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Intermediate Microeconomic Theory

Labor Supply

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Endowments vs. production

In our simple exchange model, our individuals were endowed with coconut milk and mangos.

We then considered an example where individuals had to “produce” goods using their time and skill.

We now want to model this more concretely.

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Budget Constraint in the Context of Labor Supply Assume every individual is endowed with

time (e.g. 100 hrs/wk)

What can individual’s do with their endowment of time?

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Labor Supply

So consider an individual who is also endowed with $m in non-labor income and can earn $w for each hour he works. How would we write down his budget constraint?

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Budget Constraint in the Context of Labor Supply

So a budget constraint in this context will be of the form:

qc = m + wL

(qc – dollars of composite good/consumption)(w – wage rage per hr of work)(L – number of hours of work)

Re-write as qc – wL = m

or again as qc + w(100 – L)= m + 100w

or again as qc + wℓ = m + 100w

(ℓ = 100 – L, or ℓ is leisure time or hrs spent not working)

Why am I writing it in this way?

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Budget Constraint in the Context of Labor Supply “Living is nothing but consuming time until you die”

- Tehching Hsieh (performance artist)

qc + wℓ = (m + 100w) Same form as budget constraint from desert island

endowment world, But now an individual is endowed with m units of

composite good and 100 units of another “good” called time, and w is just the “price” of consuming time (i.e. leisure).

What would a graph of Budget Constraint look like?

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Budget Constraint in the Context of Labor Supply How would Budget Constraint graph be

affected by a wage change?

By a change in non-labor income?

By taxes on wage earnings?

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Preferences in the Context of Labor Supply

How would we model preferences here? What would Indifference Curves look like?

How might they differ across people?

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Determination of Labor Supply

What will then determine optimal choice?

How will optimal choice change as non-labor income (m) changes? Will this depend on what kind of a good leisure is?

So why might two individuals supply different amounts of time to the labor market (i.e. work different amounts)?

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Labor Supply Curve

What is labor Supply Curve? How do we derive an individual’s labor

supply curve graphically?

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Labor Supply Analytically

Suppose a given individual’s preferences over stuff and leisure time was captured by the utility function u(qc,ℓ) = qc

aℓb. How would we analytically derive this

individual’s labor supply curve?

How will the individual’s labor supply change as his wage changes?

How will non-labor income affect his labor supply?

How will a decrease in b relative to a affect his labor supply?

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Altering the Budget Constraint

What is relationship between labor supply curve and leisure demand curve?

So what can shift the labor supply curve?

Shapes of Labor Supply Curves

Can a labor supply curve be backward bending?

What would a backward bending labor supply curve imply?

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Application: Capital Gains and Inheritance Taxes There is a lot of discussion about things

like capital gains and inheritance taxes. There are a lot of issues involved with

whether such taxes are good or bad ways of raising revenues.

One thing we might want to think about is what impact such taxes might have on labor supply behavior.

If leisure is a normal good, what would our model say about the above issue?

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Application: Poverty Policy

Will smaller benefits necessarily lead to greater labor supply among the poor?

Suppose a given individual’s best wage offer is $10/hr. and she has no non-labor income.

Consider the following two policies.1. A cash payment equal to $200 minus the individual’s

income from that month (i.e. someone who earns $50 gets $150 in assistance, someone who earns $0 gets $200).

2. A cash payment equal to $200 minus half the individual’s income from that month (i.e. someone who earns $50 gets $175 in assistance, someone who earns $0 still gets $200).

Which will likely lead to more hours of work among the poor?

Which will lead to greater utility for the poor?