolistically competitive industry from a perfectly competitive industry.

Question 1

a) There are no barriers to the entry of new firms into the market. Perfectly competitive

b) Firms in the industry produce differentiated products. Monopolistically competitive

c) The industry is characterised by a mass of sellers, each with a small market share. Perfectly competitive

d) A downward sloping demand curve means the firm has some control over the product's price.

Monopolistically competitive

e) In the long run only normal profits will be earned.Perfectly competitive

f) Advertising plays a key role in bringing the product to the attention of the consumer. Monopolistically competitive

From the list of points below select those which distinguish a monopolistically competitive industry from a perfectly competitive industry.

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.

The short run equilibrium– a firm under monopolistic competition

is similar to that of a monopoly.• Firm is in equilibrium

– Q is where MR = MC

• But AR>AC– Profit is area of PXYZ rectangle

– But unlike in a monopoly, other firms may enter• So, in the long run:

– This lowers price– And reduces market share

• Shifting demand to the left– 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– AR = AC

Question 3Draw 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.

Question 3 (ctd.)

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.

Describe the Sylos Postulate using diagrams where appropriate.Sylos Postulate: Potential entrants believe that if they were to enter the market, a monopolistic incumbent firm would maintain its pre-entry output level.– 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.

Question 5(a)

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.

Question 5(b)

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Question 6(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 unitsTR = £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

(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 – TCπ = (AR – AC)Qπ = (£50 - £35) 300

π =£15 300

π =£4500-20

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Question 6

(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)(i) What would be the price now?£70 (given by AR curve at 100 units)

(j) How much profit would now be made?

π = TR – TCπ = (AR – AC)Qπ = (£70 - £60) 100

π = £10 100π = £1000

Question 6

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(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 MaximisedWhen MR = 0, TR is no longer increasing, so it has reached a maximum point. (Note MR is the derivative of TR)

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)

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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 = 800 -10 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.

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 = 800 -10 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 * QTC = $2bil + $200 * QAC = $2bil/Q + $200

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 = 800 -10 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 = (Note: MR is the derivative, or slope, of TR)

MR = 800 – 20Q

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.

Question 7(c)

What was the profit maximising P and Q? MR = MC800 – 20Q = 200

-20Q = -600 Q = 30

At Q = 30, the demand function (P = 800 – 10 Q) gives:

P = 800 – 10 * 30 P = 800 – 300 P = $500

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 = $500*Q – $2bil – $200*Q = $300*Q – $2bil

Q = 30 million, so: = $300*30mil – $2bil

= $9bil – $2bil = $7 billion

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*Q2) 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.

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*QCountry 1:

TR1 = p1Q1

TR1 = (100-Q1)Q1

TR1 = 100Q1 - Q12

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: -2Q1 = -80

Q1=40

Step 3) This 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-Q1

p1=100-40

p1= 60

Question 8(a)Given: MC=20 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 - 2Q2

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MR2=100-4Q2

Set MR = MC 100-4Q2 = 20

Solving for Q1: -4Q2 = -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.

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. 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.

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