1 ECON 290V Canadian Microeconomic Policy Spring 2018 Homewo

1 ECON 290V Canadian Microeconomic Policy Spring 2018 Homework 3 Due on Friday, June 15, 11:59 PM. Late submissions will not be accepted. 1. The market demand for a good is given by P = 200 – Q, where P is the price ($ per unit) and Q is the quantity demanded (units). 2 companies can each produce the good at a flat cost $80 per unit. The firms are rivals in a Cournot duopoly. a. In the Cournot equilibrium, i. what is the quantity each firm produces? ii. what is the market quantity? iii. what is the market price? iv. what is each firm’s profit? b. If the firms colluded and acted as a single monopoly (each firm producing half of the monopoly profit-maximizing quantity), i. what is the quantity each firm produces? ii. what is the market quantity? iii. what is the market price? iv. what is each firm’s profit? c. If firm 1 was producing the collusive quantity (use part b above), but firm 2 decided to cheat and produce according to its own best-response function, i. what is the quantity firm 2 produces? ii. what is the market quantity? iii. what is the market price? iv. what is firm 1’s profit? v. what is firm 2’s profit? 2 2. Use the answers from question 1 to construct a bi-matrix of the firms’ payoffs (profits) in a game where each firm decides whether to stick to the collusive agreement or to cheat. Remember that when both cheat, the outcome is the Cournot duopoly equilibrium. Hint: your game should be a Prisoners’ Dilemma. a. To construct the game, fill the bi-matrix: Firm 2 Collude Cheat Firm 1 Collude Cheat b. What is the Nash equilibrium in this game? Explain. 3. State one reason why Canadian women labour force participation has increased in the last 70 years, and explain how that reason contributes to the increased women labour force participation.

Solution

Demand

P= 200- Q

Q = Q1+Q2

Q1 = Quantity produced by firm 1

Q2 = Quantity produced by firm 2

a)

i) Profit firm 1

?1 = (200- Q1 –Q2)*Q1 – 80*Q1

FOC:

d?1/dQ1 = 200 – 2Q1 – Q2 -80 =

2Q1 + Q2 = 80 ----------1)

Profit firm 2

?2 = (200- Q1 –Q2)*Q2 – 80*Q2

FOC:

d?2/dQ2 = 200 – 2Q2 – Q1 -80 =

2Q2 + Q1 = 80 ----------2)

Solve 1) and 2) simultaneously

2Q1 + Q2 = 80

Q1 + 2Q2 = 80

Q1 =40, Q2 = 40

ii) Market Quantity = Q1 + Q2 = 80

iii) Price = 200 –Q = 200- 80 = $120

iv) Profit firm 1 = (120 – 80)*40 = $1600

Profit firm 2 – (120- 80)*40 = $1600

b) Under collusion

Profit

? = (200- Q)*Q – 80*Q

FOC:

d?/dQ = 200 – 2Q -80 = 0

2Q = 120

Q= 60

i)Each firm will produce = 60/2 = 30

ii) Market Quantity =60

iii) Price = 200-60 = 140

iv) Profit = (140-80)*60 = 3600

Profit to each firm = 3600/2 =$1800