MIDTERM 4 Mars 2018, réponses PDF

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1-803-07A Microeconomic Analysis B.B.A. Midterm exam - SOLUTION

Coordinator: Nathalie Boisvert

Fall 2018

QUESTION 1 – MULTIPLE CHOICE QUESTIONS (12 POINTS – 14 MINUTES) CIRCLE THE RIGHT ANSWER. 1.1 (3 points) Madagascar and its surrounding islands have always been the world's dominant supplier of vanilla, accounting for roughly 80 per cent of the global supply of beans. Last March, Cyclone Enawo, the strongest cyclone to hit Madagascar in 13 years, tore through the island, damaging about 30 per cent of vanilla crops and reducing their expected harvest by a third. At the same time, the food industry's demand for natural vanilla has spiked considerably. (Source: Julie Van Rosendaal, Globe and Mail, June 28th, 2018) Ma

Given the information provided in this article, how will the equilibrium price and quantity on the world market for vanilla be affected? a)

The equilibrium price increases and the effect on the equilibrium quantity is ambiguous.

b) The equilibrium price increases and the equilibrium quantity increases. c)

The equilibrium price decreases and the equilibrium quantity increases.

d) The equilibrium price decreases and the effect on the equilibrium quantity is ambiguous. e)

The effect on the equilibrium price is ambiguous and the equilibrium quantity increases.

1.2 (3 points) The price elasticity of demand for broccoli is -0.8 and the cross-price elasticity between broccoli and cauliflower is 0.5. If the price of broccoli increases by 10%, and the price of cauliflower decreases by 4%, what will be the effect on the quantity demanded for broccoli? a)

The quantity demanded for broccoli will increase by 10%.

b) The quantity demanded for broccoli will decrease by 10%. c)

The quantity demanded for broccoli will increase by 6%.

d) The quantity demanded for broccoli will decrease by 6%. e)

The quantity demanded for broccoli will decrease by 3%.

1.3 (3 points) This graph illustrates the demand and supply for a good traded in a market. Suppose that the government decides to regulate this market and sets the price at $4 per unit (price ceiling). Among the following statements, which one is TRUE?

a)

There is a shortage of 2 units and the consumer surplus is equal to $16.

b) There is an excess supply of 2 units and the producer surplus is equal to $6. c)

The quantity demanded is higher than the quantity supplied and the price will increase to $5.

d) The quantity produced is 4 units and the producer surplus is equal to $16. e)

There is no welfare loss (no deadweight loss).

1.4 (3 points) A monopoly divided its market in two distinct segments. The demand functions for these two segments are given by the following equations:

Q1 = 8 - P

and

Q2 = 6 - P

where P is the price of the good in $, Q1 is the quantity for customers in segment #1 and Q2 is the quantity for customers in segment #2. The marginal cost is constant and equal to $2. There are no fixed costs. If the monopoly wants to maximize its profits, what pricing strategy should be chosen? a)

Charge a price of $3 to segment #1 and $2 to segment #2.

b) Charge a price of $5 to segment #1 and $4 to segment #2. c)

Charge a price equal to the marginal cost to two segments, which is $2.

d) Charge a higher price to segment #2, which has the most elastic demand. e)

None of these answers is correct.

QUESTION 2 – VARIOUS QUESTIONS (25 POINTS – 30 MINUTES) 2.1 Ed Sheeran’s show in Tampa Bay (9 points) You won a free ticket for Ed Sheeran’s show in Tampa Bay in Florida on November 7th.  The ticket has a market value of $250 if you decide to sell it (resale is permitted). It is certain that you will be able to resell your ticket if you wish to.  Your valuation for attending this concert is $500.  The cost of the flight to Tampa Bay is $360.  You are scheduled to work 6 hours at Reno-Dépôt on the day of the concert (you can’t work at all if you go to the concert). You are paid $12 an hour.  You are required to find someone to take your place if you can’t make it to work. The only person you can find who will take your place at work asks you $50 to do it. [Note: All prices are in Canadian dollars.] a)

What is the opportunity cost of going to the concert? (3 points)

Opportunity cost of the ticket: Your ticket could be sold at a price of $250. Opportunity cost of your time: If you go to the concert, you are giving up your salary of $72 (6 h x $12/h) The opportunity cost is then $322.

b) What is the economic cost of going to the concert? Will you attend this concert? Justify your answer clearly. (4 points) The economic cost of going to the concert includes accounting costs and opportunity costs. There is no sunk cost. The accounting costs are: - The cost of the plane ticket if you go to the concert: $360 - The compensation that you will have to give to the person taking your place at your job: $50. The economic cost is $322 + $360 + $50 = $732. You will not attend the concert since your valuation is lower than the economic cost of going to the concert ($500 < $732). c)

Finally, against all odds, you can’t sell the ticket. The day before the concert, you must decide if you will go to the concert. What will be your decision? Justify your answer very clearly. [Note: Assume that all the other information presented above is still valid.] (2 points)

The economic cost of going to the concert is now reduced by $250 and will be equal to $482 ($732 - $250). Yes, you will go to the concert since your valuation is higher than the economic cost of going to the concert: $500 > $482. 2.2 Christmas trees (8 points) A producer specializes in the production of 2-meter-tall Christmas trees. Studies have shown that, during the month of December, the Quebec and Ontario demand curves for 2-meter-tall Christmas trees are given by the following equations:

QQUE = 10,000 - 100 P QONT = 20,000 - 125 P where P is the price of Christmas trees in $ and Q is the quantity of 2-meter-tall Christmas trees. Suppose that the market price for Christmas trees is $55. a)

If the market price were to increase by 5%, in which region would the producer observe an increase in revenue? Explain and justify your answer very clearly. (4 points)

Price elasticities must be calculated at the price of $55. The quantities in both markets: QQUE = 10,000 - 100 P = 10,000 - 100 (55) = 4,500 QONT = 20,000 - 125 P = 20,000 - 125 (55) = 13,125

Price elasticities are: EP,QUE : - 100 x 55 / 4,500 = -1.22 EP,ONT : - 125 x 55 / 13,125 = -0.52 ER Ontario = 1 + EP = 1 – 0.52 = 0.48 > 0. Since the demand in Ontario is relatively inelastic at a price of $55, an increase in the market price will lead to an increase in revenue in Ontario. Other possible answer: The new price will be $57.75 ($55 x 1.05). Revenue can be calculated in both regions. Revenue will increase in Ontario as demand is more inelastic. Price $55 $57.75

Quantity Quebec 4,500 4,225

Revenue Quebec $247,500 $243,994

Quantity Ontario 13,125 12,781

Revenue Ontario $721,875 $738,117

Reminder: demand functions in Quebec and Ontario QQUE = 10,000 - 100 P QONT = 20,000 - 125 P b) (4 points) i. Draw the total demand function (Quebec + Ontario) for Christmas trees [Note: The equation is not required in your answer.] ii. On the graph, identify the situation when the market price is $55. Make sure to identify both axes and indicate all relevant information on your graph.

Note: Functions were not required in the answer. They are given for information only.

2.3 A valuation story (8 points) Consider two individuals, Alex and Ben, whose total valuation for successive units of a good are as follows: q 1 2 3 4 5 6 V(q) Alex 400 600 750 850 900 925 V(q) Ben 300 450 525 575 600 615 Initially, Alex has 2 units and Ben has 4 units. Alex and Ben plan on meeting to trade one or more units. Suppose that all mutually beneficial trades will be made. a)

Who will be the buyer? Why? You must justify your answer very clearly by indicating all the steps in your reasoning. (5 points)

Marginal valuations are the following: q 1 2 400 200 MV(q) Alex 300 150 MV(q) Ben

3 150 75

4 100 50

5 50 25

6 25 15

Alex will be the buyer. Alex has 2 units and is willing to pay up to $150 to own an extra unit of the good. Ben has 4 units and is willing to sell the 4th unit for $50 or more. b) How many units will Alex and Ben own after their meeting? Explain. (3 points) MVA (3) > MVB (4) which is $150 > $50, so one unit will be traded. MVA (4) > MVB (3) which is $100 > $75, so one extra unit will be traded. MVA (5) < MVB (2) so a 3rd unit will not be traded. Alex will own 4 units and Ben will own 2 units.

QUESTION 3 – PIG PRODUCTION (21 POINTS – 26 MINUTES) Pork producers facing a difficult time Ignored by the aid program of $863 million announced by Quebec two weeks ago, pork producers in Quebec are hit hard by the current trade wars and are demanding $50 million to help them cope with a fall of more than 50% in the price of pork since the beginning of July. Quebec producers could sell each 100 kg pork for $230 in early July. They now receive only about $110, according to David Duval, President of Quebec pork producers. And the trend is not going in the right direction. "You look at the graph, it's like Niagara Falls. There is nothing that makes us think that prices will rise." Source: La Presse, September 1st, 2018

For the purpose of this question, assume that the pork industry is perfectly competitive. Consider that the market is made up of a large number of small producers with the same cost function in both the short term and the long term. [Note: For this question, consider the production of porks of 100 kg]. The total cost function of each firm is: C(q) = 100 + 105q + q2 where q is the quantity of porks (in thousands). The demand function in this market is the following: QD = 6,625 – P where P is the price for pork ($) and Q is the quantity of porks (in thousands). QUESTIONS 3.1 AND 3.2 ARE ABOUT MARKET CONDITIONS IN THE SHORT RUN. 3.1 The newspaper article indicates that the price of pork has fallen in recent months. At a price of $110 for a 100 kg pork, are pork producers making profit? To answer this question, determine the minimum price that allows pork producers to be profitable. (7 points) In the short run, the break-even price is when MC = min AC. MC = 105 + 2q and AC = 100/q + 105 + q MC = AC → 105 + 2q = 100/q + 105 + q → q = 100/q → q2 = 100 q = 10 (10 000 porks) The break-even price is a price. We have to replace q in the MC or the AC function: MC(10) = 105 + 2(10) = $125 / pork of 100 kg. At a price of $110/ pork of 100 kg, producers will not make profit since the break-even price is higher [$125 / pork of 100 kg].

3.2 Mr. Duval is very pessimistic about the current situation: "You look at the graph, it's like Niagara Falls. There is nothing that makes us think that prices will rise ". If the situation remains the same in the short run, will pork producers be able to continue producing? To answer this question, determine the minimum price at which producers will continue their activities. (6 points) In the short-run, the shutdown price is when MC = min AVC. MC = 105 + 2q and AVC = 105 + q MC = AVC → 105 + 2q = 105 + q q=0 To find the shutdown price, we have to replace q in the MC or the AVC function: MC (0) = 105 + 2(0) = $105 /pork of 100 kg. At a price of $110/ pork of 100 kg, they will continue producing in the short run because the shutdown price is $105/ pork of 100 kg.

QUESTION 3.3 CONCERNS MARKET CONDITIONS IN THE LONG RUN. 3.3 (8 points) a)

What will be the long-run equilibrium price in this market? (2 points)

The long-run equilibrium price is this market is $125/ pork of 100 kg since it is the minimum of the AC: P = minACLR. In the long run, firms will all produce at the minimum of the average cost since the breakeven price is also the shutdown price. b) How many pork producers will be producing in this market in the long-run? (4 points) QD = 6,625 – P = 6,625 – 125 = 6,500 → Q* = 6,500 (6,500,000) The quantity produced by each producer is q = 10 (found in 3.1). Then n = Q/q = 6,500 / 10 = 650 pork producers. c)

What will be the profit of each producer in the long run? Explain briefly. (2 points)

If P = minACLR, the profit will be equal to 0 (zero economic profit).

QUESTION 4 – PUBLIC TRANSIT MONOPOLY (30 POINTS – 36 MINUTES) The Réseau Express Métropolitain (REM)* obtained monopoly zones In the draft agreement between the Metropolitan Regional Transit Authority and the REM partnership, we learn that the REM will have access to large territories, with non-competition clauses, to ensure its profitability. The document states that the Authority is committed to ensuring that "no other public transit service is offered on the routes between the south shore and the downtown area using the Champlain Bridge", that "no other public transit service be offered on routes directly connecting Trudeau Airport and the downtown area", and that "no other public transit service is offered between the airport and the Lionel-Groulx metro station". Source: La Presse, March 21st, 2018

* The Réseau express métropolitain (REM) is a major public transit project under construction. It will include 26 stations and span the Greater Montréal metropolitan region with 67 km of tracks, simplifying commutes. (Source: https://rem.info/en/home)

In light of the information presented in the draft agreement, it appears that the Réseau Express Métropolitain (REM) will have monopoly zones for public transit. For the purpose of this question, we will study the public transit service between Trudeau Airport and downtown Montreal. One study shows that the demand for each ride between Trudeau Airport and downtown is given by the following equation:

P = 20 - 0.01 Q where Q is the number of passengers for each ride and P is the price of a ticket in dollars. For the REM, each ride between the Trudeau airport and downtown Montreal will cost $1,000, plus $5 per passenger. [Note: All questions are about the market in the short run.] 4.1 Given the fact that the REM will have the monopoly on public transit for rides between Trudeau Airport and downtown Montreal, answer the following questions. (18 points) a) What price will be chosen by the REM to maximize profits? How many passengers will buy a ticket? What will be the profit made by the REM? (7 points) The REM will maximize profits when MR(q) = MC(q). P = 20 – 0.01 Q → R = 20 Q – 0.01 Q2 → MR = 20 – 0.02 Q MR = MC → 20 – 0.02 Q = 5 (The MC is equal to $5) QMON = 750 passengers P = 20 – 0.01 Q → P = 20 – 0.01 (750) = 12.50 $ → PMON = 12.50 $ π(Q) = R(Q) – C(Q) = (12.50 x 750) – [1,000 + (5 x 750)] = 4,625 so πMON(Q) = 4,625 $

Price

Quantity

Profit

$12.50

750

$4,625

b) Given the results in a), complete the graph below. (4 points)  Indicate all the relevant information on the axes.  Identify the price and the quantity which maximize the profit of the REM.  Illustrate and clearly identify the marginal revenue curve and the marginal cost curve (indicate all the relevant information about these two curves).

c)

Compute and illustrate on the graph in b), the consumer surplus, the producer surplus and the deadweight loss. (7 points) CS = [(20 – 12.50) x 750] / 2 = $2,812.50 PS = (12.50 – 5) x 750 = $5,625 DWL = [(12.50 – 5) x (1,500 – 750)]/2 = $2,812.50

4.2 The managers of the future REM realize that after the 100th passenger, each ride between Trudeau Airport and the downtown area will cost $15 per passenger (instead of $5 per passenger). What price would be chosen by the REM if the objective is still to maximize profits? What would be the profit made by the REM? (5 points) MR = MC → 20 – 0.02 Q = 15 QMON = 250 passengers P = 20 – 0.01 Q → P = 20 – 0.01 (250) = $17.50 → PMON = $17.50 π(Q) = R(Q) – C(Q) = (17.50 x 250) – [1,000 + (5 x 100) + (15 x 150)] π(Q) = 4,375 – 1,000 – 500 – 2,250 = 625 so πMON(Q) = $625

4.3 LERNER index and market power (7 points) a)

Compute the LERNER indexes for the situations described in 4.1 and 4.2. (3 points) L = (P – MC) / P LERNER index - situation 4.1 Case in 4.1: L = (P – MC) / P and then L = (12.50 – 5)/12.50 = 0.60 LERNER index - situation 4.2 Case in 4.2: L = (P – MC) / P and then L = (17.50 – 15) / 17.50 = 0.14

b) In which situation does the REM have the greatest market power? Explain why. [Note: you must absolutely refer to the price elasticities in both situations to justify your answer]. (4 points) The REM has more market power in situation 4.1 as L is larger. In situation 4.1, where the price is $12.50, the demand is more inelastic than in 4.2 and this gives more market power to the REM. We can also say that in 4.2, the difference between the price and the MC is smaller, which reduces the market power for the REM. Case in 4.1: L = -1/Ep = 0.6 and Ep = -1.66 Case in 4.2: L = -1/Ep = 0.14 and Ep = -7.14.

QUESTION 5 – PILATES LESSONS (12 POINTS – 14 MINUTES) The studio Pilates plus offers private pilates lessons. The studio’s clientele is made up of two categories of customers: type 1 (the undecided) and type 2 (the passionate). The individual demand curves for both types of customers are given by the equations below, where q indicates the number of lessons and P is the price of lessons in dollars ($).

P = 40 - 8 q1

and

P = 40 - 1.8 q2

The studio is studying the possibility of offering packages that include the number of lessons desired. A customer could then buy a package of 5, 10, 15 or 20 lessons. The prices considered for the various packages are indicated in the table below.

Package #1 #2 #3 #4

Number of lessons 5 10 15 20

Price ($) 120 200 240 260

The « price line » representing these different packages is illustrated on the graph below:

5.1 What type of price discrimination is this studio using? Briefly describe this type of discrimination. (2 points) 2nd degree price discrimination or implicit price segmentation. The pricing strategy is based on non-observable characteristics.

5.2 Customers : type 1 (the undecided) (5 points) a)

Draw the demand curve for type 1 customers in the graph below. [Reminder: The demand function is P = 40 - 8 q1] (1 point)

b) Demonstrate, with calculations, why this group of consumers will not buy any package. (2 points) The total CS is negative, so type 1 consumers won’t buy any package. By replacing P = 24 in the demand function, 24 = 40 – 8q1, we find that q1 = 2 o CS1 = [(40 – 24) x 2]/2 = $16 o CS2 = [(24-0) x 3]/2 = $ -36 (negative consumer surplus as the marginal valuation is smaller than the price) o Total CS = 16 – 36 = $ -20 c)

Illustrate the consumer surplus by assuming that consumers buy package # 1. Make sure to identify the positive and negative portion(s) of the consumer surplus. (2 points)

Note: I was only necessary to indicate that CS1 was positive and CS2 was negative.

5.3 Customers : type 2 (the passionate) (5 points) a)

Draw the demand curve for type 2 customers in the graph below. [Reminder: The demand function is P = 40 - 1.8 q2] (1 point)

b) (4 points) i. Indicate which package will be chosen by type 2 customers. Briefly explain your choice. [Note: No calculation is required.] (2 points) They will buy package #4. We can see on the graph that the CS is the largest when consumers choose this package. CS for pac...