solution 27-29 rev - 1 let Qc be the number of pumpkins...

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1. let c Q be the number of pumpkins produced by Carl. Then 16400 400 C S Q Q Q P = + = - => 41 400 S C Q Q P + = - . Max the profit of Carl: C C MR MC = => 41 ( ) 1 200 400 C S Q Q - + = => 8000 / 2 C S Q Q = - A) 2. let 1 Y and 2 Y be number of production of two firms. And each firm has the same MC=40. As for the firm 1, 1 2 940 5( ) P Y Y = - + . According to 1 1 MR MC = => 2 1 900 5 10 Y Y - = . Using the same way we can get that 1 2 900 5 10 Y Y - = => 1 2 60 Y Y = = D) 3. Using the same method, we can get that 1 2 50 Q Q = = =>P=35=>Profit=400 for each firm A) 3. first, we consider the follower, the follower’s profit depends on the output choice of the leader. 1 2 1 2 2 1280 4( ) TR Q Q Q Q = - + and 1 MR MC = => 1 2 300 2 Q Q - = . Then we can get that 1 2 2 2 2 300 1280 4( ) 2 Q TR Q Q Q - = - + .By 2 MR MC = => 2 150 Q = => 1 75 Q = C) 5. Because the two firms form a cartel. So they will behave as a single firm. the total profit of the single firm is 2 2 2 1 2 1 2 1 2 4500( ) 4( ) q q q q q q + - + - - . The optimality result is 1 2 1 1 2 2 4500 8( ) 2 0 4500 8( ) 2 0 q q q q q q - + - = - + - = => 1 2 250 q q = = A) 6. Apply the method we used in question 1, we can get thet 1 1 1 2 1000000 / ( ) TR Q Q Q = + => 1 1 MR MC = => 1 2 25000 Q Q = = =>P=20 D) 7.
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