Suppose that two firms are producers of spring water, which can be obtained at zero cost. The market demand curve for their combined output is p = 100 - Q where p is the price and Q is the amount of spring water sold by both together. If the two producers act in accord with the Cournot model, their combined output will be

Question

Quizplus · Accepted Answer

In the Cournot model, firms assume that their competitor's output remains constant when deciding their own output levels, and they maximize their profits accordingly.

To find the optimal output level for each firm, we need to use the profit maximization equation:

π = (p - c)Q

where π is profit, p is price, c is marginal cost, and Q is output. Since the cost of obtaining spring water is zero, the marginal cost is also zero.

The market demand curve is:

p = 100 - Q

To obtain the total quantity demanded, we add the quantity demanded by each firm:

Q = Q1 + Q2

The profit maximization condition for each firm is:

dπ1/dQ1 = p - Q1 - Q2 = 0

dπ2/dQ2 = p - Q1 - Q2 = 0

Solving for Q1 and Q2, we get:

Q1 = Q2 = 33.33

Total output, Q = Q1 + Q2 = 66.66

Therefore, the optimal combined output for both firms is 66.66. Hence, the answer is B) 66.66.

Suppose That Two Firms Are Producers of Spring Water, Which