Question: You are the same crop consultant as in problem 1, but now you are determining the economically optimal nitrogen rate using Extension nitrogen fertilizer recommendations. You will first derive the optimal rate using calculus, and then using an online tool.

Suppose expected corn yield is Y = 150 +0.994N – 0.00228N2, where Y is corn yield in bushels per acre and N is the total nitrogen applied as pounds of N per acre.

1. If the expected corn price is $5.00/bu and Urea N nitrogen fertilizer solution (which is
   45% N by weight) costs $400/ton, what is the nitrogen rate to apply that will maximize net returns? (Note, first convert the price of the fertilizer from $/ton of fertilizer to $/lb of
   N). (Don’t forget to check the second order condition.) At this nitrogen rate, what is his yield (bu/ac) and what is his per acre revenue? How much will it cost ($/ac) to buy this much nitrogen fertilizer? Assuming $1000/ac in other costs, what are his per acre returns at this nitrogen rate? Now assume you find some cheaper Urea fertilizer for a price of $360/ton and the price of corn is now $5.50/bu. What is the optimal nitrogen rate to apply? What is the expected yield at this nitrogen rate? Again, assuming $1000/ac in other costs, what are his per acre returns at this nitrogen rate?
2. Many Midwestern states use this method to develop extension recommendations for

nitrogen fertilizer use in corn. Go to the Corn Nitrogen Rate Calculator at

http://extension.agron.iastate.edu/soilfertility/nrate.aspx and choose "Wisconsin - Irr

Sands" and select the "Corn following corn" on the right. Choose the right form of nitrogen "Urea (45% N)" and the nitrogen and corn prices from part a and hit calculate.

1. Does the price of N as $/lb match your answer in part a? (It should!)
2. At this Urea N fertilizer price of $400/ton and a corn price of $5.00/bu, what does the tool indicate is the optimal N rate?
3. What if the Urea N nitrogen fertilizer price is $360/ton and the corn price is $5.50/bu?
4. How do these compare to your answers in parts a and b?

Price: $2.99

Solution: The downloadable solution consists of 6 pages
Deliverable: Word Document