Developing parallel efforts: Where two is less than one

96 Part II: Considering Which Side You’re On in the Decision-Making Process

in the average quantity of corn produced per acre of land, what farmers call yield, and economists call average product, or you may be interested in how much corn output increases when you plant one more acre, marginal product to economists. Each of these relationships is important, and each offers considerable insight into the production process.

✓ Total product refers to the entire quantity of output produced from a given set of inputs. In the equation, q represents total product.

Therefore, if you plant 100 acres of corn, total product equals

or 11,357 bushels of corn produced. ✓ Average product refers to the output per unit of input. For a production function that has a single variable input, average product equals the total product divided by the quantity of input used. Therefore,

If you plant 100 acres of corn, the average product equals

or 113.57 bushels per acre. ✓ Marginal product is the change in total product that occurs when one additional unit of a variable input is employed. In Table 6-1, the marginal product of the 100th acre of land is 102 bushels of corn. The total product for 99 acres is 11,255 bushels, and the total product for 100 acres is 11,357 bushels. Thus, the difference or change between the two is 11,357 – 11,255 or 102 bushels of corn.

Marginal product is also determined with calculus.

To determine marginal product with calculus, take the following steps:

1. Take the derivative of total product with respect to the input. In the example, this is land (N).

Chapter 6: Production Magic: Pulling a Rabbit Out of the Hat

2. Substitute in the appropriate value for the input. So, to determine the marginal product of the 100th acre of land, substitute 100 for N and solve (with the help of your computer or calculator).

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Thus, if you start at 100 acres, adding another acre of land increases output by 102 bushels.

Diminishing returns

The law of diminishing returns states that ceteris paribus, as the quantity employed of an input increases, eventually a point is reached where the marginal product of an additional unit of that input decreases.

The term ceteris paribus indicates that all other things — for example, the quantities employed of other inputs and technology — are held constant. Therefore, the law of diminishing returns indicates that after some point, additional units of a variable input aren’t as productive as preceding units of the input.

Making Production More Realistic with Multiple Input Production Functions

Although single-input production functions are useful for illustrating many concepts, usually, they’re too simplistic to represent a firm’s production decision. Therefore, it’s useful for you to understand the firm’s employment decision when the quantities employed of two or more inputs are changed. In other words, you’re dealing with two or more variable inputs.

Consider the production function q = f(L,K), which indicates the quantity of output produced is a function of the quantities of labor, L, and capital, K, employed. The specific form of this function may be the following Cobb-Douglas function