Agricultural Economic Students and Faculty! What: Annual Department COOKOUT! Where: Lawn of Agriculture Administration Building (AGAD) When: Thursday, August 23rd Time: 4:30pm until the food is gone! Sponsored by Free Food & Games!

Announcements Do not go to scheduled lab locations. Labs will be virtual. Labs will start next week. Dr. Keeney will go over lab instructions on Monday. Key to Monday’s level exam is on course website.

Lecture 1: Basics of Math and Economics AGEC 352 Fall 2012– August 22 A. Remble

Basic Algebra Number of unknowns Number of equations What relationship between these two is required to solve for the unknowns?

Applied Algebra 20 acres of land 40 hours of labor Planting requirements Corn = 1 acre of land; 2 hours of labor Soybean = 1 acre of land; 2 hours of labor What’s an algebraic description of my situation assuming I will use all resources and plant some combination of these two crops?

Applied Algebra Let C = planted corn Let B = planted soybeans Land C + B = 20 Labor 2C + 2B = 40 Can we ‘solve’ this?

‘Solving’ C + B = 20 2C + 2B = 40 C = 20 – B (rewrite 1st equation) Substitute into 2nd equation 2*(20-B) + 2B = 40 40 – 2B + 2B = 40 40 + 2B = 2B + 40???

‘Solving’ C + B = 20 2C + 2B = 40 ½*(2C + 2B = 40) => C + B = 20 We can divide the second equation by 2 without changing the relationship ½*(2C + 2B = 40) => C + B = 20 The 2nd equation provides no ‘different’ information about my planting problem Tradeoffs between the two crops Limits I face in my planting

‘Solution’? 40 + 2B = 2B + 40 E.g. : set B = 50 => C = -30 Any value works for B Once you plug in a choice for B, then you just need to set the value of C to make sure the equation B + C = 20 holds E.g. : set B = 50 => C = -30 But, we might not want a value of planted acres that is < 0 so we could change our problem

‘Solution’? Choose values of B and C with 1) B + C = 20 II) B >=0, C>=0 These are called non-negativity conditions Then B will be some choice on the interval [0,20] C = 20 – B What then is your solution to this problem?

Graphical ‘Solution’ Any combination that appears on the line connecting (0,20) and (20,0) is a legitimate ‘solution’.

Economic information Corn Net Returns/acre Soybean Net Returns/acre $100 Soybean Net Returns/acre $50 First, how do we represent this information mathematically?

Back to algebra The equation should describe total net returns, so let’s call that R. Every acre of corn is $100 so that gives 100*C Every acre of soybeans is $50 50*B R = 100C + 50B

Collecting our mathematical information we have… C + B =20 R = 100C + 50B That’s two equations for 3 variables We’re no better off algebraically with the new information

But, we know the solution if… We are willing to assume that the operator with limited land and labor wants to maximize net returns Step 1: Compare the net returns between the 2 crops (C > B) Step 2: Choose to produce as much of that crop as is feasible (C = 20) Step 3: If resources remain, use those for the other crop (B = 0)

Optimization The optimization assumption takes care of R for us Says, 1st find B and C that will make R bigger than any other value it can have Then, calculate R at the end C = 20, B =0 R = 2,000

Simple with two choices When we have a large number of choices this gets more complicated Spreadsheet modeling Formulate the model on paper Input it correctly into a spreadsheet Solve Graphical methods Algorithm methods Understand, interpret, and communicate the final solution

In general Most of the work in this course is in developing the mathematical representation of the problem Identifying objectives that decision makers use as optimization criteria Identifying choices available to the decision maker that adjust their objective Identifying the limits decision makers control in adjusting their objective

Next Class Monday: review some of the stuff from the 2nd page of the level exam Calculus, elasticity, optimization Review virtual lab procedures