If market demand is P = 100 - Q and MC is 40, what is the Cournot Equilibrium for N firms?

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To find the Cournot equilibrium for N firms, we need to determine the quantity that each firm will produce, taking into account the market demand and the marginal cost (MC) of production.

In the Cournot model, firms assume that their competitors' quantities will remain constant when making production decisions.

Here's how to find the Cournot equilibrium for N firms:

1. Start by setting up the profit maximization problem for each firm. The profit for each firm is given by the formula:

Profit = (Price - MC) * Quantity

2. Substitute the market demand equation, P = 100 - Q, into the profit equation. Since there are N firms, the total quantity in the market is the sum of the quantities produced by each firm, Q_total = Q1 + Q2 + ... + QN.

So, Profit = (100 - Q_total - MC) * Qi, where "Qi" is the quantity produced by the ith firm.

3. Take the first derivative of each firm's profit function with respect to Q_i, and set it equal to zero to find the profit-maximizing quantity for each firm. This step involves finding the best response function for each firm.

Mathematically, d(Profit_i)/dQi = 0

4. Solve the system of best response functions for each firm simultaneously to find the Cournot equilibrium quantities for each firm.

For example, if there are two firms, the best response functions would be:

For Firm 1: d(Profit_1)/dQ1 = 0
For Firm 2: d(Profit_2)/dQ2 = 0

Solve these equations simultaneously to find the quantities Q1* and Q2*.

5. Once you have the Cournot equilibrium quantities for each firm, substitute them into the market demand equation (P = 100 - Q) to find the equilibrium price (P*) in the market.

For example, if Q1* = 40 and Q2* = 30, then Q_total* = Q1* + Q2* = 70. Substitute this value into the market demand equation (P = 100 - Q) to find the equilibrium price, P*.

Therefore, by following these steps, you can find the Cournot equilibrium quantities for N firms in the given scenario.