Maximum Economic Yield: A Mathematical Definition

 Maximum economic yield (MEY) of a crop results in maximum

profit per acre. Profit is determined by yield response to

production inputs, cost of inputs, and price of output. It has

been suggested that maximum economic yield is about 95% of maximum

yield, however, high input-costs and low commodity prices may

reduce MEY further. Therefore, a mathematical definition of MEY

would be helpful in setting yield goals for specific cost-price

situations. When maximum yield is reached an increase of

production inputs does not increase yield. Furthermore, the ratio

of change in output/change of input becomes less as maximum yield

is approached and is equal to zero at maximum yield.

 It is not economical to add more production inputs when the

cost of added inputs is greater than the value of the increase in

output. Therefore, MEY occurs when the cost of added input is

equal to the value of the yield increase produced. This can be

expressed mathematically as follows:

 (AY)(Yp) = (AX)(Xc)

 where AY = yield increase

 AX = increase of production input

 Yp = commodity price

 Xc = production cost per unit of input.

Making use of calculus the above equation can be expressed as dy/dx

= Xc/Yp

 where dy/dx = slope of the yield versus input

 function and


Xc/Yp = cost/price ratio.