A, B, and C own the only three shrimp fishing boats on the island of Cournot. Each
Question:
A, B, and C own the only three shrimp fishing boats on the island of Cournot. Each incurs a cost of $5.00 per pound of shrimp caught (including fuel, opportunity cost of time, etc.). Each is of the same vintage, and can catch between 0 and 75 pounds of shrimp per day. The smallest fish a boat can catch weighs 1 pound, so at the end of a fishing day, a boat's total catch is an integer between 0 and 75. All shrimp is of equally good quality near the island of Cournot.
At the end of each day, they bring their catch to market where price is determined by market demand and the supply of fish. Let , , and denote A's, B's and C's catch, respectively. Once each has decided when to stop fishing and has brought his or her shrimp to market, the price is determined by the following equation: = = 45 .2 ( + + )
On the island of Cournot, shrimp goes bad after one day, so a boat cannot keep shrimp off the market and sell it the next day. The profits for each shrimp boat equals the number of pounds caught multiplied by its profit margin, that is: A's Profits = QA (P - 5), B's Profits = QB (P - 5), C's Profits = QC (P - 5).
You will take over A, B, and C in one of several different parallel worlds for multiple days. A "day" in class may last as long as 5 minutes or be as short as 1 minute. Each day you will be asked to set that day's level of production and record it, in pen, on a note card, before you arrive at the Cournot Fish Market for that day. At the market, each boat reads off its production, the equilibrium price is realized, and boat profits are determined by the equations described above.
The three boats have a history of family feuds. Each fishes far from the others, and will have to set its tuna production for the day without knowing the levels the other two boats will set. However, as described above, at the end of each day all boats meet at the Cournot Fish Market where the production levels of each boat become public knowledge (after profits are earned). Please remember that your goal is to maximize your profits, not to outperform the other boats.