'Output per Worker' as the Opportunity cost of Unemployment: Rough notes

ALP (Average Labour Productivity) or OPW (Output Per Worker) as an Opportunity cost of Unemployment to society

It is very much plausible to look at Output Per Worker (OPW) or Average Labour Productivity (ALP) as a measure of Opportunity Cost of Unemployment to society. Unemployment theories and the theory of natural rate of unemployment [probably the Classical theory of Labour markets], talk about Unemployment and its related costs (in long-run & very long-run). So does the Keynesian theory of Output determination (in short-run).

Opportunity Cost means:

The cost of the next best alternative forgone is the Opportunity cost of the chosen alternative.

In Microeconomic theory, Consumer Behaviour theories like indifference preference theory, revealed preference theory; Production theories like Optimization behaviour of firms regarding their output under various market structures, etc.; Cost theories like Optimization behaviour by firms regarding their costs, etc. utilize this concept extensively.

In Macroeconomic theory too, Opportunity cost concept is utilized in various theories- for e.g. the Aggregate Labour Supply theory uses it in deriving the Aggregate Labour Supply curve from Individual labour supply curves. This is done by the means of the Microeconomic theory of Leisure-Income trade-off. Many other applications of this concept exist in Macroeconomics such as Production Possibilities frontiers, etc.

A simple model for Output Per Worker:

If the Production function is:
Y = A*f[K, N]
then OPW = Y/N.

This is but per labourer output in the economy.

OPW as such a measure:

OPW as above [at macroeconomic level] can be thought of as one such cost that the society has to forgo on account of there being people who cannot find work/do not want to work. Were they employed, we would have gained at least that much amount of output per labourer as produced by the current labour force of an economy [country]

Some Assumptions required here are:

Indeed, many qualifications arise here as below:

1. We need to assume that the Production function [Y = A*f(K, N)] remains the same even if the currently unemployed labourers become employed. It means even if N increases on account of increased labour force, Y changes in such a manner so as to keep ALP constant as before the unemployed became employed.
2. Technological parameter [A] remains constant. 
3. Production function continues to exhibit the same returns to scale as it did before the unemployed become employed. Probably a restatement of Assumption 1.
4. No change in Marginal Productivity of the inputs including labour [as well as others].  This means that the slopes of Total Product curves of Labour and Capital remain constant. In other words the partial derivatives of Total Product curves of Labour and Capital remain the same as they were before the unemployed become employed. Some other assumptions may be needed too.

Empirical research possibilities:

If above assumptions are satisfied, then OPW can be a proxy measure of the Output per unemployed labourer forgone by society on account of their unemployment. Data on Aggregate Output and Labour statistics, at least in the case of the U.S., where Labour statistics are available to some extent can be extensively used. As for India, proxy variables can be used. More on this later.

P.S.: Couldn't add mathematical equations I wanted to as such a feature isn't available here.

-Regards.