Problem 1 (10 points)

New Yorkers rely on the Hudson River for a large share of their drinking water. As such they

like the water to be clean and free of toxins and incur significant costs for purification if the

river is polluted. Factories upstream produce plastics and chemicals and often use the Hudson

as a giant drain for their euents. The euent level is directly proportionate to the production

level of a factory. Since New Yorkers suer as a consequence, there is considerable litigation

between the upstream factories and the downstream cities about the level of euents. Consider

the following costs and benefits of euents.

Thousand Tons of

upstream euents

Purification costs to

New York City (in $

MM)

Production benefit

to upstream factories

(in $MM)

0 0 0

1 24 60

2 52 108

3 96 148

4 144 180

5 204 204

(a) What level of upstream euents maximize social welfare? [2 points]

1. one thousand tons

2. two thousand tons

3. three thousand tons

4. four thousand tons

(b) With bargaining, if city residents have a right to clean water, what will be the level of

euents? [2 points]

1. one thousand tons

2. two thousand tons

3. three thousand tons

4. four thousand tons

(c) With bargaining, if city residents have a right to clean water, what is the minimum amount

the factories have to pay to the city? [2 points]

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Indian School of Business Managerial Economics, 2019-20

1. 60 MM

2. 108 MM

3. 52 MM

4. 96 MM

(d) Before the enactment of clean water laws in the 1970s, factories had the right to dump

waste in rivers. If back then residents wanted cleaner water and engaged in bargaining with the

factories what would be the level of euents? [2 points]

1. one thousand tons

2. two thousand tons

3. three thousand tons

4. four thousand tons

(e) If the residents engaged in bargaining with the factories what is the minimum amount the

city would have to pay to the factories? [2 points]

1. 60 MM

2. 108 MM

3. 52 MM

4. 96 MM

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Indian School of Business Managerial Economics, 2019-20

Problem 2 (10 points) The market for cigarettes in Mohali is perfectly competitive. The demand

for cigarettes in Mohali is given by 20QD = 300 P , where price (P) is measured in

rupees per packet of cigarette and quantity (Q ) is measured in thousands of packets. The aggregate

supply curve of cigarettes is known as P = 50 + 5QS .

(a) What is the equilibrium quantity of cigarettes consumed in this market? [2 points]

1. 8 thousands of packets

2. 10 thousands of packets

3. 12 thousands of packets

4. 15 thousands of packets

A researcher from the Max Institute of Health Care at ISB reports a strong link between

cigarettes consumption and lung cancer among children due to passive smoking, implying that

consumption of cigarettes causes a negative externality. The researcher has calculated that

the cost of the externality is |50 per packet of cigarettes. As a result, the municipality has

recommended imposing a tax of |50 per packet. Determine:

(b) What is the new equilibrium quantity of cigarettes consumed in this market? [2 points]

1. 6 thousands of packets

2. 8 thousands of packets

3. 10 thousands of packets

4. 12 thousands of packets

(c) What is the new equilibrium price paid by buyers? [2 points]

1. Rs. 100 per packet

2. Rs. 120 per packet

3. Rs. 140 per packet

4. Rs. 150 per packet

(d) What is the new equilibrium price received by sellers? [2 points]

1. Rs. 50 per packet

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Indian School of Business Managerial Economics, 2019-20

2. Rs. 70 per packet

3. Rs. 90 per packet

4. Rs. 100 per packet

(e) What is the new equilibrium tax revenue received by the city. [2 points]

1. Rs. 400000

2. Rs. 500000

3. Rs. 200000

4. Rs. 300000

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Indian School of Business Managerial Economics, 2019-20

Problem 3 (10 points)

Firms Alpha and Apple serve the same market. They have constant average costs of |2 per

unit. The firms can choose either a high price (|10) or a low price (|5) for their output. When

both firms set a high price, total market demand is 10,000 units which is split evenly between

the two firms. When both set a low price, total demand is 18,000, which is again split evenly.

If one firm sets a low price and the second a high price, the low priced firm sells 15,000 units,

the high priced firm sells only 2,000 units.

(a) The Payo matrix is as follows.

Apple

High Price Low Price

High Price R,R S,T

Alpha

Low Price T,S P,P

What are the values of T; R; P; S ? [4 points]

1. The values areT = 40, R = 50, P = 16, S = 27

2. The values are: T = 45, R = 40, P = 27, S = 16

3. The values are T = 50, R = 40, P = 40, S = 6

4. The values are T = 40, R = 50, P = 6, S = 40

(b) Does any player have a dominant strategy? [3 points]

1. Yes, high price is the dominant strategy for both players

2. Yes, low price is the dominant strategy for both players

3. Alpha has a dominant strategy but Apple does not have a dominant strategy

4. No, there is no dominant strategy

(c) What is the equilibrium set of strategies? [3 points]

1. (High price, High price)

2. (High price, Low price)

3. (Low price, High price)

4. (Low price, Low price)

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Indian School of Business Managerial Economics, 2019-20

Problem 4 (10 points)

Meghan owns a company that produces TV shows and employs her friend Harry. Harry has to

decide whether to pursue a training course to learn the latest television production technology.

The cost of the training to Harry is |1,000. Meghan neither oers the training nor pays for it.

Meghan has to decide whether to pay a fixed wage of |10,000 to Harry or share the profits of the

enterprise 50:50 with him. The gross profit of the company (before paying Harry) is positively

aected by both training and profit sharing. Indeed, with no training and a fixed wage total

profit is |20,000, while if either training or profit sharing is implemented the profit of the company

rises to |22,000. If both training and profit sharing are implemented, the profit is |25,000.

(a) The Payo matrix is :

Harry

Training No Training

Fixed Wage a,b 10,10

Meghan

Profit Sharing c,d 11,11

What are the values of a; b; c; d?[4 points]

1. The values are: a = 10, b = 9, c = 12:5, d = 12:5

2. The values are: a = 12, b = 10, c = 11, d = 11

3. The values are: a = 12, b = 9, c = 12:5, d = 11:5

4. The values are: a = 12, b = 10, c = 12:5, d = 12:5

(b) Does Harry have dominant strategies? [2 points]

1. Yes, training is the dominant strategy for Harry

2. Yes, no training is the dominant strategy for Harry

3. No, Harry does not have a dominant strategy

(c) Does Megan have dominant strategies? [2 points]

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Indian School of Business Managerial Economics, 2019-20

1. Yes, fixed wage is the dominant strategy for Megan

2. Yes, profit sharing is the dominant strategy for Megan

3. No, Megan does not have a dominant strategy

(d) What will be the equilibrium strategy profile in this game? [2 points]

1. (Profit Sharing, No Training)

2. (Fixed wage, Training)

3. (Profit Sharing, Training)

4. (Fixed wage, No Training)

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Indian School of Business Managerial Economics, 2019-20

Problem 5 (10 points)

A parent and a child are getting ready for the night. The parent moves first and decides whether

to set an alarm or not. The child then decides whether to get up early or not. Getting up early

gives a payo of 10 to the parent and 0 to the child; conversely, getting up late gives 10 to the

child and 0 to the parent. Setting an alarm costs 2 to the parent. Getting up early costs 1 to the

child. Sleep in costs nothing if the alarm does not ring, but sleep in while the alarm rings has

irritation cost of 15 for the child. The net payo is the payo minus the cost. Both parent and

child want to maximize their own individual net payo.

(a) The game tree is as follows.

Parent

Child

Child

Set Alarm

Don't set alarm

Parent Payo Child Payo

a b

c d

Get up early

Sleep in

10 1

0 10

Get up early

Sleep in

What are the values of a; b; c; d? [4 points]

1. The values are: a = 8, b = 1, c = 0, d = 6

2. The values are: a = 10, b = 10, c = 2, d = 5

3. The values are: a = 10, b = 0, c = 2, d = 6

4. The values are: a = 8, b = 1, c = 2, d = 5

(b) Solve for the equilibrium outcome using backward induction. [6 points]

1. The parent will not set up the child will sleep in

2. The parent will set the alarm and the child will wake up early

3. The parent will not set up the alarm and the child will wake up early

4. The parent will set up the alarm and the child will not get up early

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Indian School of Business Managerial Economics, 2019-20

Problem 6 (10 points) There are two routes for driving from Hizibizbiz to Golmal Airport. One

is a flyover (F) and the other is a local road (R). The local road takes 1 hour irrespective of

trac. The flyover can be much faster but the commute time depends on the trac. Suppose

1000 people play this game - decide which way to take. If x fraction of them take the flyover,

then it takes x hours. A traveler's utility is the negative of the hours taken to commute.

(b) Which one of the following is a Nash Equilibrium? [2 points]

1. Each player takes the local road

2. Each player takes the flyover

3. Half of them takes the local road and the other half takes the flyover

(c) In equilibrium, how many hours in total will it take to commute for all the agents? [2

points]

1. 500 hours

2. 1000 hours

3. 750 hours

(d) Suppose that the agents do not use personal cars but use Uber (which decides centrally the

route its cars should take). Uber wants to minimize the total commute time. How many drivers

should Uber send on flyover? [4 points]

1. All the cars

2. 250 cars

3. 500 cars

4. 0 cars

(e) What is the total commute time when Uber optimally chooses the trac? [2 points]

1. 250 hours

2. 500 hoyrs

3. 750 hours

4. 1000 hours

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Indian School of Business Managerial Economics, 2019-20

Problem 7 (10 points) Consider the wholesale market for haleem that is a duopoly with two

firms, Shah Ghouse and Pista House. The market demand for haleem is

P =

8>>><>>>:

140 Q Q < 140

0 otherwise

The marginal cost of production for both the firm is |20, and the firms can choose any quantity.

(a) What is the Best Response functions of Shah Ghouse? [2 points]

1. Best response function for Shah Ghouse is qSG = 60 14

qPH

2. Best response function for Shah Ghouse is qSG = 60 12

qPH

3. Best response function for Shah Ghouse is qSG = 120 32

qPH

(b) What is the Best Response functions of Pista House? [2 points]

1. Best response function for Pista House is qPH = 60 1

4qSG

2. Best response function for Pista House is qPH = 60 1

2qSG

3. Best response function for Pista House is qPH = 120 3

2qSG

(c) What is the Cournot equilibrium output? [2 points]

1. (30,30)

2. (40,40)

3. (48,48)

(d) Compare the Cournot equilibrium to the perfectly competitive outcome. [1 points]

1. The Cournot is higher than the perfectly competitive output

2. The Cournot is lower than the perfectly competitive output

3. The Cournot is same as the perfectly competitive output

(e) Compare the Cournot equilibrium to the monopoly outcome. [1 points]

1. The Cournot is higher than the Monopoly output

2. The Cournot is lower than the perfectly competitive output

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Indian School of Business Managerial Economics, 2019-20

3. The Cournot is same as the perfectly competitive output

(f) One possible strategy for each firm is to produce half of the monopolist quantity. This

would increase profit for both of them. Is this a Nash equilibrium? [2 points]

1. Yes

2. No

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Indian School of Business Managerial Economics, 2019-20

Problem 8 (10 points)

The managers of two solar power companies Photon Energies and Aditya Power are deciding

to set up solar power plants in Ladakh. The only source of electricity in Ladakh is solar power

and the market demand for electricity is P = 100 Q , where P is the price per MW and Q

is the demand for energy in MW. You have been hired by Aditya Power for consulting on the

capacity of their plant. Aditya Power has already received the necessary government permissions,

and their plant is going to come up before Photon's plant. However, both the company

will start their production at the same time. Production is completely determined by initial

capacity choice and price of energy is determined by the market. While building the capacity

is expensive, per MW cost of producing solar energy is only |20 for both the firms.

(a) What is the reaction function for Photon Energies? [2 points]

1. Best Response function for Photon Energies is qP = 40 1

2qA

2. function for Photon Energies is qP = 80 3

2qA

3. function for Photon Energies is qP = 40 14

qA

(b) How much capacity should you advice Aditya Power to build? [2 points]

1. 60 MW

2. 50 MW

3. 40 MW

4. 20 MW

(c) What is the capacity choice of Photon Energy in equilibrium? [2 points]

1. 30 MW

2. 25 MW

3. 20 MW

4. 10 MW

(d) What is the equilibrium price of solar energy in the market. [2 points]

1. Rs. 50 per MG

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Indian School of Business Managerial Economics, 2019-20

2. Rs. 40 per MW

3. Rs. 30 per MW

4. Rs. 20 per MW

(e) In equilibrium how much profit each firm earns? [2 points]

1. Aditya Power's profit is Rs. 1200 and Photon Energy's profit is Rs. 600

2. Aditya Power's profit is Rs. 1000 and Photon Energy's profit is Rs. 750

3. Aditya Power's profit is Rs. 800 and Photon Energy's profit is Rs. 400

4. Aditya Power's profit is Rs. 900 and Photon Energy's profit is Rs. 500

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Indian School of Business Managerial Economics, 2019-20

Problem 9 (10 points)

Gilbert wants to maximize his expected utility. His preferences are represented by the utility

function U(w) =

p

w where w is his monetary payo. Gilbert is oered the following bet on the

toss of a fair two-sided coin by Anne. If the coin comes up tails, Anne pays Gilbert |10,000. If

the coin comes up heads, Gilbert pays Anne |10,000. Gilbert's initial wealth is |10,000 which

he retains in its entirety if he does not take the bet.

(a) What is Gilbert's expected utility if he accepts the bet? [3 points]

1. 0

2. 70:71

3. 100

(b) Is Gilbert risk averse, risk neutral or risk loving? [1 point]

1. risk averse

2. risk neutral

3. risk loving

(c) Will he accept the bet? [2 points]

1. He will accept the bet

2. He will reject the bet

3. He is indierent between accepting and rejecting the bet

(d) Given that Gilbert loses his entire |10,000 if the coin comes up heads, what is the smallest

amount that Anne has to pay Gilbert in the event of tails to persuade him to take the bet? [4

points]

1. 30; 000

2. 5; 000

3. 10; 000

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Indian School of Business Managerial Economics, 2019-20

Problem 10 (10 points)

ISB Insurers is considering an insurance policy for households that possess |90 lakh worth of

movable valuables. In addition, each household owns immovable assets worth |40 lakh that

burglars cannot steal. Suppose there are two types of households. High-risk households, which

are 50% of all households, face a 40% chance of a burglary. Rest of the households are lowrisk,

facing a 20% chance of a burglary. During a burglary, all movable assets are lost. The

household's utility function is given by U(w) =p

w, where w denotes the total wealth of the

household. The households know if they are high risk or low risk. The insurance company

knows that households have equal probability of being high risk or low risk, but they can't

distinguish between the two types.

(a) If ISB Insurers were to oer an actuarially fair insurance premium, what would it be? [2

points]

1. |45,000

2. |9 lakhs

3. |27 lakhs

(b) Will high-risk households purchase this insurance policy at the actuarially fair price? [2

points]

1. Yes

2. No

(c) Will low-risk households purchase this insurance policy at the actuarially fair price? [2

points]

1. Yes

2. No

(d) Should the ISB insurer charge the actuarially fair insurance premium as in part (a)? [4

points]

1. Yes

2. No

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