ECON 102 Tutorial: Week 7

Ayesha Aliwww.lancaster.ac.uk/postgrad/alia10/econ102.html

a.ali11@lancaster.ac.ukoffice hours: 8:00AM – 8:50AM tuesdays LUMS C85

Ch. 8, Problem 2(a)

True or False: In a perfectly competitive industry the industry demand curve is horizontal, whereas for a monopoly it is downward-sloping.

False. The industry demand curve is downward sloping in both cases, but from the individual perfectly competitive firm’s point of view, the demand curve is horizontal. Because the individual firm is too small to affect the market price, it can sell as many units as it wishes at that price. (that’s why we say it is a price taker)

Ch. 8, Problem 2 (b)

True or False: Perfectly competitive firms have no control over the price they charge for their product.

True. If they try to charge a higher price they will lose all their business; if they try to charge a lower price, they will not be maximizing profit.

Ch. 8, Problem 2 (c)

True or False: For a natural monopoly, average cost declines as the number of units produced increases over the relevant output range.

True. This is the essential feature of natural monopoly.

Ch. 8, Problem 3

A single-price profit-maximising monopolist:a. Causes excess demand, or shortages, by selling too few units of a good or service.b. Chooses the output level at which marginal revenue begins to increase.c. Always charges a price above the marginal cost of production.d. Also maximises marginal revenue.e. None of the above statements is true.

The answer is c. The monopolist chooses the output level at which marginal revenue equals marginal cost and then charges a price consistent with demand at that level of output. Since price always exceeds marginal revenue, price is greater than marginal cost. There is no shortage: at the output chosen, demand and supply coincide. And the monopolist has no reason to maximize marginal revenue (which would require producing zero units of output).

Ch. 8, Problem 4

If a monopolist could perfectly price discriminate:a. The marginal revenue curve and the demand curve would coincide.b. The marginal revenue curve and the marginal cost curve would coincide.c. Every consumer would pay a different price.d. Marginal revenue would become negative at some output level.e. The resulting pattern of exchange would still be socially inefficient.

The answer is a. The demand curve and the marginal revenue curve would coincide, because the monopolist would sell each successive unit of output at exactly its reservation price, so that unit would generate revenue identical to the reservation price. The final unit of output would be sold at a price equal to marginal cost, so e is wrong: the outcome would be socially efficient. Because two or more consumers might have the same reservation price, c is wrong.

Ch. 8, Problem 6

What is the socially desirable price for a natural monopoly to charge? Why will a natural monopoly that attempts to charge the socially desirable price invariably suffer an economic loss?

What do we mean by socially desirable price? This just means the equilibrium price when there is no deadweight loss. It’s basically the same thing as the equilibrium price in a perfectly competitive market, when S = D, or when P = MC. The textbook solution is given in the next slide.

Ch. 8, Problem 6

What is the socially desirable price for a natural monopoly to charge? Why will a natural monopoly that attempts to charge the socially desirable price invariably suffer an economic loss?The socially desirable price to charge is the one at which the marginal benefit to consumers equals the marginal cost of production. However, natural monopolies are usually characterized by very large fixed costs and relatively low marginal costs. The high fixed costs mean that average cost is greater than marginal cost, so that charging a price equal to marginal cost implies economic losses. An example is the London Underground, which incurred huge fixed costs tunneling, laying railway line, building stations and acquiring rolling stock. However, this transport system incurs virtually no additional cost when an additional passenger travels from Heathrow airport to Trafalgar Square. Charging a price equal to the marginal cost would thus fail to cover the average cost of a ride. One way the London Underground deals with this problem is by selling a rail-card that entitles customers to unlimited travel within a certain period. With this card, the marginal cost to the consumer of an additional journey is zero.

MR and the Monopolist

• Useful fact: If demand is given by: p = a – bQ, then MR is given by the equation: p = a – 2bQ.

Slide 16 from Prof. Rietzke’s Week 6 Slides:

Note: We use this rule to find the Marginal Revenue in Problem 8.

Ch. 8, Problem 8 (a)

Suppose that a university student cinema is a local monopoly whose demand curve for adult tickets on Saturday night is P = 12 – 2Q, where P is the price of a ticket in euros and Q is the number of tickets sold in hundreds. The demand for children’s tickets on Sunday afternoon is P = 8 – 3Q, and for adult tickets on Sunday afternoon, P = 10 – 4Q. On both Saturday night and Sunday afternoon, the marginal cost of an additional patron, child or adult, is €2.What is the marginal revenue curve in each of the three sub-markets?

Finding the equation for the marginal revenue curve is straightforward, we will apply the rule from the previous slide:If demand is given by: p = a – bQ, then MR is given by the equation: p = a – 2bQ

Ch. 8, Problem 8 (a)

Suppose that a university student cinema is a local monopoly whose demand curve for adult tickets on Saturday night is P = 12 – 2Q, where P is the price of a ticket in euros and Q is the number of tickets sold in hundreds. The demand for children’s tickets on Sunday afternoon is P = 8 – 3Q, and for adult tickets on Sunday afternoon, P = 10 – 4Q. On both Saturday night and Sunday afternoon, the marginal cost of an additional patron, child or adult, is €2.What is the marginal revenue curve in each of the three sub-markets?The demand curve for adult tickets on Saturday night: P = 12 – 2QWe can apply our rule: If demand is given by: p = a – bQ, then MR is given by the equation: p = a – 2bQSo then,Marginal revenue curve for adult tickets on Saturday night: P = 12 - 4QSimilarly:Marginal revenue curve for kids’ tickets on Sunday afternoon P = 8 - 6QMarginal revenue curve for adult tickets on Sunday afternoon P = 10 - 8Q

Ch. 8, Problem (b)

What price should the cinema charge in each of the three sub-markets if its goal is to maximise profit?To maximise profit, they should set marginal revenue equal to marginal cost in each market. We know MR from part (a); And we are told that on both Saturday night and Sunday afternoon, the marginal cost of an additional patron, child or adult, is €2.

Ch. 8, Problem (b)What price should the cinema charge in each of the three sub-markets if its goal is to maximise profit?

To maximise profit, they should set marginal revenue equal to marginal cost in each market. We know MR from part (a); And we are told that on both Saturday night and Sunday afternoon, the marginal cost of an additional patron, child or adult, is €2.

Let’s look at the Saturday night adult tickets; MR is given by P = 12 – 4Q.So we set MR = MC 12 – 4Q = 2And solve for Q: -4Q = -10

Q = 2.5 But, remember, Q is in terms of hundreds of tickets, so actually the profit maximizing number of tickets will be 250.To find profit-maximizing price, we can plug Q in to our equation for Demand:

P = 12 – 2(2.5) P = 12 – 5 P = €7

Doing the same thing in the other two markets, we should get: Sunday Children tickets; Q = 100 tickets, P = €5Sunday Adult tickets; Q = 100 tickets, P = €6

Ch. 8, Problem 9 (a)

Suppose you are a monopolist in the market for a specific video game. Your demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q. Your fixed costs equal €400.Graph the demand and marginal cost curve.

Ch. 8, Problem 9 (a)

Suppose you are a monopolist in the market for a specific video game. Your demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q. Your fixed costs equal €400.Graph the demand and marginal cost curve.

Ch. 8, Problem 9 (b)

Suppose you are a monopolist in the market for a specific video game. Your demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q. Your fixed costs equal €400.Derive and graph the marginal revenue curve.

Ch. 8, Problem 9 (b)

Suppose you are a monopolist in the market for a specific video game. Your demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q. Your fixed costs equal €400.Derive and graph the marginal revenue curve.Using our rule to find the MR curve, we get: MR=80 - Q.

Ch. 8, Problem 9 (c)

Suppose you are a monopolist in the market for a specific video game. Your demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q. Your fixed costs equal €400.Calculate and indicate on the graph the equilibrium price and quantity.

Ch. 8, Problem 9 (c)

Suppose you are a monopolist in the market for a specific video game. Your demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q. Your fixed costs equal €400.Calculate and indicate on the graph the equilibrium price and quantity.

P

Q

p*=

8040

60

160

MC=Q80

q*=

Profit is maximized where MR = MC; looking at the graph, this is when q = 40. Because we are a monopolist, we will produce at this quantity, but set the price where q = 40 is equal to our Demand curve. So, Price will set at €60.

Ch. 8, Problem 9 (d)

Suppose you are a monopolist in the market for a specific video game. Your demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q. Your fixed costs equal €400.In part (c), we found that P* = 60 and Q* = 40. What is your profit?

Ch. 8, Problem 9 (d)

Suppose you are a monopolist in the market for a specific video game. Your demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q. Your fixed costs equal €400.What is your profit?

In part (c), we found that P* = 60 and Q* = 40. We know that Profit = total revenue - total cost And that TR = PQ and TC = FC + VC. We are told FC = 400. And, we should have been given VC = ½(Q)2

So we can plug all of this in to our equation for profit: π = total revenue - total cost π = (P)(Q) – FC – VC π = (60)(40) - 400 - (40)(40)/2 π = 1200

Ch. 8, Problem 9 (e)

Suppose you are a monopolist in the market for a specific video game. Your demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q. Your fixed costs equal €400.

What is the level of consumer surplus?P

Q

p*=

8040

60

160

MC=Q80

q*=

Ch. 8, Problem 9 (e)

Suppose you are a monopolist in the market for a specific video game. Your demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q. Your fixed costs equal €400.

What is the level of consumer surplus?

P

Q

p*=

8040

60

160

MC=Q80

q*=

Consumer Surplus is the difference between what consumers are willing to pay (the demand curve) and the actual price that they do pay. So, it is the area of this triangle here:We use the equation: area = ½(b)(h) to find the area of a triangle.So, Consumer Surplus = (½)(40)(20)

CS = 400

Ch. 8, Problem 10 (a)

Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand each day are listed in the table below:

Beth knows the distribution of reservation prices (that is, she knows that one person is willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s reservation price.

Person A B C D E F G H I JReservation price (€) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

Ch. 8, Problem 10 (a)

Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand each day are listed in the table below:

Beth knows the distribution of reservation prices (that is, she knows that one person is willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s reservation price.Calculate the marginal revenue of selling an additional cup of lemonade. (Start by figuring out the price Beth would charge if she produced only one cup of lemonade, and calculate the total revenue; then find the price Beth would charge if she sold two cups of lemonade; and so on.)

Person A B C D E F G H I JReservation price (€) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

Quantity 1 2 3 4 5 6 7 8 9 10Price €1 €.90 €.80 €.70 €.60 €.50 €.40 €.30 €.20 €.10

Total Revenue €1 €1.80 €2.40 €2.80 €3.00 €3.00 €2.80 €2.40 €1.80 €1

Ch. 8, Problem 10 (a)

Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand each day are listed in the table below:

Beth knows the distribution of reservation prices (that is, she knows that one person is willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s reservation price.Calculate the marginal revenue of selling an additional cup of lemonade. (Start by figuring out the price Beth would charge if she produced only one cup of lemonade, and calculate the total revenue; then find the price Beth would charge if she sold two cups of lemonade; and so on.)

Person A B C D E F G H I JReservation price (€) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

Quantity 1 2 3 4 5 6 7 8 9 10Price €1 €.90 €.80 €.70 €.60 €.50 €.40 €.30 €.20 €.10

Total Revenue €1 €1.80 €2.40 €2.80 €3.00 €3.00 €2.80 €2.40 €1.80 €1

Marginal Revenue €1 €.80 €.60 €.40 €.20 €0 €-.20 €-.40 €-.60 €-.80

Ch. 8, Problem 10 (b)

Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand each day are listed in the table below:

Beth knows the distribution of reservation prices (that is, she knows that one person is willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s reservation price. In part (a), we calculated the marginal revenue for selling an additional cup of lemonade:

What is Beth’s profit-maximising price?

Profit is maximised where MR=MC. We know that Beth’s MC = 0.20, so her MR = 0.20 at a price of €.60.

Person A B C D E F G H I JReservation price (€) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

Price €1 €.90 €.80 €.70 €.60 €.50 €.40 €.30 €.20 €.10Quantity 1 2 3 4 5 6 7 8 9 10

Total Revenue €1 €1.80 €2.40 €2.80 €3.00 €3.00 €2.80 €2.40 €1.80 €1

Marginal Revenue €1 €.80 €.60 €.40 €.20 €0 €-.20 €-.40 €-.60 €-.80

Ch. 8, Problem 10 (c)

Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand each day are listed in the table below:

Beth knows the distribution of reservation prices (that is, she knows that one person is willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s reservation price. In part (a), we calculated the marginal revenue for selling an additional cup of lemonade:

In part (b) we found Beth’s profit-maximising price is €.60.At that price, what is Beth’s economic profit?

Profit = TR – TC → Profit = (AR – ATC)*Q → Profit=5*(.6 - .2) → Profit = €2.

Person A B C D E F G H I JReservation price (€) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

Price €1 €.90 €.80 €.70 €.60 €.50 €.40 €.30 €.20 €.10Quantity 1 2 3 4 5 6 7 8 9 10

Total Revenue €1 €1.80 €2.40 €2.80 €3.00 €3.00 €2.80 €2.40 €1.80 €1

Marginal Revenue €1 €.80 €.60 €.40 €.20 €0 €-.20 €-.40 €-.60 €-.80

Ch. 8, Problem 10 (c)

Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand each day are listed in the table below:

Beth knows the distribution of reservation prices (that is, she knows that one person is willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s reservation price. In part (a), we calculated the marginal revenue for selling an additional cup of lemonade:

In part (b) we found Beth’s profit-maximising price is €.60.At that price, what is Beth’s total consumer surplus?

Consumer Surplus is the difference between what consumers are willing to pay (i.e. their reservation price) and the actual price that they do pay.

Consumer surplus = (€1 - €0.60)+ (€0.90 - €0.60)+(€0.80 - €0.60)+(€0.70 - €0.60)= €1.

Person A B C D E F G H I JReservation price (€) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

Price €1 €.90 €.80 €.70 €.60 €.50 €.40 €.30 €.20 €.10Quantity 1 2 3 4 5 6 7 8 9 10

Total Revenue €1 €1.80 €2.40 €2.80 €3.00 €3.00 €2.80 €2.40 €1.80 €1

Marginal Revenue €1 €.80 €.60 €.40 €.20 €0 €-.20 €-.40 €-.60 €-.80

Ch. 8, Problem 10 (d)

Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand each day are listed in the table below:

Beth knows the distribution of reservation prices (that is, she knows that one person is willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s reservation price. In part (a), we calculated the marginal revenue for selling an additional cup of lemonade:

In part (b) we found Beth’s profit-maximising price is €.60.

What price should Beth charge if she wants to maximise total economic surplus?Total economic surplus is maximised at the perfect competition equilibrium, or where S = D, or where P = MC.

So if Beth wanted to maximise total economic surplus, she should set P = MC; so P = €.20.

Person A B C D E F G H I JReservation price (€) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

Price €1 €.90 €.80 €.70 €.60 €.50 €.40 €.30 €.20 €.10Quantity 1 2 3 4 5 6 7 8 9 10

Total Revenue €1 €1.80 €2.40 €2.80 €3.00 €3.00 €2.80 €2.40 €1.80 €1

Marginal Revenue €1 €.80 €.60 €.40 €.20 €0 €-.20 €-.40 €-.60 €-.80

Ch. 8, Problem 10 (e)

Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand each day are listed in the table below:

In part (a), we calculated the marginal revenue for selling an additional cup of lemonade:

In part (b) we found Beth’s profit-maximising price is €.60.In part (c) we found Beth’s economic profit is €2 and total consumer surplus is €1.

Now suppose that Beth can tell the reservation price of each person. What price would she charge each person if she wanted to maximise profit? She would sell to each person whose reservation price is below her marginal cost, and she would charge these people (persons A through I) their respective reservation prices.

Compare her profit to the total surplus calculated in part (c).Doing so would earn her a profit of €3.60, which is the same as the total economic surplus in part (d).

Person A B C D E F G H I JReservation price (€) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

Price €1 €.90 €.80 €.70 €.60 €.50 €.40 €.30 €.20 €.10Quantity 1 2 3 4 5 6 7 8 9 10

Total Revenue €1 €1.80 €2.40 €2.80 €3.00 €3.00 €2.80 €2.40 €1.80 €1

Marginal Revenue €1 €.80 €.60 €.40 €.20 €0 €-.20 €-.40 €-.60 €-.80

Next Week

Check Moodle for the Week 8 worksheet. It’s on game theory – Chapter 9 of the textbook should be helpful if you have not studied game theory before.

Exam results should be coming out soon. You can check on Moodle for your results.