# Consider a Cournot duopoly facing market demand p(Q) = 50 – 4Q. Suppose that firm 1 has cost function C1(q) = 0, and that firm 2 has cost function C2(q) = cq.a) Derive firm 1’s best-response function b1(q2). Derive firm 2’s best-response function b2(q1). Note: Since the firms are asymmetric, you cannot use a symmetry argument.

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Consider a Cournot duopoly facing market demand p(Q) = 50 – 4Q. Suppose that firm 1 has cost function C1(q) = 0, and that firm 2 has cost function C2(q) = cq.

a) Derive firm 1’s best-response function b1(q2). Derive firm 2’s best-response function b2(q1). Note: Since the firms are asymmetric, you cannot use a symmetry argument.

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Step 1

Oligopoly is a market structure where there are only few sellers. Certain features of oligopoly are:

1. Interdependence among firms
2. Product differentiation
3. Most of the production in the market is by few firms
5. Indeterminate demand curve (because of interdependence in output decisions)

Duopoly is a special case of oligopoly with two sellers in the market. In particular, Cournot duopoly is a simultaneous move game where firms simultaneously choose output. Each firm assumes the output chosen by the rival to be constant while choosing its quantity (This is Cournot Conjecture). Firms produce homogeneous products.

Step 2

Now, we are given the market demand curve as

P(Q) = 50 – 4Q; where, Q = q1 + q2

And, the cost function for firm 1 and 2 are given as

C1(q) = 0

C2(q) = c q2

Best Response Function: Best Response function of a firm is the functional relationship between the profit maximizing quantity of that firm and output of the rival (that the firm assumes the rival would produce).

Step 3

To find the Best response function for firm 1, we write the profit function for firm 1 (π1). Profit function is the d...

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