If a company has project A and project B it can decide what is more profitable. The math in this example is straightforward.

If human has activity A and activity B, how can someone calculate what is more efficient from economical standpoint? For example, take a taxi or use public transit to get from A and B. If human takes taxi, it will cost him 18 dollars, he or she will spend 20 minutes mostly sitting. If human takes public transit, he or she will spend $2.5, it will take 45 minutes including 10 minutes walking.

How to account "energy", "motivation", "missing time", etc?


A useful framework for analysing personal activities involving both monetary and time costs is a household production model. A simple example of such a model (adapted from Chiappori & Lewbel (2015) pp 411-2) is below. Note that a "household" could be one person (the assumption that members of a multi-person household cooperate to maximise their joint utility can be regarded as an optional extra of the model).

The model distinguishes between commodities, which directly affect utility, and goods, which affect utility only indirectly. The taxi ride, for example, would be a good, not a commodity, because it is just a means of getting from A to B. A household is assumed to maximise utility which is a function of commodities:

$$max\quad U(Z_1,\dots,Z_m)$$

For each commodity there is a production function:


Here $\mathbf{x}$ is a vector of goods and $T$ is time taken by a household member in producing the commodity using the goods. Production here should be understood broadly: it would include, for example, using a combination of public transport and time to "produce" a journey from A to B. Leisure activities such as visiting an entertainment can also be produced in this sense.

The goods used in producing $Z_i$ can be bought at prices $\mathbf{p}_i$, and income can be earned, over any chosen time period, at a wage $w$ (this is a simplification, eg because working hours are often fixed by an employer). Considering a period of, say, a week (and simplifying again by ignoring saving and storage of goods between weeks), the monetary constraint is ($T_w$ is time worked):

$$\Sigma_{i=1}^m \mathbf{p}_i\mathbf{x}_i\leq wT_w$$

The time constraint is ($T_{tot}$ is total time available):

$$T_w + \Sigma_{i=1}^m T_i \leq T_{tot}$$

The two constraints can be combined (by substituting for $T_w$) as:

$$\Sigma_{i=1}^m \mathbf{p}_i\mathbf{x}_i \leq w[T_{tot} - \Sigma_{i=1}^m T_i]$$

This formalises the trade-off between money and time: more time used as an input to commodities means less time available for wage-earning work and so less income with which to purchase goods inputs to commodities.

One way to bring personal energy and motivation within the model would be via the value assigned to $T_{tot}$. Starting from 168 hours in a week, deductions might be made for sleeping time, quiet relaxation, etc to arrive at what might be termed effective time available for activities, with smaller deductions for a more energetic and motivated person.


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