# Production function

Production function Y = F (K, L) describe the relationship between inputs capital (K) and labor (L) to the size of the manufactured product (s).

Assuming there are only two production factors L and K, function is:

X = f (L, K), ceteris paribus

- Where:
- L, K - size of each of the factors of production used,
- X-maximum production possible within a specified time using the specified amount and combinations of the factors of production.

Assumptions:

- For each K, L > = 0 F (K, 0) = F (0, 1) = 0

Both K and L are necessary in the production process.

- For each K, L > 0 lim F (K, L) = lim F (K, L) = + &infin,

With very large capital and non-zero work and very large work and a non-zero capital corresponds to the very large size of the manufactured product.

- The marginal product of capital (MPC) and marginal product of labor (MPL), is a relationship of product increment to increment of capital (MPK) or work needed (MPL).

If MPL and MPC > 0, then:

- The marginal products of each of the factors of production (K, L) are positive.
- If K is increasing (decreasing) and L = constans then Y rises (declines), and if L is increasing (decreasing) and K = constans then Y grows (decreases).

## Interpretation

Production function shows technically possible production volume, which can be achieved at any given time using the inputs of a certain size and structure. The specified input structure is called: method of production. If only the size of the inputs will be increased, with unchanged production method, we will have to deal with the increase in the scale of production while maintaining unchanged production method. Each level of production can be achieved using different production methods. Therefore, important for the company becomes to specify such a combination of factors of production to achieve optimal level of technical efficiency.

## References

- Kleindorfer, P. R., Singhal, K., & Wassenhove, L. N. (2005).
*Sustainable operations management*. Production and operations management, 14(4), 482-492.