Use this question as a reference to the question above: PLEASE ANSWER QUESTION 1

Question

Use this question as a reference to the question above:

PLEASE ANSWER QUESTION 1 NOT QUESTION 3

Return to #3 of Problem Set 3 and suppose that Abby and her rivals plan to remain in the fudge industry for the foreseeable future. Their goal is to maximize their discounted profits over their lifetimes. With this goal in mind, they would like to stick to the plan that they came up with over dinner. They plan on supporting this plan with Grim Trigger Strategies-that is, each one promises to produce the agreed upon output as long as their rival does; but, if they ever catch their rival cheating, they vow to compete forever after Assuming that a firm that deviates from this plan only gets away with it for N periods, what must discount factor be for this plan to be successful? Show your work and explain your logic (you should get a critical discount rate that depends on N) 1.

Explanation / Answer

If they collude, then monopoly profit is shared by each 4 of them

Monopoly MR=450-2Q and MC=50 thus Q=200 and P=250 thus profit=40000

Which is shared by 4, thus each gets profit of 10000

Now if other collude and one deviate

Then others will produce 50 each and remaining mkt demand=300-Q and MR=300-2Q

300-2Q=50 which implies Q=125 and P=450-125-150=450-275=175 and profit of deviating=125*125=15625

Cournot output for each firm will be 450-50/5=80 this Q=320 and price=130

Profit in cournot=6400

For collusion

10000/1-d>15625+6400d/1-d

10000-6400d>15625-15625d

9225d>5625

d>0.6097

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