What is the cournot model ?
Two firms producing a product that is indistinguishable from the consumers point of view
How is the cournot model represented?
p= a-b(q1+q2)
Where a>o, b>0, q1 is the quantity produce by firm i
What costs do the firm face ?
Firms face the same type of costs when producing their goods
Total cost of firm i: Ci=Cqi
What are the firms decisions in the cournot model?
- Conjecture on what the other firm will do
2. Choose how much to produce
What is the firms profit function in the cournot model ?
- What is firm i’s total revenue
- What is firm i’s total cost
- What is firm i’s profit
How do you calculate revenue ?
Total revenue = cost x quantity (PxQ)
TRI Total Revenue of Firm 1: p.q1
P= a-b(q1+q2)
TR1= [a-b(q1+q2)]q1
How to calculate the total cost ?
Total cost of firm 1: TC1= C.q1
How do you calculate total profit ?
Total profit of firm 1: (profit is Pi - represent it as K)
K1= TR1 - C1
K1= [a-b(q1+q2)]q1-C.q1
K1= aq1-bq1^2- bq2q1-cq1
When calculating profit -
The higher the quantity …
The lower the profit!
How many strategies are there in the cournot model
Players have a continuum of strategies, defined as the quantity they are going to produce
Assumptions of the basic court not model
- There are two firms producing the same good, which means that consumers are indifferent between buying the good from firm 1 or firm 2
- firms do not set their prices, but decide on how much to produce (qj represents the amount firm j produces)
- demand can be described by one function Q=a=BP, where Q=q1+q2 is total production and P is the price of the good
Demand = P=a-bQ - when deciding about how much to produce, each firm makes a conjecture about their opponents level of production
- each firms goal is to maximise its own profit
- the cost of producing an additional amount of the good is c which means that if firm j produces qj, its total cost will be Cqj
What is firm 1s best response ?
q1 = a-c/2b + q2/2
Nash equilibrium occurs when both firms are performing their…
Best response
