寡头垄断企业竞争-Oligopoly/Cournot Competition-留学生经济学建模essay写作

Part 2 – Oligopoly/Cournot Competition
essay  Suppose that Jade is one of N competitors in the market which sells a homogenous product. The demand function that Jade and her competitors face is given by:

指导essay Where and qi represents the quantity produced by the ith firm. Jade has the following marginal cost function:

Her competitors face the same marginal cost function. Use this information to answer the questions below.
(a) Write down Jade's profit maximising problem and solve for her reaction function. Prove that it is a maximum.
 

(b) Assume that Jade's competitors are identical. Find an expression for Q and solve for the Nash Equilibrium quantity
 

(c) Find the Nash Equilibrium price and hence the profit each firm will earn. What happens to the profit and the quantity supplied by each firm as N∞?
 

(d) Suppose that Jade is now competing in price, that is, Bertrand competition. If she is even slightly cheaper, she will obtain the entire market but if she is more expensive, she will lose the entire market, and if she prices exactly the same as the other firms, she will share the market equally with her competitors. What is the Nash Equilibrium price and quantity in this case? What is Jade's profit?
指导essay Let us suppose that Jade is slightly more efficient than her competitors by , that is her marginal cost is what is the new Nash equilibrium now?

(e) Suppose that Jade only has one other competitor and holds the first mover advantage. Everything else remains the same. Determine the Nash Equilibrium in this Stackelberg game. Find the quantity Jade and her competitor will each produce. What can you say about the quantity that Jade sells now? Calculate Jade's profit and compare it with the Cournot game in the earlier parts of the question.