It is said that cost is derived from production function. Do you agree?Substantiate your arguments
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Answer:
We can summarize the ideas so far in terms of a production function, a mathematical expression or equation that explains the relationship between a firm’s inputs and its outputs:
\displaystyle Q=f\left[NR\text{,}L\text{,}K\text{,}t\text{,}E\right]Q=f[NR,L,K,t,E]
A production is purely an engineering concept. If you plug in the amount of labor, capital and other inputs the firm is using, the production function tells how much output will be produced by those inputs. Production functions are specific to the product. Different products have different production functions. The amount of labor a farmer uses to produce a bushel of corn is likely different than that required to produce an automobile. Firms in the same industry may have somewhat different production functions, since each firm may produce a little differently. One pizza restaurant may make its own dough and sauce, while another may buy those pre-made. A sit-down pizza restaurant probably uses more labor (to handle table service) than a purely take-out restaurant. We can describe inputs as either fixed or variable.
Fixed inputs are those that can’t easily be increased or decreased in a short period of time. In the pizza example, the building is a fixed input. Once the entrepreneur signs the lease, he or she is stuck in the building until the lease expires. Fixed inputs define the firm’s maximum output capacity. This is analogous to the potential real GDP shown by society’s production possibilities curve, i.e. the maximum quantities of outputs a society can produce at a given time with its available resources. Fixed inputs do not change as output changes.
Variable inputs are those that can easily be increased or decreased in a short period of time. The pizzaiolo can order more ingredients with a phone call, so ingredients would be variable inputs. The owner could hire a new person to work the counter pretty quickly as well. Variable inputs increase or decrease as output changes.
Economists often use a short-hand form for the production function:
\displaystyle Q=f\left[L\text{,}K\right]Q=f[L,K]
where L represents all the variable inputs, and K represents all the fixed inputs.Economists also differentiate between short and long run production. The short run is the period of time during which at least some factors of production are fixed. During the period of the pizza restaurant lease, the pizza restaurant is operating in the short run, because it is limited to using the current building—the owner can’t choose a larger or smaller building. The long run is the period of time during which all factors are variable. Once the lease expires for the pizza restaurant, the shop owner can move to a larger or smaller place.
Note that there is another important distinction between fixed and variable inputs. In the short run, since the firm’s fixed inputs are fixed, the only way to vary a firm’s output is by changing its variable inputs.