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Some work and some play: microscopic and macroscopic approaches to labor and leisure.

Niyogi RK, Shizgal P, Dayan P - PLoS Comput. Biol. (2014)

Bottom Line: However, averaging over the more microscopic processes that govern choices is known to pose tricky theoretical problems, and also eschews any possibility of direct contact with the neural computations involved.We develop a microscopic framework, formalized as a semi-Markov decision process with possibly stochastic choices, in which subjects approximately maximise their expected returns by making momentary commitments to one or other activity.We show macroscopic utilities that arise from microscopic ones, and demonstrate how facets such as imperfect substitutability can arise in a more straightforward microscopic manner.

View Article: PubMed Central - PubMed

Affiliation: Gatsby Computational Neuroscience Unit, University College London, London, United Kingdom.

ABSTRACT
Given the option, humans and other animals elect to distribute their time between work and leisure, rather than choosing all of one and none of the other. Traditional accounts of partial allocation have characterised behavior on a macroscopic timescale, reporting and studying the mean times spent in work or leisure. However, averaging over the more microscopic processes that govern choices is known to pose tricky theoretical problems, and also eschews any possibility of direct contact with the neural computations involved. We develop a microscopic framework, formalized as a semi-Markov decision process with possibly stochastic choices, in which subjects approximately maximise their expected returns by making momentary commitments to one or other activity. We show macroscopic utilities that arise from microscopic ones, and demonstrate how facets such as imperfect substitutability can arise in a more straightforward microscopic manner.

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Related in: MedlinePlus

Indifference curves (ICs) of the labor supply theory model in Eq.(1).Left: Returns from work exceed those from leisure () and right: vice versa (). Solid black lines show the budget constraint (BC): trial duration  is constant. Open circles show optimal combination of rewards and leisure for which macroscopic utility is maximised subject to BC. Dashed black lines denote the path through theoretically predicted optimal leisure and reward combinations as  is increased. A) perfect substitutability between rewards (work) and leisure (). Optimal combination is when the subject works all the time and claims all rewards if , and engage in leisure all the time otherwise. B) imperfect substitutability (e.g. ). Optimal combination comprises non-zero amounts of work and leisure.
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pcbi-1003894-g001: Indifference curves (ICs) of the labor supply theory model in Eq.(1).Left: Returns from work exceed those from leisure () and right: vice versa (). Solid black lines show the budget constraint (BC): trial duration is constant. Open circles show optimal combination of rewards and leisure for which macroscopic utility is maximised subject to BC. Dashed black lines denote the path through theoretically predicted optimal leisure and reward combinations as is increased. A) perfect substitutability between rewards (work) and leisure (). Optimal combination is when the subject works all the time and claims all rewards if , and engage in leisure all the time otherwise. B) imperfect substitutability (e.g. ). Optimal combination comprises non-zero amounts of work and leisure.

Mentions: In labor supply theory [1], subjects are assumed to maximize their macroscopic utility by trading (i) income from working (worth per reward), against (ii) leisure (worth, in the simplest case, a marginal utility of per unit time). Let be the total number of rewards that a subject accumulates, and be the cumulative amount of time spent in leisure. A commonly assumed form of macroscopic utility function is [14], [15]. (1)where is a dimensionless number representing the degree of substitutability, the willingness to replace rewards (or work) with leisure. Fig.1 shows the indifference curves (IC)–contours of equal utility. A subject is indifferent between combinations of these goods along an IC, but combinations on an IC with greater utility are preferred. The slope of an IC, the negative of which is called the marginal rate of substitution, shows how willing a subject is to substitute one good with the other, depending on how much of each it has already accumulated. Given a fixed total trial time (a budget constraint; BC Eq. (A-1) in Text S1), subjects must maximise their macroscopic utilities; this occurs for the combination of goods at which the BC is tangent to an IC or is at a boundary.


Some work and some play: microscopic and macroscopic approaches to labor and leisure.

Niyogi RK, Shizgal P, Dayan P - PLoS Comput. Biol. (2014)

Indifference curves (ICs) of the labor supply theory model in Eq.(1).Left: Returns from work exceed those from leisure () and right: vice versa (). Solid black lines show the budget constraint (BC): trial duration  is constant. Open circles show optimal combination of rewards and leisure for which macroscopic utility is maximised subject to BC. Dashed black lines denote the path through theoretically predicted optimal leisure and reward combinations as  is increased. A) perfect substitutability between rewards (work) and leisure (). Optimal combination is when the subject works all the time and claims all rewards if , and engage in leisure all the time otherwise. B) imperfect substitutability (e.g. ). Optimal combination comprises non-zero amounts of work and leisure.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4256012&req=5

pcbi-1003894-g001: Indifference curves (ICs) of the labor supply theory model in Eq.(1).Left: Returns from work exceed those from leisure () and right: vice versa (). Solid black lines show the budget constraint (BC): trial duration is constant. Open circles show optimal combination of rewards and leisure for which macroscopic utility is maximised subject to BC. Dashed black lines denote the path through theoretically predicted optimal leisure and reward combinations as is increased. A) perfect substitutability between rewards (work) and leisure (). Optimal combination is when the subject works all the time and claims all rewards if , and engage in leisure all the time otherwise. B) imperfect substitutability (e.g. ). Optimal combination comprises non-zero amounts of work and leisure.
Mentions: In labor supply theory [1], subjects are assumed to maximize their macroscopic utility by trading (i) income from working (worth per reward), against (ii) leisure (worth, in the simplest case, a marginal utility of per unit time). Let be the total number of rewards that a subject accumulates, and be the cumulative amount of time spent in leisure. A commonly assumed form of macroscopic utility function is [14], [15]. (1)where is a dimensionless number representing the degree of substitutability, the willingness to replace rewards (or work) with leisure. Fig.1 shows the indifference curves (IC)–contours of equal utility. A subject is indifferent between combinations of these goods along an IC, but combinations on an IC with greater utility are preferred. The slope of an IC, the negative of which is called the marginal rate of substitution, shows how willing a subject is to substitute one good with the other, depending on how much of each it has already accumulated. Given a fixed total trial time (a budget constraint; BC Eq. (A-1) in Text S1), subjects must maximise their macroscopic utilities; this occurs for the combination of goods at which the BC is tangent to an IC or is at a boundary.

Bottom Line: However, averaging over the more microscopic processes that govern choices is known to pose tricky theoretical problems, and also eschews any possibility of direct contact with the neural computations involved.We develop a microscopic framework, formalized as a semi-Markov decision process with possibly stochastic choices, in which subjects approximately maximise their expected returns by making momentary commitments to one or other activity.We show macroscopic utilities that arise from microscopic ones, and demonstrate how facets such as imperfect substitutability can arise in a more straightforward microscopic manner.

View Article: PubMed Central - PubMed

Affiliation: Gatsby Computational Neuroscience Unit, University College London, London, United Kingdom.

ABSTRACT
Given the option, humans and other animals elect to distribute their time between work and leisure, rather than choosing all of one and none of the other. Traditional accounts of partial allocation have characterised behavior on a macroscopic timescale, reporting and studying the mean times spent in work or leisure. However, averaging over the more microscopic processes that govern choices is known to pose tricky theoretical problems, and also eschews any possibility of direct contact with the neural computations involved. We develop a microscopic framework, formalized as a semi-Markov decision process with possibly stochastic choices, in which subjects approximately maximise their expected returns by making momentary commitments to one or other activity. We show macroscopic utilities that arise from microscopic ones, and demonstrate how facets such as imperfect substitutability can arise in a more straightforward microscopic manner.

Show MeSH
Related in: MedlinePlus