Question

Consider an industry for a homogeneous product with a single firm (firm 1) that can produce at zero cost. The demand function in the industry is given by Q-20-P. Now suppose that a second firm (firm 2) considers entry into the industry. Firm 2 can also produce at zero cost. If firm 2 enters, firm 1 and 2 compete by setting quantities. Answer the following four questions. Qi Suppose that Firm 2 enters the market. What are the Stackelberg equilibrium quantities and profits for the Firm 1 and Firm 2? Q2. Suppose firm 2s entry cost F16. To what level of output would the Firm 1 have to commit in order to deter the Firm 2 from entering the market? Q3. Suppose firm 2s entry cost f16. Should Firm 1 accommodate or deter entry? Show your arguments.
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Answer #1

In Stackleberg duopoly model the market leader is the first mover and the other firm follows sequentially.

In this model th total quantity demanded in the market is give by both firm 1 firm 2.

QD = Q1+Q2

So the price of Market = 20 - QD and the price for firm 1 = 20-Q2 and for firm 2 = 20 - Q1.

When cost for firm 2 is 16 to stop him entering into the market the quantity firm 1 should produce is Qd= 20-16= 4.

I fthe firm 2 is producing for 16$ then firm 1 should not deter him as he will be better well off to sell his product at 15$ as his cost is Zero.  

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