Production Function

Production function is a model (usually mathematical) that relates possible levels of physical outputs to various sets of inputs, eg.

Q = f (Labour, Kapital, Land, technology,...).

To simplify the world, we will use two inputs Labour (L) and Kapital (K) so, Q = f (L, K, technology,...).

Here we will use a Cobb-Douglas production function that usually takes the form; Q = ALaKb. In this simplified version, each production function or process is limited to increasing, constant or decreasing returns to scale over the range of production. In more complex production processes, "economies of scale" (increasing returns) may initially occur. As the plant becomes larger (a larger fixed input in each successive short-run period), constant returns may be expected. Eventually, decreasing returns or "diseconomies of scale" may be expected when the plant size (fixed input) becomes "too large." This more complex production function is characterized by a long run average cost (cost per unit of output) that at first declines (increasing returns), then is horizontal (constant returns) and then rises (decreasing returns).

Time and Production

As the period of time is changed, producers have more opportunities to alter inputs and technology. Generally, four time periods are used in the analysis of production:

" Market period " - A period of time in which the producer cannot change any inputs nor technology can be altered. Even output (Q) is fixed.

" Short-run "- A period in which technology is constant, at least one input is fixed and at least one input is variable.

" Long-run " - A period in which all inputs are variable but technology is constant.

" The very Long-run " - During the very long-run, all inputs and technology change.

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