2. Labour Supply

KAT.TAL.322 Advanced Course in Labour Economics

Nurfatima Jandarova

August 27, 2025

Static labour supply

Comparative statics

How does optimal labour supply change with ?

Marshallian (uncompensated) wage elasticity:

Hicksian (compensated) wage elasticity:

Decomposition into substitution and income effects:

Given the solution of the simple static model, we can form predictions about labour supply. In particular, we can evaluate how does optimal labour vary with and .

The first kind of elasticity is called Marshallian elasticity. We can easily find it by differentiating the optimal solution with respect to . This will give us total change in the optimal labour supply.

However, the total change in labour supply comes from two sources. When , the opportunity cost of leisure goes up. That is, every hour that she’s not working, she is foregoing the opportunity of earning higher . Therefore, the worker has higher incentive for increasing her labour supply . This is called substitution effect.

At the same time, now that she’s earning higher for every hour spent working, she is also enjoying higher overall income . Conversely, she can decrease her labour supply (and increase her leisure ) and still maintain same budget as before rose. This is called income effect.

The Hicksian elasticity is crucial part of the decomposition of these two effects. If you recall, the duality principle allows you to solve optimisation problems by either

maximising utility holding budget constant, or
minimising expenditure holding utility constant.

If you solve the dual of the original optimisation problem, you will get optimal solution and . You can then derive Hicksian elasticity by differentiating with respect to . Since it fixes the utility at , this elasticity only captures the substitution effect.

The decomposition of Marshallian elasticity into substitution and income effect is known as Slutsky equation.

Despite the simplicity, knowing these elasticities can be useful tools. For example, if you need to quickly assess implications of some labour policy or some external shock to wages.

Intertemporal labour supply

Example

Period utility

FOC:

Evolutionary changes along anticipated wage profile
Transitory changes
Permanent changes
Lottery win

Consider one of the FOC . Substitute the functional form of utility derivatives to get the expression .

Now, if we take derivative of with respect to treating as constant in this expression, we can study the evolutionary changes in labour supply along anticipated wage profile.

For example, consider that I expect to get low wage for the next 10 years and high wage from there onwards, I will plan to work less in the coming 10 years and more later.
Using the graph from notes to previous slide, this gives us response of optimal labour as we move along the original wage profile (red line, without any shocks).
This is Frisch elasticity.
And we know from previous derivations in the book that this quantity is always positive.

In addition to anticipated changes in wages, we can experience unanticipated changes, or shocks. If the shock is transitory in nature, i.e., only changes for some and leaves the overall lifetime wealth relatively unaffected, the elasticity will still be close to Frisch elasticity positive.

Imagine that you are a waiter in a Venetian restaurant and Jeff Bezos hosts his wedding there. Now, this is pretty extraordinary event that doesn’t happen regularly. And you can anticipate that the event will increase your wages. In this case, you would want to temporarily reduce all other non-work activities and increase hours worked.

If the shock is permanent, then it will affect considerably. The sign of this elasticity depends on the lifetime income effect.

Now, instead of Bezos hosting a wedding, imagine a popular movie is shot in Venice that brings an even bigger flock of tourists every summer. You know that you can count on higher wages every summer from now on. Well, now you may still decide to work more, or you can decide that you can still maintain overall lifetime wealth and work a little less every summer.

Consumption measure	Marshall	Hicks	Income	Frisch
PSID unadjusted	-0.442	0.094	-0.536	0.148
Food + imputed (food prices, demographics)	-0.468	0.328	-0.796	0.535
Food + imputed (house value, rent)	-0.313	0.220	-0.533	0.246

Uncompensated dynamic elasticity
Eckstein and Wolpin (1989)	5.0
Van Der Klaauw (1996)	3.6
Francesconi (2002)	5.6
M. P. Keane and Wolpin (2010)	2.8

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2. Labour Supply KAT.TAL.322 Advanced Course in Labour Economics Nurfatima Jandarova August 27, 2025

2. Labour Supply
Today
Labour supply
Static model
Static labour supply
Static labour supply
Static labour supply
Static labour supply
Static labour supply
Static labour supply
Static labour supply
Household model
Intrahousehold labour supply
Intrahousehold labour supply
Intrahousehold labour supply
Intertemporal model
Intertemporal labour supply
Intertemporal labour supply
Intertemporal labour supply
Intertemporal labour supply
Estimations
Empirical specifications
Empirical specifications
Empirical specifications
Empirical specifications
Estimates
Estimates
Estimates
Estimates
Estimates
Estimates
Estimates
Summary
References