# Essays on Agribusiness Economics and Management Math Problem

The paper “ Agribusiness Economics and Management” is an engrossing variant of the math problem on macro & microeconomics. The joint probability involves statistical measures where there is a chance of two or more events at the same point in time. The joint probability for the three events that include not infected, slightly infected, and seriously infected is given byJoint probabilities P (NSS) = P (N) * P (S) * P (S) P (z1) = 0.4 * 0.7 + 0.6 * 0.4 + 0.2 * 0.2 = 0.56 P (z2) = 0.4 * 0.2 + 0.4 * 0.2 + 0.3 * 0.2 = 0.22 P (z3) = 0.4 * 0.1 + 0.4 * 0.2 + 0.5 * 0.2 = 0.22 Letchford, & Conitzer, (2013) defines Marginal probabilities as collection of random event happening and is thought to be unconditional.

In this case the conditional probability is calculated as; P (z1) = 0.56 P (z2) = 0.22 P (z3) = 0.22 According to Cheung & Beck (2010) In Bayesian statistics, posterior probabilities involve random events allocated after the relevant background is taken into account. In this case, the posterior probability is calculated as; P (z1) = P (A)P(B|A)P(C|A and B) = 0.28 * 0.24 * 0.04 = 0.002688 P (z2) = 0.08* 0.08 * 0.06 = 0.000384 P (z3) = 0.04 *0.08 *0.1 = 0.00032 Type of prediction Joint probabilities Marginal probabilities posterior probabilities Unlikely (z1) 0.56 0.56 0.002688 Possible (z2) 0.22 0.22 0.000384 Probable (z3) 0.22 0.22 0.00032 b) Question 2 Alternative i Interest = principal * rate * time = 500,000 * 2% * 4 Income earned per year = \$40,000 Alternative ii Income annually earned from Tomato = 10,500 *0.6 + 13,300 * 0.4 – 10,000 = 1620 * 50 acres = \$81,000 Investment in safe money fund Money remaining after planting tomato = wealth – cost per acre * number of acres = \$500,000 – 10,000*50 = \$0 Interest earned = principal * rate * time = 0 * 2% * 4 = 0 Alternative iii Wheat Income annually = 7,500 * 0.6 + 6,800 *0.4 -6500 = 720 * 50 acres = \$36,000 Investment in safe money fund Money remaining after planting wheat = wealth – cost per acre * number of acres = \$500,000 – 6500*50 = \$325,000 Interest = principal * rate * time = 325,000 * 2% * 4 =\$26,000

References

Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments, 10e. McGraw-Hill Education.

Cheung, S. H., & Beck, J. L. (2010). Calculation of posterior probabilities for Bayesian model class assessment and averaging from posterior samples based on dynamic system data. Computer‐Aided Civil and Infrastructure Engineering, 25(5), 304-321.

De Barros, J. A. (2012, December). Joint probabilities and quantum cognition. In AIP Conference Proceedings (Vol. 1508, No. 1, pp. 98-107). AIP.

Earle, T. C. (2010). Trust in risk management: a model‐based review of empirical research. Risk analysis, 30(4), 541-574.

King, R. P., Boehlje, M., Cook, M. L., & Sonka, S. T. (2010). Agribusiness economics and management. American Journal of Agricultural Economics, 92(2), 554-570.Letchford, J., & Conitzer, V. (2013, July). Solving Security Games on Graphs via Marginal Probabilities. In AAAI.

Knoke, T., Hildebrandt, P., Klein, D., Mujica, R., Moog, M., & Mosandl, R. (2008). Financial compensation and uncertainty: using mean-variance rule and stochastic dominance to derive conservation payments for secondary forests. Canadian journal of forest research, 38(12), 3033-3046.

Mian, M. A. (2011). Project economics and decision analysis: deterministic models (Vol. 1). PennWell Books.