Public Economics

Question 1

government roles in modern economy (5)

Answer 1

price intervention (taxes, welfare etc); regulation (min wages); taxation; spending; macro-economic stabilisation (fiscal policy)

Question 2

where is the tax base more elastic

Answer 2

tax base is more elastic at the top because the rich have more avenue to respond to taxation to reduce their tax burden

Question 3

what do top 1% earners do when tax rate increases

Answer 3

reduce working hours, migrate, tax avoid/evade

Question 4

How much tax income you raise is a result of 2 things:

Answer 4

1. how elastic is your tax base? will people migrate if you raise taxes? 2. what are the citizens political preferences?

Question 5

contract curve

Answer 5

all pareto efficient point

Question 6

first fundamental theorem of welfare economics

Answer 6

private market outcomes are pareto efficient under a set of conditions. outcome due to market conditions will be efficeint but it is not necessarily fair

Question 7

pareto efficiency

Answer 7

no one can be made better off without making someone else worse off

Question 8

second fundamental theorem of welfare economics

Answer 8

under a broad set of conditions, any pareto-efficeint allocation can be achieved through a redistribution of initial endowments and then letting the markets work freely. if initial outcome unfair, pick another allocation (take from one and give to another), then go away and let them trade freely until they reach a new point

Question 9

first welfare theorem assumptions (4)

Answer 9

no externalities, perfect competition (no price makers, free entry), perfect information, rational agents

Question 10

when the first welfare theorem assumptions hold…

Answer 10

no need for a government

Question 11

when the first welfare theorems do not hold…

Answer 11

market failure –> govt intervention may be desirable

Question 12

internality

Answer 12

cost you impose on the future version of yourself

Question 13

fallacy of 2nd welfare theorem

Answer 13

it requires lump-sum taxes based on individual characteristics and not behaviour (1st best tax) but govt doesnt have enough info to do this, so govt use distortionary taxes and transfers leads to conflict between efficiency and equity (2nd best taxation)

Question 14

efficiency-equity trade off

Answer 14

as a result of private actions, you arrive at an allocation that isn’t fair. you redistribute. if you redistribute using taxes, you end up inside the utility possibility frontier. you must give up some efficiency to gain equity.

Question 15

wealth tax - economic efficiency

Answer 15

a wealth tax could discourage investment and savings, impacting economic growth and job creation. it could correct inefficiencies and imbalances caused by extreme wealth concentration

Question 16

wealth tax - fairness and equity

Answer 16

means to address increasing income & wealth inequality, ensuring that the wealthiest pay their fair share. it penalises success and could lead to double taxation

Question 17

wealth tax - administrative challenges

Answer 17

valuation of assets, especially non-liquid assets like real estate and art. concerns about costs of complexities of admin and compliance.

Question 18

excess burden

Answer 18

measure of the costs of substituting away from taxed activities - more leisure time, find loopholes in tax code, migrate. measures the cost of the changes in behaviour caused by the substitution effect

Question 19

lump-sum taxes

Answer 19

the only taxes that create no excess burden as taxpayers cannot avoid or evade them. they create no behavioural responses and hence no excess burden

Question 20

substitution effect

Answer 20

refers to the change in demand or supply due to a relative price change caused by the tax

Question 21

income effect

Answer 21

change in demand for a good or service caused by a change in a consumer’s purchasing power, due to a change in real income. generally reinforces substitution effect of reducing consumption

Question 22

when does income effect not reinforce substitution effect after tax

Answer 22

labour supply - lower disposable income means lower consumption of leisure and therefore higher labour supply

Question 23

tax incidence

Answer 23

the effects of tax policies on prices and the distribution of utilities

Question 24

effects of a tax change or introduction

Answer 24

effect on price –> distributional effects on consumers, profits of prodcuers, shareholders, farmers etc

Question 25

economic incidence vs statutory incidence

Answer 25

statutory incidence is who is legally required to pay the tax, economic incidence is who ultimately ends up paying the tax

Question 26

partial equilibrium incidence assumptions (5)

Answer 26

two good economy: one relative price, no close substitutes/complements; tax revenue not spent on the taxed good; perfect competition among producers

Question 27

excise or specific tax

Answer 27

tax levied on a quantity

Question 28

ad-valorem tax

Answer 28

tax levied on price

Question 29

partial equilibrium incidence model setup

Answer 29

two goods x and y. government levies an excise tax on good x. let p denote the pre tax price of x and q = p + t be the taxed price

Question 30

partial equilibrium incidence model: demand

Answer 30

consumer has wealth Z and utility u(x,y). price elasticity of demand: eD = ∂D/∂q * q/D(q) = ∂logD/∂logq

Question 31

price elasticity of demand

Answer 31

percentage change in quantity demanded following a change in price - elasticities are unit free

Question 32

partial equilibrium incidence model: supply

Answer 32

cost of production c(S) units of y to produce S units of x. cost of production is increasing and convex: c’(S)>0 & c’‘(S)>=0. profit at pretax price is: pS - c(S). with perfect optimisation, the supply function for good x is implicitly defined by the marginal condition: p = c’(S(p)). price elasticity of supply: eS = ∂S/∂p * p/S(p)

Question 33

partial equilibrium incidence model: equilibrium

Answer 33

equil condition: Q = S(p) = D(p + t).

Question 34

perfectly inelastic demand graph

Answer 34

vertical demand curve

Question 35

perfectly elastic demand graph

Answer 35

horizontal demand curve

Question 35

formula for tax incidence

Answer 35

implicitly differentiate D(p+t)=S(p). incidence on consumers: dq/dt = 1 + dp/dt = eS / (eS - eD)

Question 36

the more open an economy is to capital movements….

Answer 36

the more the burden is likely to fall on labour

Question 37

evans, ringel, and stech 1999

Answer 37

idea: suppose federal govt implements a tax change, compare cigarette prices before and after the change: D = [P_A1 - P_A0]. identification assumption - absent the tax change, there would have been no change in cigarette price

Question 38

evans, ringel, and stech 1999: difference-in-differences

Answer 38

what if price fluctuates because of climatic conditions or trends in demand? relax ID assumption using diff-in-diff: DD = [P_A1 - P_A0] - [P_B1 - P_B0]. state A: experienced a tax change (treatment), state B: does not experience a tax change (control). captures changes due to external factors. identification assumption for DD - ‘parallel trends’ absent the policy change, P1 - P0 would have been the same for A and B

Question 39

tax is …

Answer 39

regressive on an absolute level

Question 40

general equilibrium analysis

Answer 40

all prices are flexible, move beyond 2-good partial equil model to analyse impacts on all prices. typical goal: trace out full incidence of taxes back to original owners of factors. capital owners vs. labour vs. landlord etc

Question 41

static general equilibrium model

Answer 41

many sectors or many factors of production

Question 42

dynamic general equilibrium model

Answer 42

characterise impacts over time or across generations

Question 43

static vs dynamic GE models

Answer 43

static models assume that all prices and quantities adjust immediately. in practice, adjustment of capital stock and reallocation of labour takes time. dynamic GE models incorporate these effects. static models can be viewed as a description of steady states

Question 44

deadweight loss of commodity taxation

Answer 44

consume X units of commodity at price p, govt imposes per unit tax t. q = p+t is consumer price. Change in DWL from small tax change: dDWL = - t dX. PED = (dX/X) / (dq/q). Obtain: dDWL/dt = t/q * e * X

Question 45

partial equilibrium analysis deadweight loss

Answer 45

consumer demand function Xi = Xi(qi). Assume: no income effect (uncompensated demand = compensated demand); independent market (no cross price effects). Choose optimal tax rate to minimise DWL: ∑_(i=1)^n DWL_i subject to revenue requirement R = t1X1 + … + tnXn >= R0. Lagrange: ∑DWLi - λ(R - R0). FOC: (∂DWLi/∂ti) / (∂R/∂ti) = λ = (∂DWLi/∂R). use dDWL/dt = t/q * e * X from before to obtain ramsey rule

Question 46

ramsey rule

Answer 46

ti/qi = (λ / 1 + λ) (1/ei). The tax rate on a good should be inversely related to its elasticity of demand. tax inelastic goods at higher rates

Question 47

optimal tax rule

Answer 47

choose tax rates such that the equiproportionate reduction in demand is equal across all commodities

Question 48

issues with differentiation in taxes (4)

Answer 48

ignorance - lack knowledge of elasticities; admin and complexity - costly, complex, line drawing problem; creation of new goods - how to treat new goods?; political economy - lobbying, bribery

Question 49

income tax marginal DWL

Answer 49

dDWL = - τ * w * dh = τ / (1-τ) * e * wh * dτ, where e = (dh/h) / (d(1-τ) / (1-τ))

Question 50

income tax DWL insights

Answer 50

first $ of tax had no DWL, marginal DWL is increasing in marginal tax rate, marginal DWL is increasing in labour supply elasticity, marginal DWL is increasing in the earnings level wh

Question 51

optimal income tax problem + simplifications

Answer 51

objective: a social welfare function W = W(U1, .., Un). choice: tax function T(Z) where z = wh is earnings. constraints: govt budget constraint and individual optimising behaviour. problem: design T(.) to max SWF subject to GBC and individual optimisation. Simplify by: restricting tax system (linear or piecewise linear taxes), consider special SWF

Question 52

Linear income tax problem

Answer 52

constant marginal tax rate and guaranteed minimum income G>0: T(z) = τz - G –> flat tax or negative income tax. Average tax rate: a = T(z)/z = τ - G/z. Implies ∂a/∂z = G / z^2, which is positive for G>0. System is progressive

Question 53

rawlsian SWF

Answer 53

W = min(U1, .., Un) so gov only care about the worst off person. Assume worst of person unable to work and lives on transfer G. Rawlsian gov wants to maximise G –> optimal income tax maximises revenue –> goes to top of Laffer curve

Question 54

laffer curve and optimal taxation

Answer 54

laffer rate is optimum under rawlsian social preferences. laffer rate represents an upper bound on tax rates: any tax system above is pareto inefficeint, any tax system below may be optimal under some SWF. laffer rate is only value-free statement on optimal tax policy

Question 55

high-income laffer rate setup

Answer 55

top MTR applies to income above z. denote ¯z the average income among taxpayers above z. total rev at top: R = τ(¯z - z)N. marginal change dτ creates: a mechanical revenue effect dM = dτ (¯z - z)N; a behavioural revenue effect dB = τ dz N.

Question 56

high income laffer rate

Answer 56

determined by dR = dM + dB = 0 and is: τ* = 1 / (1 + eα) where e = (d¯z / ¯z) / (d(1-τ) / (1-τ)) is the elasticity of taxable income and α = ¯z / (¯z - z*) >= 1

Question 57

tax base

Answer 57

amount of economic activity subject to the tax

Question 58

deadweight loss occurs because

Answer 58

economic agents move away from the taxed activity, substituting toward its alternatives

Question 59

what is the Lagrange multiplier of the Ramsey problem

Answer 59

the marginal cost of public funds. It represents the additional deadweight loss generated by extracting an additional unit of revenue on the good i

Question 60

fiscal externality

Answer 60

a situation in which an economic agent’s behaviour changes the cost of some subsidy or alters the revenues collected from some tax, thereby affecting the well-being of taxpayers in general