Assignment:
1. (Monte Carlo analysis) The poultry farm stand at the farmers' market will sell turkeys for Thanksgiving this year to customers who pre-order. The poultry farm has received orders for 450 turkeys. Customers will pick up the turkeys at the farm stand on Broadway on the Sunday before Thanksgiving. Customers who pre-order are not required to make a deposit - the farmer trusts that they will show up on the Sunday and pay for their turkeys. The farmer knows from experience that some of the orders will be no-shows, but he is not concerned because last-minute customers generally show up to buy turkeys without pre-ordering.
Each turkey costs the farmer $30 and will sell for $90. Assume that the number of no-shows is uniformly distributed between 4% to 10% of the pre-orders. Last-minute demand is forecasted to be approximately normally distributed with a mean of 75 turkeys and a standard deviation of 30 turkeys. Assume that last-minute demand for turkeys cannot be less than zero. Any unsold turkeys are given to a homeless shelter and the farmer receives a tax deduction worth $6 per turkey for the donation. Suppose initially that the farmer is not concerned if he has to turn away customers because he runs out of turkeys.
(a) What is the number of turkeys that the farmer should expect to sell on the Sunday before Thanksgiving? Approximate your answer to the nearest integer.
(b) Assume the farmer brings the number of turkeys you computed in (a) to the farm stand on the Sunday before Thanksgiving. Construct a simulation of 10,000 trials to evaluate the distribution of pro?t. What is average pro?t over your trials? What is the con?dence interval within which pro?t is likely to fall 95% of the time?
(c) Graph the distribution of pro?t in your simulation. How does it differ from the uniform distribution and/or the normal distribution?
(d) How many turkeys would you recommend that the farmer brings to the farm stand if he wants to maximize expected pro?t? Is this quantity equal to the number computed in (a)? If equal, why is it equal? If not, why not?
(e) Now suppose that the farmer wants to avoid running out of turkeys for lastminute customers. He feels that not having turkeys for such customers will cause them to go to the grocery store in future, limiting his potential future customer base. He values his future loss at $12 per last-minute customer he has to turn away due to sold-out turkeys. How many turkeys would you now recommend that the farmer brings to the farm stand if he wants to maximize expected pro?t? Is this quantity equal to the number computed in (d)? If equal, why is it equal? If not, why not?
2. Answer any TWO of the following three questions. DO NOT answer all questions. If you answer all questions, then ONLY the FIRST TWO answers will be graded. Please remember that quality counts for far more than quantity. Limit each essay to 750 words. It is often useful to spend 15 minutes planning your essay and writing down an outline before you start writing. You should expect to spend a total of 2 hours on each essay. Please check your ?nal essays for typos and awkward phrasing.
(a) Describe sensitivity analyses, expected value analyses and Monte Carlo analyses as three potential methods of addressing uncertainty in the parameters of cost-bene?t analyses. What are advantages and disadvantages of these three methods? What is the value of information? Using a real-world example, qualitatively describe how you would compute the value of information.
(b) Read the article entitled "The Business of Biodiversity," and review the report on the "Natural Capital Protocol." Outline the costs and bene?ts of biodiversity in a speci?c location of your own choosing (for example, corn?elds in Iowa or palm oil plantations in south-east Asia). Be precise in establishing standing. List the different types of parties who stand to lose or gain from reduced biodiversity and describe in qualitative terms their expected gains or losses.
Discuss any trade-offs between effiency, equity and sustainability in this context. Try to make educated guesses about the quantitative parameters of your analysis. Consider the impact on those without standing, such as consumers or shareholders who live outside the location you have chosen. Would you argue that quantitative cost-bene?t analysis of biodiversity is a useful exercise? If so, why? If not, why not? It may be helpful for your planning to search for other news coverage or academic articles discussing the quantitative measurement of biodiversity.
(c)Read the articles entitled "Taxonomy for Understanding Digital Community Currencies" and "Alternative Currencies are Bigger than Bitcoin." Outline the costs and bene?ts of a digital community currency that can only be locally produced and locally consumed. Be precise in establishing standing. List the dfferent types of parties who stand to lose or gain and describe in qualitative terms their expected gains or losses.
Discuss the advantages and disadvantages of local community currencies for e?ciency, equity and sustainability. Try to make educated guesses about the quantitative parameters of your analysis, even if such parameters are merely stated in percentage terms. Based on your analysis, should digital community currencies focused on local production and consumption be encouraged? It may be helpful for your planning to search for other news coverage and academic articles discussing community currencies.
Readings:
1. How They're Building Prosperity From London to Kenya
by Raúl Carrillo
2. The Business of Biodiversity
By Sofia Faruqi
3. Digital Payment Platforms and Virtual Community Feelings
Eduardo H. Diniz, Erica S. Siqueira