La Hacienda Musa in Costa Rica was a long way from Leuven, Belgium. But for Maria Keller, the transition was as natural as it could be. She had spent 20 years in Leuven studying banana genetics at the catholic university of Leuven's labratory of tropical crops, world center of banana research. She had learned about the challenges of banana growing industry faced from a variety of diseases, why bananas seemed to be specifically susceptible, and how difficult it is to develop new strains of the world's most popular fruit.But after 2 decades of study, Maria was ready for something new. She did her homework, packed her few possessions and headed to her newly purchased costa Rican banana plantation.

To say that La hacienda Musa was already a banana plantation was overstating the case. In fact, maria owned 100 hectares of previosuly cleared land on which banas ahd never been grown. Because this plot was isolated from established banana growing operations in Costa Rica, the land was expected to be reasonally free from the most important and virulent of banana diseases, black Sigatoka, a fungal leaf blight.The isolation, coupled with Maria's expert knowledge of banana culture, and especially the new varieties she had brought with her from Belgium, suggested that she ought to be able to make a success of her new venture. The question that faced Maria at the moment was how much, if any, of her 100 hectares should be dedicated to organic bananas. There were good reasons to go organic: top-quality organic produce would command a premium, and her isolated location would be ideal for growing organic bananas. In 2007, Costa Rica had announced its intention to become the first fully carbon-neutral country.As part of its efforts to offset all Costa Rican carbon emissions, tourists and businesses would pay a voluntary “tax” that would be used to fund conservation, reforestation, and other enterprises that would help move the country toward carbon neutrality. Some of those tax revenues would support organic farming in order to reduce the use of petrochemical-based fertilizers. Although Maria did not expect any rebates that would reduce her costs, she knew that if she went organic, she would receive support in a variety of small ways, such as special soil analyses, access to compost, and help locating workers with organic farming experience.

Any land that was not planted in organic bananas would be used to grow bananas conventionally. Under conventional growing methods, La Hacienda Musa would produce an expected yield of 10 metric tonnes of bananas per hectare. Because of the vagaries of the weather, pests, and diseases, the actual yields were uncertain. Maria had good access to historical data, and so she knew that, with conventional growing methods, the actual yield on her plantation would be approximately normally distributed with mean 10 tonnes per hectare and a standard deviation of 0. 8 tonnes per hectare.

The uncertainty associated with organic farming was greater than conventional methods because the methods were less established in general and particularly because less was known about how to mitigate diseases and insect infestations using organic means. Maria estimated that yields would be normally distributed with a mean of 9. 2 tonnes per hectare and a standard deviation of 2. 4 tonnes per hectare.

The prices for bananas were also uncertain. The price (paid to the grower) for conventional bananas was normally distributed with a mean of $220 per tonne and a standard deviation of $28 per tonne .

Organic bananas would sell at a premium over conventional bananas, but how much this premium would be was uncertain. Maria thought the percentage premium would have a lognormal distribution with a mean of 15% and standard deviation of 2. 5%. (A premium of 5%, for example, meant that the price paid for organic bananas would be 5% more than the price for conventional bananas. ) This premium depended mainly on market factors – how many growers were in the organic business, consumer demand for organic produce – and was independent of all of other uncertainties Maria faced.

Finally, the costs associated with growing bananas were uncertain and approximately normally distributed with a mean of $1800 per hectare and a standard deviation of $300 per hectare. Because the uncertainty in growing costs was primarily due to labor rates and water use, the growing costs were identical under the two growing methods. These costs were uncorrelated with the other uncertainties.

Maria smiled to herself as she realized that her dilemma was actually quite simple to state: how much of her land should she plant in organic bananas and how much in conventional? Although the question seemed straightforward, the answer was not obvious!

Questions:-

1) Construct a simulation model of Maria Keller's Decision.

a. Suppose that Maria Keller plants all 100 hectares in organic bananas. What is the expected profit? What is the probability of a loss (i.e., negative profit)?

b. What is the probability that organically grown bananas will be more profitable per hectare than conventionally grown bananas?

c. Suppose that Keller plants 50 hectares in organic and 50 in conventional bananas. What is the expected total profit in this scenario? What are the 10th, 50th, and 90th percentiles for profit?

d. How would the distribution for profit change as the area planted in organic varies? Describe the changes in words and support your statements with appropriate documentations. (It will suffice to consider the cases where the area planted in organic is 0, 25, 50, 75, 0r 100 hectares.)

2) To help stimulate growth in the supply of organic produce, a major fruit and vegetable company is contemplating giving growers like Maria Keller a guaranteed minimum price (GMP) for organic bananas. For example, if the GMP were $260 per tonne, Maria would get $260 per tonne or the market price, whichever was greater. The company's hope is that such a price guarantee would help overcome growers’ concerns about the risks of growing bananas organically.

a. Assuming the GMP is $260 per tonne, model simulations to find the total benefit with GMP, for the cases where the area planted in organic is 0, 25, 50, 75, or 100 hectares (5 different simulation models).

b. Suppose the company will buy all of Maria's organic bananas, regardless of the amount she grows.

i. If the GMP is set to $260 per tonne, what is the company's expected incremental cost (i.e., incremental relative to paying the market price for keller's organic bananas)?