Consider a Cournot duopoly, composed of firms A & B ¡V which produce identical products and face identical costs.

(a) Draw a set of reaction functions in one diagram for this Cournot duopoly.
(b) Label the monopoly outputs that would be produced by firms A & B.
(c) Label the Cournot equilibrium set of outputs.
(d) If the fixed costs of firm A go up ¡V what happens to its reaction curve?
(e) In a new diagram, with identical reaction functions to those used in parts (a) ¡V (c), if the marginal cost for firm A, at every level of output, increases, demonstrate what will happen to its reaction curve. How will the Cournot equilibrium outputs of each firm change?
(f) In a new diagram, with identical reaction functions to those used in parts (a) ¡V (c), if the demand curves for firms A & B shift inwards, demonstrate what will happen to their reaction curves. How will the Cournot equilibrium outputs of each firm change?

(a) The reaction functions in a Cournot duopoly can be represented by best response functions, which show how each firm adjusts its output based on the output chosen by the other firm.

Let's assume the output of firm A is represented by Qa and the output of firm B is represented by Qb. Both firms aim to maximize their profits, given the output choices of their rivals.

The reaction function for firm A can be represented as:
Qa = f(Qb)

Similarly, the reaction function for firm B can be represented as:
Qb = g(Qa)

(b) In a monopoly scenario, there is only one firm in the market. Therefore, the output produced will be the monopoly output, which is determined by the firm's marginal cost and demand conditions. Let's label the monopoly outputs of firm A as Qa_m and the monopoly output of firm B as Qb_m.

(c) The Cournot equilibrium occurs when both firms produce output levels such that they maximize their profits, taking into account the output choices of their rivals.

Let's label the Cournot equilibrium output levels of firm A as Qa_c and the Cournot equilibrium output level of firm B as Qb_c.

(d) If the fixed costs of firm A increase, its reaction curve will shift inward. This is because higher fixed costs increase its average and marginal costs, reducing the firm's profitability at any given level of output. As a result, firm A will choose to produce less quantity to maximize its profits.

(e) In a new diagram, if the marginal cost for firm A at every level of output increases, the reaction curve of firm A will shift upward. This is because higher marginal costs increase the firm's average overall costs, resulting in lower profitability. Therefore, firm A will reduce its output to maximize its profits.

The Cournot equilibrium outputs of both firms will change. Firm A will produce less quantity, and the Cournot equilibrium output level of firm B will increase as it adjusts its output in response to firm A's decreased output.

(f) In a new diagram, if the demand curves for firms A and B shift inward, the reaction curves for both firms will shift downward. This is because a decrease in demand reduces the price firms can charge, resulting in lower profits. Firms will respond by reducing their output levels to maximize their profits.

The Cournot equilibrium outputs of both firms will decrease as they adjust their output to the decreased demand conditions.

(a) To draw the reaction functions for this Cournot duopoly, we need to consider the firms' best response to each other's output levels. In a Cournot duopoly, each firm assumes that the other firm's output is fixed when determining its own output level.

Let's say Q_A represents the output of firm A and Q_B represents the output of firm B. The reaction function for firm A shows the output level that maximizes its profit given the output level of firm B. Similarly, the reaction function for firm B shows the output level that maximizes its profit given the output level of firm A.

To draw the reaction functions, we need the following information:
- The demand function, which shows how total quantity demanded in the market depends on the sum of the outputs of both firms.
- The cost function, which shows the costs of production for each firm.

(b) To label the monopoly outputs produced by firms A and B, we need to find the output level that maximizes each firm's profit when it is the only producer in the market. This output level is where the firm's marginal cost equals the market demand.

(c) The Cournot equilibrium set of outputs is the point where both firms' reaction functions intersect. In other words, it's the level of output for each firm that maximizes its profit given the output level of the other firm.

(d) If the fixed costs of firm A go up, it will increase the firm's total costs. This increase in costs will cause firm A's reaction curve to shift up or to the left. The reason is that with higher fixed costs, firm A needs to cover these costs by producing more output to maintain its profit level. This means the firm will produce less output compared to the situation when fixed costs were lower.

(e) If the marginal cost for firm A increases at every level of output, its reaction curve will shift upward or to the left. As the marginal cost represents the additional cost of producing one more unit, the increase in marginal cost makes it less profitable for firm A to produce higher levels of output. Therefore, the firm will reduce its output level at each corresponding level of firm B's output.

The Cournot equilibrium outputs of each firm will also change. With higher marginal costs for firm A, both firms will reduce their output levels compared to the initial Cournot equilibrium.

(f) If the demand curves for firms A and B shift inward, it means the total quantity demanded in the market decreases at each price level. As a result, the reaction curves for both firms will shift down or to the right. The reason is that with a decrease in market demand, firms need to adjust their output levels downward to maximize their profits.

The Cournot equilibrium outputs of each firm will also change. With the inward shift in demand, both firms will reduce their output levels compared to the initial Cournot equilibrium.