In looking at a firm’s production practices, we made several simplifying assumptions. Most importantly, we assume that cost minimization—minimizing the total cost of producing the firm’s desired output quantity—
A production function relates the quantities of inputs that a producer uses to the quantity of output it obtains from them. Production functions typically have a mathematical representation in the form Q = f(K, L). A commonly used production function is the Cobb–
In the short run, a firm’s level of capital is fixed. Differences in output must be achieved by adjusting labor inputs alone. We looked at properties of the production function including an input’s marginal and average product (we focused on labor in this case, because capital is fixed). We saw examples of diminishing marginal products for labor, where the incremental output obtained from using another unit of labor in production decreases. [Section 6.2]
The ability to adjust capital inputs, which firms enjoy in the long run, has two important implications. One is that the firm can alleviate diminishing marginal products of labor by increasing the amount of capital it uses at the same time. Second, it has an ability to substitute between capital and labor. [Section 6.3]
An isoquant curve shows all combinations of inputs that allow a firm to make a particular quantity of output. The curvature and slope of the isoquant represent the substitutability of the inputs in the production of the good. In particular, the negative slope of the isoquant is equal to the marginal rate of technical substitution of labor for capital. [Section 6.4]
An isocost line connects all the combinations of capital and labor that the firm can purchase for a given total expenditure on inputs. The relative costs of capital and labor determine the slope of the isocost line. [Section 6.4]
A firm aims to minimize its costs at any given level of output. The firm’s cost-
Returns to scale is a property of production functions that describes how the level of output changes when all inputs are simultaneously changed by the same amount. Production functions can have returns to scale that are constant (if all inputs increase by a factor, output changes by the same factor), increasing (if all inputs increase by a factor, output changes by more than that factor), or decreasing (if all inputs increase by a factor, output changes by less than that factor). [Section 6.5]
When there is technological change, a production function changes over time so that a fixed amount of inputs can produce more output. This is reflected by a shift of a production function’s isoquants toward the origin. [Section 6.6]
A firm’s cost curves are derived from its expansion path, which uses isoquants and isocost curves to show how its input choices change with output. The total cost curve relates the costs tied to the isocost lines and the quantities tied to the isoquants that intersect the expansion path. [Section 6.7]
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