Assume wheat is produced in the Sacramento Valley using irrigation water and nit
ID: 1149410 • Letter: A
Question
Assume wheat is produced in the Sacramento Valley using irrigation water and nitrogen fertilizer (together with land, labor, machinery, seed and other inputs.) Assume for this question that using 35 pounds of nitrogen per acre and 20 acre-inches of irrigation water produces 600 pounds of wheat (approximately 10 bushels) which sells for $0.50 per pound. Nitrogen costs $0.40 per pound. 1. Assume that if 30 pounds of nitrogen were applied (with the same costs for all other inputs) yield would be 594 pounds and that if 40 pounds of nitrogen were used; yield would be 602 pounds of wheat. Use these numbers to explain why an application rate of 35 pounds of nitrogen may seem reasonable for a grower deciding simply how much fertilizer to use. 2. Now consider irrigation. Assume the water costs S6 per acre-inch and applying 19-acre inches rather than 20 would reduce yield to 580 pounds and increasing irrigation water to 21 acre-inches would increase yield to 605. Explain why 20 inches may seem like a reasonable choice for water application. 3. Now the farmer learns that at an application rate of 35 pounds per acre some of the nitrogen leaches into the water he uses for irrigation and contaminates it with salts. With 35 pounds of applied nitrogen, wheat yield will still be 600 the first year, but lower in the following year and decline very gradually in future years to 520. Assume that the application rate of 30 would continue to yield 594 the first year and into the future. Assume the farmers' best guess is that prices of wheat and all inputs will remain unchanged. a. b. c. Explain why this information would cause the farmer to use less fertilizer than 35 Is there an externality associated with the choice of fertilizer use in question 3? Why does the interest rate or discount rate affect the farmers choice of fertilizer? Now UC Davis scientists discover that "excess" fertilizer use affects the quality of drinking water for rural communities. For wheat, nitrogen use at 30 pounds per acre or less has adverse effects but use above 30 pounds per acre reduces water quality. Start with the situation of question 1. (That is do not use the situations in questions 2 and 3.) Is there an externality to nitrogen fertilizer use on wheat? b. Does that mean fertilizer should be banned on wheat? Name two potential government policies that might help to deal with the externality?Explanation / Answer
5) Area of crop involved = 75000
produce if 35 pound of fertilizer used in a acre land = 600 pounds of wheat
price of 1 pound of fertilizer = $ 0.4
price of 1 pound of wheat = $0.5
cost of irrigation of 1 acre of land = $6
total profit = revenue - cost
total profit = 600*75000*0.5 - 75000*35*0.4 - 75000*6
total profit = $21000000
produce if 30 pounds of fertilizer used in a acre land = 594
total profit = 594*75000*.5 - 75000*30*.4 - 75000*6
total profit = $20925000
profit difference = total profit when 35 pound fertilizer - total profit when 30 pound fertilizer
profit difference = $ 75000
a) Al least $75000 in total farmers need to paid to use 30 pounds of fertilizer.
b) change in price of per acre inches of drinking water * 500000 = 75000
change in price = 75000/500000
change in price = $0.15
$ 0.15 increase in water price is needed to pay $75000 to the farmers.
6) Farmers will be better off earning more than $2092500. It means farmers can pay any amount less than $75000 to be allowed to continue polluting the water
7) It is not mentioned about the towns maximum willingness to pay. If it is completely inelastic than any price increase would be feasible for making farmers use fertilizer and at the same time no money can shift towns from using non polluted water to polluted water.
8) Town can use unpolluted water at $12 per acre of drinking water
profit when 35 pound of fertilizer = 600*75000*0.5 - 75000*35*0.4 - 75000*12
profit =$20550000
profit when 30 pound of fertilizer would remain the same. Hence there is a significant difference of $375000 between profits.
In this situation, the only possible solution seems that farmers should use 30 pounds of fertilizer per acre of land to earn maximum.