<p>Without more details it is impossible to tell what you are after. Indivisible labor usually means that you either work full-time (40 hours a week) or you are unemployed (0 hours). That gives rise to a discontinuity in the choice problem as households cannot select hours smoothly. Typically, you need a technical fix to solve the model.</p>
<p>The usual workaround is the one by <a href="https://www.sciencedirect.com/science/article/pii/030439328590039X" rel="nofollow noreferrer">Hansen (1985)</a>: with perfect consumption insurance and an assumed lottery who works and who is unemployed, households can be shown to choose the probability of working full-time. This gives rise to a linear disutility of labor in expected hours. The important twist for macroeconomists is that the Frisch elasticity of labor supply in hours worked at the individual level can be low (consistent with microeconomic data), but it will be equal to 1 in the aggregate, which is what you need to fit the data.</p>
<p>It is well-explained in Eric Sims's lecture notes at <a href="https://www3.nd.edu/%7Eesims1/rbc_extensions.pdf" rel="nofollow noreferrer">https://www3.nd.edu/~esims1/rbc_extensions.pdf</a>, Section 2.1.</p>

CC BY-SA 4.0
2022-03-13T08:46:27.960Z
2022-03-13T08:46:27.960Z
jpfeifer
<p>I am still an amateur in the field of economics and I came a cross a problem that I had little knowledge about.
I was given a question where it talks about static utility maximization using this utility function: max u(c, l) = ln c
which is subject to a function with unemployment benefit.</p>
<p>What does it mean for labor to be indivisible?
How do I approach this question because the only method I am very comfortable with was the lagrangian method with FoC
And finally what changes if labor becomes divisible?</p>
<p>Thank you for reading!</p>

<macroeconomics>
Indivisible Labor VS Indivisible Labor in Consumer's problem
CheesyAsian
# Indivisible Labor VS Indivisible Labor in Consumer's problem

(Asked by: username_0 on 2022-03-12)

I am still an amateur in the field of economics and I came a cross a problem that I had little knowledge about.
I was given a question where it talks about static utility maximization using this utility function: max u(c, l) = ln c
which is subject to a function with unemployment benefit.

What does it mean for labor to be indivisible?
How do I approach this question because the only method I am very comfortable with was the lagrangian method with FoC
And finally what changes if labor becomes divisible?

Thank you for reading!

**Tags:** macroeconomics


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## 1 answers

### Answer by username_1 on 2022-03-13. Score: 1

Without more details it is impossible to tell what you are after. Indivisible labor usually means that you either work full-time (40 hours a week) or you are unemployed (0 hours). That gives rise to a discontinuity in the choice problem as households cannot select hours smoothly. Typically, you need a technical fix to solve the model.

The usual workaround is the one by [Hansen (1985)](https://www.sciencedirect.com/science/article/pii/030439328590039X): with perfect consumption insurance and an assumed lottery who works and who is unemployed, households can be shown to choose the probability of working full-time. This gives rise to a linear disutility of labor in expected hours. The important twist for macroeconomists is that the Frisch elasticity of labor supply in hours worked at the individual level can be low (consistent with microeconomic data), but it will be equal to 1 in the aggregate, which is what you need to fit the data.

It is well-explained in Eric Sims's lecture notes at [https://www3.nd.edu/~esims1/rbc\_extensions.pdf](https://www3.nd.edu/%7Eesims1/rbc_extensions.pdf), Section 2.1.


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