New Mexico State University Homework, chapter 11, ProfitAEEC 501 Fall XXXXXXXXXXpointsThe friendly cotton grower who we met in our Production (9) and Cost (10) chapters is experiencingbigger and...

New Mexico State University Homework, chapter 11, ProfitAEEC 501 Fall 202125 pointsThe friendly cotton grower who we met in our Production (9) and Cost (10) chapters is experiencingbigger and better challenges. She has graduated from 2 inputs to 3. She now uses labor, water, andland, for which production is governed by the familiar Cobb Douglas production function as we showedearlier:Q = 1.000 N 0.10 L0.20 W 0.70Where N = months of labor; L = ha of land; W = water in 1000 cubic meters applied; Q = tons of cottonproduced. This time, we know input costs and productivity parameters. But now we also know the all‐importantcotton price. Price makes economics sing. The price of water is $50 per thousand cubic meters. Theprice of labor is $1000 per month, while the land price is $200 per ha per year. The price of cotton is$2000 per ton. See example 11.5 in the book for a similar setup.Her goal is to maximize profit when facing the constraint that she has only 60 units (1000 cubic meters)of a water right under base conditions, a full water supply. Most of you probably know that surfacewater supply for irrigation is heavily constrained in New Mexico and in most dry parts of the world, sotreating water as a fixed input for a period like one year is reasonable. The other inputs are variable. Please answer these questions for the base water supply (60) as well as the reduced level of water (30),reflecting recent drought conditions. 1. (5 pts) Derive the (long run) demand schedule for both N and L. 2. (5 pts) Find the profit‐maximizing quantity of labor (N) and land (L), that is the numerical amount. 3. (5 pts) Calculate the profit‐maximizing quantity of cotton supplied, and find the optimized profitearned from that cotton supplied. 4. (5 pts) Calculate the economic losses (optimized income reductions) associated with reducing waterfrom the full supply level (60 units) to the drought level of water (30 units). 5. (5 pts) Calculate the economic gains (maximum willingness to pay) for measures that could be takento avert the water losses from drought. 6. (5 points extra credit). Derive the first order conditions to optimize the discounted net presentvalue of profits over two years when there are only 30 units of water to use for those two yearswhen using a discount rate of five percent (0.05). This is a dynamic optimization problem, not welldeveloped in the text anyplace I could find.