Tax Incidence: Economic Model of Labour

Question 1

How to calculate the partial derivative?

Answer 1

fx ≡ ∂f (x, y)/∂x,
fy ≡ ∂f (x, y)/∂y

Question 2

How to calculate the total derivative?

Answer 2

dz ≡ ∂f (x, y)/∂x * dx + ∂f (x, y)/∂y * dy

Question 3

How to calculate Tax Revenue?

Answer 3

R = twl

Question 4

How to calculate Total Marginal effect of income taxation?

Answer 4

1. First Derive the Total Derivative
2. Derive the Total Derivative with respect to t

1. dR = ∂R(t,w, l)/∂t * dt + ∂R(t,w, l)/∂w * dw + ∂R(t,w, l)/∂l * dl

2. dR/dt = ∂R(t,w, l)/∂t * dt/dt + ∂R(t,w, l)/∂w * dw/dt + ∂R(t,w, l)/∂l * dl/dt

Question 5

What are the 3 key components of the model of the Labor Market?

Answer 5

1. Labor Demand
2. Labor Supply
3. Wages

Question 6

What are the 3 key components of the model of the Labor Market?

Are there any Taxes involved?

Answer 6

1. Labor Demand
2. Labor Supply
3. Wages

An income tax on the employer and an income tax on the employed

Question 7

How to calculate after-tax wage rate?

Answer 7

ω ≡ (1 − t)w

t = employee part of the labor income tax.

w = before-tax wage rate

t the employee part of the labor income tax.

Question 8

How to calculate household budget constraint?

Answer 8

c = ωl

l is units of labor

Question 9

For u = u(c, l s ), tell if the marginal utility for c and l are + or - and if they are increasing or declining?

Answer 9

Positive and decreasing for c and Negative and decreasing for l

uc > 0, ucc ≤ 0, ul < 0, ull < 0

Question 10

What is the Marginal rate of substitution of leisure for consumption?

Answer 10

Household’s valuation of leisure relative to consumption

How much a household would give up of leisure to get more of consumption

−ul (ωl , l)/uc (ω, l)

Question 11

What is Relative consumer price of leisure?

Answer 11

The marginal rate of substituation of leisure for consumption

Question 12

What is the income effect?

Answer 12

The effect that higher wages will lead to less labour supply/more leisure and more consumption

Question 13

What is the subsitution effect ?

Answer 13

The effect that higher wages will lead to higher prices for leisure relative to commodities and, meaning there will be less leisure and more more consumption, thus leading to more labour supply

Question 14

Negative income effect of ω on l will lead to ….

And net effect is

Answer 14

Positive subisitution effect of of ω on l

a priori ambiguous

Question 15

How does the substitution effect
dominate the income effect?

Answer 15

After an increase in the after-tax wage rate, the budgetconstraint will become more steep and a intersect with a higher indifference curve. If the laboursupply has increased in its new point rather than decreased, it can be implied that the subsitution effect dominates the income effect.

Question 16

How is the responsiveness of the labour supply to changes in the wage rate given?

Answer 16

by the wage elasticity of labor supply:
es ≡ ∂l/∂ω * (w/l) ≥ 0

a one-percent increase in net wages leads to a es percent
increase in la

es is an uncompensated elasticity and represents a
combination of income and substitution effects
27

Question 17

How is the productive function given and are its marginal returns postive/negative or increasing/decreasing?

Answer 17

f(l), with l as labour, postive and decreasing

f ′(ld ) > 0 and
f ′′(ld ) < 0

Question 18

How can profits be given and be maximized?

Answer 18

1. π = f (l) − W * l
2. f(l) = π + W * l
3. f’(l) = W

**f’(l) **marginal rate of transformation and W relative producer pr

Question 19

Why is** labour demand** unambiguously
decreasing in after-tax wage costs W?

Answer 19

if you take the derivative of marginal rate of transformation and the derivative of the relative producer price you will end up with 1 divided by the derivative of the relative producer price which is negative

Question 20

How can the wage elasticity of labour demand be defined?

Answer 20

ed ≡ −∂l(W)/∂W * W/l ≥ 0

1% increase in wage leads to ed-%
decrease in labor demand

Question 21

In which equations can the economic model be summarized?

Answer 21

ω = (1 − t)w
W = (1 + τ )w
ls(ω) = ld(W)
l = ls(ω)

Question 22

How can the economic model be summarized?

Answer 22

By using the after-tax wage rate for the employee and employer to define the functions for labour supply and labour demand. The model states that wages adjust so that supply and demand will intersect each other. The point of intersection denotes the ammount of labour which is needed for an equillibrium.

Question 23

How can we come up for answer for how an equilibrium can be affected by changes in the tax rates t and τ?

Answer 23

Finding the total derivative of all conditions in the economic model:
1. Find the derivative of after-tax wage rate for employee and employer
2. Find derivative of labour demand and supply
3. Use and Substitute for the wage elasticitity

Question 24

Which conclusions can we derive from the economic model?

Answer 24

• Higher employee taxes(ω) reduce labor supply, thereby raising wages
• Higher employer taxes(W) reduce labor demand, thereby lowering wages
• The degree to which the tax burden is shifted crucially
  depends on demand and supply elasticities

Question 25

What is the condition if we also take taxes on consumption in consideration?

Answer 25

A proportional tax on income is equivalent to a
proportional tax on all consumption expenditures

(1 + θ)c = (1 − t)wl

Question 26

Does taxing income or consumption make a difference in the economic model? Why?

Answer 26

Household only care what they can consume with their income thus no.
The burden of a proportional consumption tax is thus shared between households and firm owners according to their
elasticities of labor supply and demand

Question 27

When does equivalence break down in the model?

Answer 27

• Downward wage rigidity due to a minimum wage
• Bounded rationality / tax salience
• in the short term

Question 28

Does having taxes on specific commodities make a difference in the model?

Answer 28

Kind of, The demand and supply function of a commodity will shift by a tax increase or decrease and taxes but the side(supply or demand) with a smaller price elasticity will carry most of the tax incidence

Question 29

What are the key insights of this model?

Answer 29

• elasticities of supply and demand determine to which side the tax will be imposed
• The more elastic supply , the harder it is to pass on a tax to the supply
• The least elastic side of the market carries most of the economic
  incidence of a tax, vice versa.