Q.Distinguish between the short-run production function and the long-run production function, giving one example of a fixed factor and one example of a variable factor.

The distinction turns entirely on whether ANY factor is fixed or whether ALL factors can be varied.

The short-run production function describes output when AT LEAST ONE factor of production is held fixed, and only the remaining (variable) factor(s) can be changed. A typical fixed factor is capital — plant, machinery and factory building — since expanding capital genuinely takes time to plan, build and install; a typical variable factor is labour, since the number of workers hired can be changed almost immediately. Short-run production is governed by the Law of Variable Proportions, which examines what happens as more of the variable factor (labour) is combined with the FIXED quantity of capital.

The long-run production function describes output when there is enough time for EVERY factor of production, including capital, organisation and even the scale of plant itself, to be varied. There is NO fixed factor at all in the long run — a firm can build an entirely new, larger factory, or scale down and close an old one. Long-run production is governed by the Laws of Returns to Scale, which examine what happens as ALL factors, including capital, are increased together in the SAME proportion. …

A common misunderstanding is treating "short run" and "long run" as fixed calendar periods (like "a year" versus "five years") — in economics the distinction is purely about whether any factor remains FIXED, not about how much liter …