Cost/production functions?

Question

If you are examining output as a function of labour and capital in the UK's railway industry, how easy is it, using raw statistical data, to figure out what the indices pertaining to K and L are?

Also, does a regression analysis (to ascertain if K and L really affect output) make any kind of sense? If you've accepted a Ouput = f(K, L) model, surely a regression can't tell you anything useful (other than give you an example of measurement error). I ask this on behalf of a friend. Perhaps you can improve on his paragraph:

For question 3, a cost function has to be formulated. Taking into account output, labour and capital, the cost function can establish the relationship between the three. Regression analysis is used to establish first and foremost that the relationship exists and is statistically significant. Once it is established, the productivity is found by seeing how much output was produced for the given level of inputs and whether this has decreased or increased over time.

Answer 1

The production function is postulated to include the influences of capital, labour, materials, technological development and innovation, and enterprise (risk-taking).  If you draw a simple graph of production against capital and/or labour, then it will not show high correlation.  Some decent correlation, because you've built the model to show a connection, but not a very high association.  That's because the other parameters are not easily measurable on the cardinal scale, and would be expected to affect the production function by "jumps" or "slides" in its position.  Most production functions I've analysed will show partial K and L correlation coefficients (R') around 0.6 or 0.7; that's less than 50 per cent explanation of the variability in output.

The most likely explanations for this result relate to technological development and enterprise.  Even quite small changes in technology and business risk can affect production considerably, whereas quite large changes in labour or capital cost will often have only minor effects.  It seems obvious really: if a production process is going to be endangered by a 10 per cent rise in capital and labour costs, then it wasn't a robust process in the first place.  However, if technology permits a 2 per cent increase in productivity, then the process will adopt it quickly and output could rise significantly.

The third paragraph does not say very much.  It needs greater depth of awareness of production processes and functions.  In the rail industry, the major cost influences are infrastructural and historical, and they change massively but slowly.  About half of the present rail network needs refurbishment and about 10 per cent of it is over a century old.  Even if no new lines are built and no new routes offered to operators, the cost of the system and especially cost per passenger mile will continue to rise as the network creaks and collapses at various points.  That's the technological influence in the production function and should be measured, if possible.

Sorry to be negative but hope this is helpful.

Answer 2

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