AEEC 501, Fall 2020;last homework assignmentGeneral Equilibrium, chapter 13 Passed out Tuesday Dec 1 Due Tuesday, Dec 8 (Final Exam is 4 pm T Dec 8 to 3:59 pm Th Dec XXXXXXXXXXpointsNM farmers produce...

AEEC 501, Fall 2020;last homework assignmentGeneral Equilibrium, chapter 13 Passed out Tuesday Dec 1 Due Tuesday, Dec 8 (Final Exam is 4 pm T Dec 8 to 3:59 pm Th Dec XXXXXXXXXXpointsNM farmers produce cotton and alfalfa (and other things). Each requires the use of land and water in the Rio Grande Basin. Arecently published estimate of the crop yield function for cotton and alfalfa (“Economic impacts on irrigated agriculture of waterconservation programs in drought,” Journal of Hydrology, pages 114‐127, 2014) for EBID, an irrigation district near Las Cruces, is: Cotton: Yield_c = 0.53 ‐ XXXXXXXXXX * Lc. Alfalfa: Yield_a = 10.88 ‐ XXXXXXXXXX * La. The terms Yield_c and Yield_a are yields of cotton and alfalfa, respectively, in tons per acre. These yields are unknown until theacreage by crop is known. That is, you need to solve for them.Total water use per acre is:Wc = 3.00 acre feet per acre. So total water use over all acres of cotton is: Wc * LcWa = 5.00 acre feet per acre. So total water use over all acres of alfalfa is: Wa * LaAssume that the upper bound on the total amount of the water resource available for the entire district is: W = Wc * Lc + Wa * La = 90,000 acre feet A recent price for cotton (Pc) is $2700 / ton, and for alfalfa (Pa) is $160 / ton. Estimated recent costs of production per acre for thecrops are C_c = 819 and C_a = 847.Total EBID area farm income from those two crops is summarized by the equation Y = (Pc * Yield_c – C_c) * Lc + (Pa * Yield_a – C_a) * La Where bolded terms are unknowns you need to find. Y is total farm income. Note that Y is a quadratic function of land inproduction for each of the two crops. That’s because yield is a linear function of each crop’s land in production, based on thenotion of Ricardian Rent, in which the highest yielding lands are planted before lower yielding lands are brought into production. Theuse of a quadratic objective simplifies your writing as well as solving the first order necessary conditions. 1 Use the LaGrangian multiplier method shown in class to find the optimized allocation of land by crop that maximizes EBIDfarm income from these two crops, while respecting the upper bounds on water. It requires solving three linear equationsin three unknowns, land in cotton, land in alfalfa, and the shadow price of water. The algebra requires patience. I plowedthought the algebra for about half an hour to find the two optimized levels of land and shadow price. Hint, the answer foroptimized land in alfalfa is 11,118 acres.2 What are the optimized crop yields?3 What are the optimized crop production levels? 4 What is total income earned by crop? 5 What is the shadow price of water? Please interpret that shadow price for policy analysis.