Assignments Must Be Typed And Stapled From The Organic Veg

Assignments Must Be Typed And Stapled11from The Organic Vegetable

From the Organic Vegetable Factsheet, pick two of the six vegetable crops and answer the following questions:

a. Use gross revenue per acre values in the Production and Sales Trends section and costs from Appendix 1 to estimate profit per acre for both crops. Do you feel like the market average or grower average value for gross revenue per acre is more relevant?

b. Are the histograms in the Profitability and Risk section approximations to cumulative distribution functions or probability density functions?

c. How does the histogram for gross revenue per acre change how you interpret the average values for gross revenue per acre reported in the Production and Sales Trends section?

d. Using the cost estimates from Appendix 1, what is the break-even price and break-even yield for each crop using the market average values?

e. From d, based on the histograms from the Profitability and Risk section, what is the probability of observing the break-even price and yield (may need to use the red bars for price)?

For the second part:

a. Calculate the expected value (mean), standard deviation, and coefficient of variation for the snowpack data series.

b. Construct a cumulative distribution function and probability density function (pdf approximated using a histogram) using 10-inch intervals.

c. As a farmer relying on irrigation, determine whether the PDF or CDF is more informative for assessing curtailment.

d. Consider a scenario where a contract states that if the snowpack total for the last day of March is less than 10 inches, you will not plant your field and will transfer water to another farm, receiving $500/acre for fallowing. You will plant a lower profit annual crop ($400/acre), and if you refuse the contract, you will plant a high-profit perennial crop ($800/acre with snow >10 inches) or a lower-profit perennial crop ($100/acre with snow

e. Create a line chart of snowpack totals over time and assess whether this data series can be assumed to be identically distributed over time, justifying your reasoning.

Paper For Above instruction

Introduction

The analysis of agricultural profitability and climate risk is crucial for sustainable farm management. This paper addresses two interconnected components: first, evaluating the economic viability of selected vegetable crops based on revenue and cost analysis, and second, assessing snowpack data's implication on irrigation and crop planning. By applying statistical and decision analysis tools, the study aims to inform farm decision-making amid market variability and climate uncertainties, emphasizing the importance of understanding distributional characteristics and risk management strategies.

Part 1: Vegetable Crop Profitability Analysis

To evaluate profitability for two vegetable crops, selection from the Organic Vegetable Factsheet is essential. For illustrative purposes, let's assume the chosen crops are lettuce and carrots, two common organic vegetables. Using the gross revenue per acre figures from the Production and Sales Trends section, alongside costs from Appendix 1, we can estimate the profit per acre for each crop.

Suppose the gross revenue per acre for lettuce is $4,000, and the costs per acre from Appendix 1 amount to $2,500. The estimated profit per acre would then be $1,500 ($4,000 - $2,500). For carrots, if the gross revenue per acre is $3,500 with similar costs, the profit per acre would be $1,000. Whether the market average or grower average gross revenue per acre better reflects realistic earnings depends on the context; market averages tend to smooth out variability and might underrepresent a grower's individual risk profile, whereas grower averages incorporate specific farm-level factors.

The histograms in the Profitability and Risk section reveal the distribution of revenue and profit outcomes for these crops. These histograms approximate probability density functions (PDFs), especially when normalized, as they depict the likelihood of various revenue levels. These PDFs facilitate understanding the variability and risk associated with each crop, in contrast to cumulative distribution functions (CDFs), which show the probability of revenue being below a certain threshold.

Analyzing the histograms alters the interpretation of average gross revenue. Instead of relying solely on mean values, it becomes essential to consider the entire distribution, especially the frequency of extreme low-profit outcomes which influence risk. Such insights are critical for decision-makers concerned with risk management and profit stability.

Using Cost estimates from Appendix 1, the break-even price per unit yield is calculated by dividing total costs by expected yield. If the costs per acre are $2,500 and the expected yield is 10,000 pounds, then the break-even price per pound is $0.25 ($2,500 / 10,000). Similarly, the break-even yield at given market prices can be determined. For example, with a market price of $0.30 per pound, the minimum yield to break even is calculated by dividing total costs by the price, resulting in approximately 8,333 pounds per acre. These calculations help establish thresholds for profitability and inform planting decisions.

Based on the histograms, the probability of observing the break-even price or yield can be assessed by locating the corresponding point on the distribution and calculating the area under the PDF up to that point. For example, if the histogram indicates that achieving a yield of 8,333 pounds has a 60% probability, then the likelihood of breaking even at current market conditions is 60%. If the break-even market price is within a certain range, the probability can similarly be estimated.

Part 2: Snowpack Data Analysis and Decision-Making

The snowpack dataset from the CleElumMonthlySnowHistorical.xlsx file provides valuable information regarding snow accumulation, a primary factor for irrigation water availability. First, the mean, standard deviation, and coefficient of variation are calculated to quantify central tendency and variability. Assuming the dataset yields a mean of 15 inches, with a standard deviation of 7 inches, and the coefficient of variation (CV) is calculated as the ratio of standard deviation to mean (CV = 0.467), indicating moderate variability relative to the mean.

Constructing a cumulative distribution function (CDF) and probability density function (PDF) through histograms allows visualization of snowpack distribution. Using 10-inch intervals (0-10, 10-20, etc.), the histogram approximates the PDF, while the cumulative summation of these probabilities provides the CDF. The CDF is particularly valuable for assessing the probability of snowpack being below critical thresholds, such as 10 inches, which directly impacts irrigation curtailment.

As an irrigation-dependent farmer, the CDF provides a comprehensive view of the probability of snowpack levels falling below certain thresholds, making it more informative for planning purposes than the PDF alone. The PDF illustrates the likelihood of specific snowpack ranges, but the CDF directly indicates the risk of insufficient snowmelt to support irrigation needs.

Regarding the contract scenario, decision analysis involving expected profit calculations is applied. If the snowpack is less than 10 inches, the farmer abstains from planting the perennial crop, earning $100 per acre. Accepting the contract results in falling fallow with a guaranteed $500, but prevents planting high-value crops. Calculating the expected value (EV) for both options involves multiplying the profit outcomes by their respective probabilities derived from the snowpack distribution. For example, if the probability of snow $500) + (0.7 $400) = $150 + $280 = $430. Likewise, the EV if refusing the contract considers the probabilities of snow levels and subsequent crop profits, calculated similarly.

The decision tree analysis indicates that the farmer should accept the contract if the EV exceeds that of refusing it, which, in this case, appears favorable given the calculations. However, variability and risk preferences could influence this choice further.

Line Chart and Distribution Assumptions

Plotting snowpack totals over time reveals trends and variability across years. Examining the line chart shows fluctuations, which suggest that the snowpack data may not be identically distributed over time due to climate change effects, shifting weather patterns, or other temporal factors. Such variability implies the assumption of identical distribution might be unjustified without further statistical testing, such as stationarity or trend analysis.

Conclusion

In conclusion, integrating statistical analysis of crop profitability with climate risk assessments enables more informed farm management decisions. Understanding the distributions of snowpack and their impact on irrigation permits farmers to evaluate risks systematically. Decision tree analysis provides a structured approach to optimize profit under uncertainty, highlighting the critical role of data-driven strategies in sustainable agriculture. Recognizing the temporal variability of snowpack further emphasizes the importance of continual monitoring and adaptive management techniques.

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