Intermediate Microeconomic Theory Labor Supply
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. • Before, we just assumed each person supplied a fixed amount of time to production. • Is this appropriate? What else can individuals do with their time?
Labor Supply • So consider an individual who is endowed with 100 hours of time per week. Furthermore, assume he also has $m in non-labor income and can earn $w for each hour he works. How would we write down his budget constraint?
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?
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 (in this case also the numeraire) and 100 units of another “good” called leisure, and w is just the “price” of consuming time (i.e. leisure). • What would a graph of Budget Constraint look like?
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?
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?
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)?
Labor Supply Curve • What is labor Supply Curve? • How do we derive an individual’s labor supply curve graphically?
Labor Supply Analytically • Suppose a given individual’s preferences over stuff and leisure time was captured by the utility function u(qc,ℓ) = qcaℓb. • 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?
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?
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?
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. • 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). • 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?