# Production function and its properties

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Production Function may be defined as the functional relationship between input (factors of production) and physical output. It shows the maximum amount of output that can be produced from a given  set of inputs in the existing state of technology.
Input Firm Output
Production function can be expressed as
q = f(x1, x2,..., xn)
where q = quantity of output produced
(x1, x2,..., xn) = factor of production

Properties of Production function/Assumptions:
1. Production function is a single valued and continuous function with continuous first and second order partial derivative.
2. The production function is defined only for non-negative value of input and outputs.
3. The production function is normally assumed to be increasing with its domain.
4. It is strictly quasi-concave function when output is maximized or cost minimized and strictly concave function when profit is maximized.

to be continued......