Final answer:
In Cournot competition, the equilibrium outputs are 4 units for firm 1 and 5 units for firm 2, with a market price of 6. The firms' profits are 20 each, and the total profit in the market is 40. Consumer surplus is 40, and deadweight loss is 6. If the firms merge and produce at the lower marginal cost of 1, the equilibrium outputs increase to 5 units for each firm and the market price decreases to 5. The change in efficiency, welfare, and deadweight loss would depend on the firms' cost structures and specific market conditions.
Step-by-step explanation:
In Cournot competition, the firms determine their outputs based on the assumption that their competitor's output will remain constant. To find the equilibrium outputs, we first determine each firm's reaction function, which shows the optimal output level for a given level of the competitor's output. In this case, firm 1's reaction function is Q1 = (15 - Q2 - 1) / 2, and firm 2's reaction function is Q2 = (15 - Q1 - 2) / 2. By solving these equations simultaneously, we find that the equilibrium outputs are Q1 = 4 and Q2 = 5. The total output in the market is 9 units.
To find the market price, we substitute the equilibrium outputs into the demand function and solve for price. D(p) = 15 - p, so 9 = 15 - p, which gives us p = 6.
To find the firms' profits, we calculate each firm's total revenue and subtract their total costs. Firm 1's total revenue is TR1 = p * Q1 = 6 * 4 = 24, and firm 1's total cost is TC1 = MC1 * Q1 = 1 * 4 = 4. Firm 1's profit is π1 = TR1 - TC1 = 20. Similarly, firm 2's profit is π2 = 20. The total profit in the market is 40.
Consumer surplus can be calculated by finding the area between the demand curve and the market price. In this case, consumer surplus is the area below the demand curve and above the market price, which is (1/2) * (15 - 6) * 9 = 40.
Deadweight loss in equilibrium can be calculated by finding the area between the supply curve (firm 1's marginal cost curve) and the demand curve. In this case, deadweight loss is the area below the demand curve, above the market price, and to the left of the quantity where MR = MC for firm 1, which is (1/2) * (4 - 1) * 4 = 6.
In the case of a merger where the firms produce at the lower marginal cost of 1, the equilibrium outputs would change. Firm 1's output would increase to match firm 2's output of 5, resulting in a total output of 10 units in the market. The market price would decrease to p = 5.
The change in efficiency in terms of average cost of producing the output would depend on the firms' cost structures. If firm 1 has a lower average cost than firm 2, the merger would result in a more efficient allocation of resources. Welfare would also depend on the specific cost and demand conditions. If the merger leads to lower prices and higher consumer surplus, welfare would increase. Deadweight loss would depend on how the merger affects the allocation of resources. If the merger leads to a more efficient allocation and reduces market power, deadweight loss could decrease.