Key West Fisheries has to decide whether to take a contract offer or not. There is uncertainty.

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Key West Fisheries has to decide whether to take a contract offer or not. There is uncertainty. Here are the details of the situation Key West Fisheries (i.e. Harry Morgan) faces. In March 1997, Harry Morgan, the founder and president of Key West Fisheries faced a difficult decision. The company has been in the tuna-fishing business for twelve years, operating a single boat. Morgan has seen the company’s fortunes rise and ebb, mainly depending upon the price of tuna. When prices are high, tuna fishermen prosper. When prices fall, they face tough times. He is uneasy about the company’s future because of uncertainties about prices and the size of future catches. Earlier in the week, Morgan received a Fax from a Spanish tuna importer to whom he has sold fish in the past. The importer is offering to make a one-season contract with Key West Fisheries to deliver 150,000 pounds of tuna at a price of $1.10 per pound. The tuna is to be delivered by October 31. Morgan has to decide in the next 10 days whether to accept or reject the Spanish contract. In considering this decision, Morgan has gathered the following information. The tuna season in the south Atlantic runs from the beginning of April to the end of October. (Not all of this time can be devoted to fishing; time in port or traveling to fishing grounds means lost fishing days.) At the risk of some over-simplification, Morgan foresees two different types of seasons, good and bad. (The type of season depends upon ocean currents, tuna migration patterns, the number of competing boats, and so on.) In a good season, the total Atlantic catch will be large, and the company can catch 300,000 pounds of tuna. In a bad season (small catches), Morgan will be able to catch only 240,000 pounds. Before the beginning of the season, it is impossible to tell whether it will be good of bad. Based on his past experience, Morgan sees good and bad seasons as equally likely. However, after the first four weeks of the season, Morgan can discern the prevailing pattern (large or small catches). Tuna is caught not only in the Atlantic but also in the Pacific, primarily by US, Russian, and Japanese fishermen. Therefore, the price of Atlantic tuna depends not only on whether the Atlantic catch is large or small but also on the size of the Pacific catch. The expected price of tuna depends upon the catches in the respective oceans as follows: Atlantic Large/Pacific Large: $.50 per pound Atlantic Large/Pacific Small: $.80 per pound Atlantic Small/Pacific Large: $.70 per pound Atlantic Small/Pacific Small: $1.00 per pound Morgan considers each of these four possibilities to be equally likely. (The type of Pacific season is fifty-fifty, and the outcomes of the two seasons are independent of one another.) As with the Atlantic catch, the size of the Pacific catch cannot be predicted prior to the season. However, the type of Pacific season will be known after the first three or four weeks of fishing. If Morgan accepts the contract, there are two options for delivering the fish to Spain. He can hire a commercial freighter to take all or part of the 150,000 pounds at a cost of $.44 per pound. Alternatively, Morgan can use his own boat to deliver the fish. This would require two round-trips since his boat can carry only 75,000 pounds. (The cost difference between operating the boat for shipping versus fishing is insignificant.) However, if the company delivers the fish itself, it will lose about 1/3 of the available fishing days (meaning a 1/3 reduction in its total catch). Revenues, Costs, and Assets, The Company’s revenues in the coming season consist of its domestic sales (at uncertain prices) plus revenues from the importer (if the contract is accepted). The company’s total cost for the entire fishing season is $180,000 (the sum of crew’s wages, interest expenses, office rent, etc.) regardless of how much fish is caught. Besides its boat, the company currently has $30,000 in liquid assets.

a) Morgan has decided to sketch a decision tree to help him determine whether to accept the contract (and if so, how to deliver the fish). He has decided to measure outcomes in terms of end-of-season liquid assets.

Draw Morgan’s decision tree and calculate the expected value of his decision. Explain how the decision tree works. Now suppose Morgan is able to delay his contract decision until after the first of May (when he will know the types of Atlantic and Pacific season.)

b) Draw Morgan’s decision tree with perfect information. Calculate how much the postponement is worth to him? Explain how the decision tree and contract decision changes.