A firm's production possibilities set contains all of the input-output combinations that are possible given the firm's technology.
A production method is efficient if there is no way to produce larger amounts of outputs using the same amounts of inputs. A firm's efficient production frontier contains all of the input-output combinations that can be achieved using efficient production methods. It can be described using a production function, a function of the form Output =F(Inputs).
Production with one variable input and one output
The average product of labor is equal to the amount of output divided by the number of workers employed, Q/L =F(L)/L.
The marginal product of labor is equal to the extra output produced by adding the marginal units of labor ΔL—the smallest amount of labor the firm can add or subtract—divided by the number of units added, [F(L)-F(L - ΔL)]/ΔL.
When the marginal product of labor is (bigger than/less than/equal to) the average product of labor, the average product is (increased by/decreased by/unchanged by) the marginal units of labor.
A multiplant firm can use the marginal product of labor to assign workers to its plants to maximize the amount it produces from any given amount of labor. If at each plant the marginal product of labor falls when more workers are assigned to the plant, then the best assignment of workers equalizes the plants' marginal products.
Production with two variable inputs and one output
An isoquant contains all of the input combinations that produce a given amount of output.
Isoquants are thin and do not slope upward. They separate input combinations that produce larger and smaller amounts of output than the combinations on the isoquant. Isoquants from the same technology do not cross and higher level isoquants lie farther from the origin.
The marginal rate of technical substitution for input X with input Y (MRTSXY) is the rate (-ΔY/ΔX) at which the firm must add units of Y to keep output unchanged when the amount of input X is reduced by a small amount. It is equal to the marginal product of X divided by the marginal product of Y, MRTSXY= MPX/MPY.
A technology using inputs X and Y has a diminishing marginal rate of technical substitution if MRTSXYdeclines as we move along an isoquant increasing input X and decreasing input Y.
Technologies differ in how much the MRTS changes as we move along an isoquant. At one extreme, inputs may be perfect substitutes, at another extreme, perfect complements. An intermediate case is the Cobb-Douglas production function Q = F(L, K) = ALα Kβ, whose MRTS changes gradually as we move along an isoquant.
Returns to scale
Economists determine whether large or small firms produce more effectively by examining returns to scale.
A firm has (constant/increasing/decreasing) returns to scale if a proportional change in all inputs leads to (the same/a greater than/a less than) proportional change in output.
Increasing returns to scale arise because of the specialization of inputs as well as certain physical laws. The reasons we observe decreasing returns to scale are more elusive. They include the presence of implicitly fixed inputs, and bureaucratic costs.
Productivity differences and technological change
A firm is more productive, or has higher productivity, when it can produce more output using the same amount of inputs. Higher productivity corresponds to an upward shift in a firm's efficient production frontier, an increase in its production function at every input combination.
Intellectual property protection (patents) helps provide incentives for firms to innovate, although at the cost of creating monopoly power.