# Short Econ Essay

Economics in Action: Labor Supply Responses to Taxation

Alisa Tazhitdinova

Economics 10A, UCSB

Why Study Labor Supply Decisions?

14

An Increase in the Wage

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A B

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Effect of wage increase on leisure, assuming leisure is a normal good

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Why Study Labor Supply Decisions?

In most economies, wages are determined within a labor market equilibrium

a point where quantity of labor supplied equals quantity of labor demanded

However, government can affect labor supply decisions (and labor demand decisions) via taxes and transfers

Income taxes decrease net wages

Lump-sum transfers from the government increase non-wage income

Why Study Labor Supply Decisions?

Understanding how individuals respond to wage and non-wage income changes allows us to:

forecast individuals’ responses to tax policy changes

forecast tax revenue changes

influence individuals’ labor supply decisions via tax policy

Taxation is a Hotly Debated Policy

Taxation is a Hotly Debated Policy

Theory: Tax Revenue

How do taxes affect tax revenue?

Two opposite forces:

Direct: higher tax means more money can be in principle collected from each person

Indirect: higher tax may make working less desirable, potentially decreasing the pre-tax income of individuals

Always a trade off!

Theory: Tax Revenue

Mathematically:

Let τ denote tax rate and z denote individuals’ income. Then

Revenue = τ · z = τ · z(τ)

How should the government determine optimal tax rate? Easiest approach: maximize revenue!

FOC = 1 · z + τ · dz dτ

= 0

Then optimal tax rate τ satisfies:

τ∗ = z dz dτ

Theory: Tax Revenue

Then optimal tax rate τ satisfies:

τ∗ = z dz dτ

optimal tax rate should be higher when labor supply responses is small (i.e. dzdτ is small)

optimal tax rate should be lower when labor supply responses is large (i.e. dzdτ is large)

Theory: Tax Revenue

If you take a Public Finance class, you will learn that the above formula can be converted into the “famous” inverse elasticity rule:

τ∗ = 1

1 + ε where

ε = dz z

d(1−τ) (1−τ)

and thus ε measures individual’s responsiveness to tax changes.

Remember: dz ≈ ∆z and d(1− τ) ≈ ∆(1− τ)

Practice: Example 1

Most empirical studies suggest that elasticities ε are relatively small, usually ε < 0.5.

But what kind of behavior does ε = 0.5 imply?

Imagine you work and earn \$100,000, and the tax rate increases from 20% to 30%.

Rewrite ε = dz z

d(1−τ) (1−τ)

as dz = ε · z · d(1−τ)1−τ

Then dz = 0.5 · 100,000 · (0.3−0.2)1−0.2 = \$6,250

⇒ Such individual reduces his income from \$100,000 to \$93,750 when the tax rate increases from 20% to 30%. ⇒ Revenue raised increases from \$20,000 to \$28,125

What does this mean for tax policy? If ε = 0.5 then optimal tax rate τ∗ = 67%.

Practice: Example 2

What if elasticity ε is large and tax rate τ are high?

What kind of behavior does ε = 1.5 imply?

Again, imagine you work and earn \$100,000, and the tax rate increases from 40% to 50%.

Then dz = 1.5 · 100,000 · (0.5−0.4)1−0.4 = \$25,000

⇒ Such individual reduces his income from \$100,000 to \$75,000 when the tax rate increases from 40% to 50%. ⇒ Revenue raised decreases from \$40,000 to \$37,500

Why does this happen? Because if ε = 1.5 then optimal tax rate τ∗ = 40%!

Laffer Curve

Estimating Responses to Taxes

It is hard!

We cannot look into the future

But we can examine the past to learn about the future

Empirical Public Economists (me!) and Empirical Labor Economists study how individuals (or firms) responded to tax changes in the past.

Estimating Responses to Taxes: In a Nutshell

The basic approach:

Identify a tax reform to study Identify two groups of individuals

A: Those who get affected by the reform B: Those who were not affected by the reform

Compare outcomes of group A to outcomes of group B Doing so allows us to account for changes unrelated to tax reform

Measure the magnitude of response (i.e. dz) to calculate

elasticity ε = dz z

d(1−τ) (1−τ)

Example from Denmark

Generalizing

The Laffer Curve logic can be applied to any type of tax. income taxes corporate taxes capital gains taxes sales taxes

To figure out the expected effect of taxes, one needs to know:

1 how the tax base will change in response to tax change

2 the starting tax rate