Aec 851 class problem 3 Spring 2006 (Due Friday, March 31, 2006)

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AEC 851


Spring 2006 (Due Friday, March 31, 2006)

Please go to the website and download the fruit enterprise budgets workbook,

  1. (20%) Use the data on the spreadsheet page “Cherries-Tart&Sweet” for tart cherries during their full bearing years. Assume that the cost of family and hired labor is $12/hour.

    1. Please calculate the break-even price of tart cherry, given yield of 7500 lb/ac.

    2. For what length of planning horizon is this break-even price useful, short-run or long-run decisions? How short or long? Please explain.

    3. Please calculate the break-even yield of tart cherry, given the price of $0.23/lb.

  2. (10%) If a fruit grower were considering replacing her tart cherry orchard with apple trees (using the central leader system) what data and analytical method should be used to analyze switching from one system to the other? Why?

    1. Break-even yield analysis

    2. Net present value

    3. Stochastic dominance

    4. Stochastic budgeting

From the AEC 851 web site, please retrieve the Excel workbook

  1. (25%) As you can see from the “TartCherry” worksheet, tart cherry prices have been quite variable. For the period 1970-2005, please:

    1. Calculate mean, median, standard deviation, minimum and maximum of tart cherry prices received by growers, as well as the empirical probability that the tart cherry price received by growers is $0.23 or higher.

    2. Discuss your results from 3(a). What can you say about the shape of the probability distribution of grower tart cherry prices? How sound is the assumption that the grower tart cherry price will be $0.23/lb? What demand factors influence product price? What leeway has a grower to affect product price?

    3. What is the empirical probability of achieving at least the break-even price you calculated in 1(a)?

    4. These price data have been inflation-adjusted to constant 1982 dollars using the Producer Price Index for Farm Products. Take a look at the index on the website in the Excel workbook. How important has inflation adjustment been for farm products during this period? How much would it matter if nominal prices had been used for this analysis?

The “InvestAlts” worksheet of the Excel workbook contains forecast data on net returns from three different investment alternatives (Alt1, Alt2, and Alt3) under 20 different states of nature. (These data could have been generated by an @RISK simulation model, such as those we will touch upon at the end if this unit.)

Please analyze these data using the risk efficiency criteria listed below. In each instance, please draw conclusions as to which investments would be preferred and why.

  1. (15%) Mean-variance

  2. (15%) First-degree stochastic dominance

  3. (15%) Second-degree stochastic dominance

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