Production Function Is a Descriptive

¶ … production function is a descriptive relation that connects inputs and outputs, It specifies the maximum possible output that can be produced for given amounts of inputs. Returns to scale refers to the relation between output and proportional variation in all inputs taken together. A production function displays constant returns to scale when a 1% change in all inputs results in a 1% change in output. Finally, with decreasing returns to scale, a 1% change in all inputs results in a less than 1% change in output.

A return to a factor refers to the relation between output and the vibration in only one input, holding other inputs fixed. Returns to a factor can be expressed as total, marginal or average quantities. The law of diminishing returns states that the marginal product of a variable factor will eventually decline as the use of the input is increased. Most production functions allow some substitution of inputs. An isoquant displays all combinations of inputs that produce the same quantity of output.

The optimal input mix to product any given output depends on the costs of the inputs. The isocost line displays all combinations of inputs that cost the same. Cost minimization for a given output occurs where the isoquant is tangent to the isocost line. Changes in input prices change the slope of the isocost line and the point of tangency. When the price of an input increases, the firm will reduce its use of this input and increase it use of other inputs (substitution effect).

Cost curves can be derived from the isoquant/isocost analysis. The total cost curve depicts the relation between total costs and output. Marginal cost is the change in total cost associated with a one-unit change in output. Marginal cost is the change in total cost associated with a one-unit change in output. Average cost is the total cost divided by the total output. Average cost falls when marginal cost is below average cost; average cost rises with marginal cost is above average cost.

Average and marginal costs are equal when average cost is at a minimum. There is a direct link between the production function and cost curves. Holding input prices constant, the slopes of cost curves are determined by the underlying production technology. Opportunity cost is the value of a resource in tis next best alternative use. Current market process more closely reflect the opportunity costs of inputs than historical costs. The relevant costs for managerial decision making are the opportunity costs.

Cost curves can be depicted for both the short run and the long run. The short run is the operating period during which at least one input (typically capital) is fixed in supply. During this period, fixed costs can be incurred even if the firm produces no output. In the long run, there are no fixed costs -- all inputs and costs are variable. Short-run cost curves are sometimes called operating curves because they are used in making near-term production and pricing decisions. Fixed costs are irrelevant for these decisions.

Long-run cost curves are referred to as planning curves, since they play a key role in longer-run planning decisions related to plant size and equipment acquisitions. The minimum efficient scale is defined as that plant size at which long-run average cost is first minimized. The minimum efficient scale affects both the optimal plant size and the level of potential competition. Industries where the average cost declines over a broad range of output are characterized as having economies of scale.

A learning curve displays the relation between average cost and cumulative volume of production. For some firms, the long-run average cost for producing a given level of output declines as the firm gains experience from producing the output (that is, there are significant learning effects). Economies of scope exist when the cost of producing a joint set of products in one firm is less than the cost.