Important production decisions are assumed to have been made prior to assembling enter­prise budgets. How much of each input to use, when to plant and harvest, which land to use, and many other control variables are treated as fixed in enterprise budgets. A crop enterprise budget is a “snapshot” or single point representation of a complex set of production possi­bilities. Usually, the crop enterprise budget portrays the profit maximizing or recommended set of practices and expected yield. Economists employ production functions to represent the physical and biological relationships inherent in crop production. Physical and biologi­cal scientists study the relationship between various input levels and management decisions and the resulting plant growth and yield characteristics of a crop. Economists are interested in analyzing which combination of inputs and management decisions results in the most

profit. Figure 15.1 illustrates a simple production function with quantity produced on the vertical axis and quantity of input used on the horizontal axis. The curved line represents the quantity produced as a function of the quantity of input used. Maximum yield y* occurs when input quantity x* is used. Profit maximizing yield y** occurs when input quantity x** is used. Profit maximizing quantities are defined by tangency of the line with slope px/py to the production function. This tangency is derived from a condition of profit maximization stated as Marginal Cost = Marginal Revenue.[4] In other words, at the profit maximizing level of input use, change in total cost equals change in total revenue. At this point on the production function, any additional use of input increases cost more than it increases revenue. Similarly, at the optimum point, any reduced use of input reduces revenue more than it reduces cost. A second order condition for this point to be a profit maximum is that the slope of the production function is declining. This characteristic reflects declining marginal yield response to additional input use as maximum yield is approached. An impor­tant general point is that the profit maximizing level of input use and yield is generally below maximum yield unless the input is free.

The identification of a profit maximizing set of inputs for a specific crop is very diffi­cult. Many inputs and interaction between inputs cause the simple input-output relation­ship depicted in Figure 15.1 to become a complex multivariate function. The relationship between control variables and other independent variables, such as prices, climate, and soils, further complicates the farmer’s decision problem. A sustained program of agricul­tural research and extension education combined with the practical experience of farmers has allowed United States agriculture to achieve very high and increasing levels of agricul­tural productivity. Yields of many crops have increased steadily over time while input use has remained constant or fallen. It is important to note that production cost per unit falls as yield increases as fixed and quasi-fixed costs are spread over more units of production. The link between productivity and sustainability is discussed in a later section.

15.1.2 Crop Rotations and Long Run versus Short Run Land Allocation

After approximating how much profit can be expected from each of several crops that could be grown, farmers must decide how much of their land and which land to allocate to which crops. Farmers may prefer to rotate crops on each field. For example, they may prefer to plant corn on a field one year and soybeans on the same field the next year. Yield and input cost may be conditional on rotation. Repeated planting of the same crop or the same class of crops on a field may result in increased pressure from disease, weeds and other pests. Increased disease and pest pressure may result in lower yields and increased rates of pesticide use. Rotating crops may allow use of a wider variety of control products and practices over time, resulting in higher yields and lower pest control costs. In dry climates, a fallow period may be included in the rotation to increase soil moisture and allow increased pest control. Crop rotations may include two or more crops being produced on the same field in a single year. Prolonged periods of temperatures above freezing and prolonged periods of absence of extreme heat and drought are conducive to more than one crop being produced on the same field in a year.

In each planting period, farmers’ crop selection decisions may be further constrained by availability of seed and other inputs. Farmers may deviate from their usual rotation when potential profit from a crop or input constraints suggest a crop mix different than their longer term crop rotation.

Multiseason and perennial crops require farmers to make a longer-term decision about land allocation. Expected profit from a perennial crop over a 3-5 year period may be compared to several single season crops and other multiseason alternatives. The importance of time in farm decision making is emphasized by perennial crop decisions.