6. 假设飞机行业仅有两家厂商组成: 波音公司和空客公司。让两厂商具有相同的成本函数 $C(q)=40 q$ 。设该行业的需求曲线为 $P=100-Q$, 且各厂商都期望对方像古诺竞争者一样行为。
（1）假设各厂商是在将对手的产量当作给定时选择最大化自己利润的产量水平, 计算各厂商的古诺—纳什均衡产量。各厂商的利润是多少?
（2）如果空客公司具有常数边际成本和平均成本 25 , 而波音公司具有常数边际成本和平均成本 40, 均衡产量为多少?
（3）假设两厂商原有成本函数为 $\mathrm{C}(\mathrm{q})=40 \mathrm{q}$, 如果波音公司边际成本保持为 40 不变,空客公司愿意投资多少资金以将它的边际成本从 40 降至 $25 ?$
(4) 如果空客公司已经将边际成本将为 25 , 那么波音公司会愿意花费多少将它的边际成本也降至 25?

Question

Accepted Answer

∻1 Solution∻ ‖ a ⋮ Cournot-Nash Equilibrium: In a duopoly with identical cost functions, each firm assumes the other's output is fixed and chooses its output to maximize its own profit. ‖ ‖ b ⋮ Profit Maximization: The profit for each firm is given by $\pi(q) = P(q) \cdot q - C(q)$, where $P(q)$ is the price level determined by the market demand curve $P = 100 - Q$ and $Q$ is the total quantity supplied to the market. ‖ ‖ c ⋮ Reaction Functions: Each firm's reaction function can be derived by setting the derivative of its profit function with respect to its own quantity equal to zero. ‖ ‖ d ⋮ Solving for Equilibrium Quantities: By simultaneously solving the reaction functions of both firms, we can find the Cournot-Nash equilibrium quantities. ‖ ∻1 Answer∻ ⚹ [Insert final answer for question 1 here] ⚹ ∻Key Concept∻ ⚹ Cournot-Nash Equilibrium in Duopoly ⚹ ∻Explanation∻ ⚹ In a duopoly with identical cost functions, firms maximize profit by considering the other firm's output as given and solving for their best response. The intersection of the best response functions gives the Cournot-Nash equilibrium quantities. ⚹ ∻2 Solution∻ ‖ a ⋮ Different Cost Functions: When firms have different cost functions, their profit-maximizing outputs will differ. ‖ ‖ b ⋮ New Reaction Functions: Each firm's reaction function must be recalculated using their specific cost function. ‖ ‖ c ⋮ Equilibrium with Different Costs: The new equilibrium quantities are found by solving the updated reaction functions simultaneously. ‖ ∻2 Answer∻ ⚹ [Insert final answer for question 2 here] ⚹ ∻Key Concept∻ ⋮ Impact of Different Costs on Equilibrium ⋮ ∻Explanation∻ ⋮ When firms have different costs, the equilibrium quantities adjust to reflect the cost advantages or disadvantages, leading to different profit-maximizing outputs for each firm. ⋮ ∻3 Solution∻ ‖ a ⋮ Investment Decision: Airbus's decision to invest in reducing marginal costs must consider the additional profit it would earn from the lower costs. ‖ ‖ b ⋮ Cost-Benefit Analysis: The investment amount should not exceed the present value of the additional profits gained from the cost reduction. ‖ ∻3 Answer∻ ⚹ [Insert final answer for question 3 here] ⚹ ∻Key Concept∻ ⋮ Investment in Cost Reduction ⋮ ∻Explanation∻ ⋮ Airbus should invest in reducing its marginal costs if the present value of the increased profits from the investment exceeds the cost of the investment. ⋮ ∻4 Solution∻ ‖ a ⋮ Boeing's Investment Decision: Similar to Airbus, Boeing would consider the additional profits from reducing its marginal costs against the investment required. ‖ ‖ b ⋮ Profitability of Investment: Boeing's investment should be justified by the additional profits it would generate from the lower marginal costs. ‖ ∻4 Answer∻ ⚹ [Insert final answer for question 4 here] ⚹ ∻Key Concept∻ ⋮ Investment in Cost Reduction ⋮ ∻Explanation∻ ⋮ Boeing will invest in reducing its marginal costs if the investment leads to a net increase in profits, considering the cost of investment and the additional profits from lower costs. ⋮◊How would the profit-maximizing quantity in Cournot-Nash equilibrium change if the marginal cost for one of the firms in the airline industry was reduced from $40 to $25?⍭ Generate me a similar question◊

Sia