Success or failure as a farmer depends in large part of the uncertainties of the weather during the growing seasons. Consider the following quote from a recent news article:

…In a summer plagued by drought and heat, many Southern crops are withering in the fields, taking farmers’ profits down with them. Some farmers are fighting to break even. But others have had to give up hope that this year’s crop will survive to harvest. “Farmers must decide if they’re going to continue to nurture that crop or give up and plow it under,” said George Shumaker, an Extension Service economist with the University of Georgia College of Agricultural and Environmental Sciences. Making that decision takes courage and careful calculation.

Assume that you are a farmer facing the decision of whether or not to plow under your crops. Suppose you have already invested $50 per acre in seed, water, fertilizer, and labor. You estimate it will require another $15 per acre to produce and harvest a marketable crop. If the weather remains favorable, you estimate your crop will bring a market price of $26 per acre. However, if the weather becomes unfavorable, you estimate your crop will bring a market price of $12 per acre. Currently, the weather forecasters are predicting favorable weather conditions with a probability of 0.70. The owner of the farm next to yours (who is growing the same product and has made the same $50 per acre investment) has just decided to plow his fields under because the additional $15 per acre to produce a marketable crop would just be “throwing good money after bad.”

a. Develop a decision tree for your decision problem.

b. What is the EMV of harvesting and bringing the crop to market?

c. Would you bring this crop to market or plow it under like your neighbor?

d. By how much would the probability of favorable weather have to change before your answer to the question in part c would change?

e. By how much would the $15 per acre cost of bringing the crop to market have to change before your answer to the question in part c would change?

f. What other factors might you want to consider in making this decision?