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Exercises · Q7

Q.Explain what a production function is, and distinguish between the short run and the long run in production analysis.

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✓ Free question

A production function is a technological relationship, Q=f(L,K,…)Q=f(L,K,\ldots), showing the maximum quantity of output (QQ) that can be produced from every possible combination of inputs (labour LL, capital KK, land, enterprise), given the existing state of technology. Two features define it: it is expressed in physical units (not money), and it assumes technical efficiency, so the output shown is the greatest obtainable from those inputs.

Short run versus long run — the distinction rests on the adjustability of factors, not on any fixed length of calendar time:

BasisShort RunLong Run
FactorsAt least one factor is FIXEDALL factors are variable
Raising outputOnly by adding more of the variable factor to the fixed factorBy changing the scale of all factors together
Governing lawLaw of Variable Proportions (returns to a factor)Returns to Scale
Factor proportionChangesCan be kept constant

In the short run a firm cannot build a new plant, so it expands output by working its existing plant harder with more variable inputs — and runs into the Law of Variable Proportions. In the long run it can vary every input, including plant size, so it can change its whole scale of operation — and its output response is described by Returns to Scale. Because the definition is about factor adjustability, the same calendar period may be 'short run' for a large steel plant but 'long run' for a small tea stall.

✓Final answer

A production function is the technological relation Q=f(L,K,…)Q=f(L,K,\ldots) giving maximum physical output per input combination; the short run has at least one fixed factor (Law of Variable Proportions applies), the long run has all factors variable (Returns to Scale applies), the two being separated by factor adjustability rather than calendar length.

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