I encountered this phrase while reading up on growth models - that is to work with a function in intensive form. What does it mean when a function is in intensive form?
Thanks!
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asked Aug 12, 2015 at 15:56
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6$\begingroup$ This question could be made of greater use to others by linking to an example of such a statement. $\endgroup$– BKayCommented Aug 12, 2015 at 18:52
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1 Answer
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The intensive form of the production function is derived from the following. Let us assume a production function, F, with inputs of capital, K, and labor and technology, AL. Thus, output, $Y = F(K,AL)$. Assuming constant returns to scale, i.e. $F(cK,cAL) = cF(K,AL)$, we can say $F(K,AL) = ALF(K/AL, 1)$. The intensive form of the production function, f, takes the argument k = K/AL. k is ratio of capital to labour, or how much capital is there per effective unit of labour. $f(k) = Y/AL = F(K/AL, 1)$, or the output per effective unit of labour.
The intensive form is relevant because although the production function may have constant returns to scale, each individual input may exhibit diminishing returns. In other words, if you increase both labour and capital, this will increase your output proportionally, but if you increase only capital, your output will rise proportionally less. It is also easier to express interest rates and wages in the intensive form. For more, you can read any graduate level macroeconomic textbook. (I've used Romer's Macroeconomics.) Hope this helps!