Assume wheat is produced in the Sacramento Valley using irrigation water and nit
ID: 1149154 • 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 S0.50 per pound. Nitrogen costs $0.40 per pound. 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. 1. *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. 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 3. 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?Explanation / Answer
= $14
Total revenue = $.50*600
= $300
Now total profit = ($300 - $14) = $286
Now, if farmer uses 30 pounds of nitrogen, his total cost will be $.40*30= $12
And, his total production will be 594units.
Then total profit will be ($.50*594) - $12 = 297 - $12
= $285
Now, if farmer uses 40 pounds of nitrogen, his total cost will be $.40*40= $16
And, his total production will be 602units.
Then total profit will be ($.50*602) - $16 = 301 - $16
= $285
We can see that if we ignore other costs and take them constantly and increase or decrease the quantity of nitrogen by 5 units, total profit is lower in both the scenarios and it is higher if we keep it 35 units. So, it is reasonable to keep the quantity of nitrogen to 35 units than 30 or 40.
(B) Total cost of irrigation = $6*20
= $120
Cost of nitrogen used = $.40*35
= $14
Total revenue = $.50*600
= $300
Total profit = ($300 - $120 - $14) = $166
If applying on 19 acre per inches
Total cost of irrigation = $6*19
= $114
Cost of nitrogen used = $.40*35
= $14
Total revenue = $.50*580
= $290
Total profit = ($290 - $114 - $14) = $162
If farmer uses 21 acre inches, total quantity produce will be = 605
Total cost of irrigation = $6*21
= $126
Cost of nitrogen used = $.40*35
= $14
Total revenue = $.50*605
= $302.5
Total profit = ($302.5 - $126 - $14) = $162.5
So, it is clear that farmers profit get lowered when he increase or decrease the irrigation by 1 acre-inches from 20 acre-inches. So it reasonable to use 20 acre-inches for him.
3 (a) Famer knows that if he continues using 35 pounds of nitrogen then in future his profit will get lowered as he can only produce 520 units in coming years which will give him low profits.
Total cost of irrigation = $6*20
= $120
Cost of nitrogen used = $.40*35
= $14
Total revenue = $.50*520
= $260
Total profit = ($260 - $120 - $14) = $126
So in long run farmer profit will get reduced to $126
And if he uses 30 pounds of nitrogen then his production will remain constant a 594, which will give him this profit.
Total cost of irrigation = $6*20
= $120
Cost of nitrogen used = $.40*30
= $12
Total revenue = $.50*594 = 297
= $260
Total profit = ($297 - $120 - $14) = $120
$163
So in long run farmer profit will remain $163
So farmer will use 30 pounds of nitrogen because his profit with 30 pounds of nitrogen is higher in long run.