Equity implications of Tax: Tax Incidence
Definitions
Concepts
▪ Gross Income
✔
▪ Deductions
✔
▪ Tax Credit
✔
▪ With holding
✔ ▪ Subtraction of estimated taxes due directly from a worker’s Y
▪ Refund
✔ ▪ Government revenue losses attributable to exclusions, exemptions, or deductions from gross income.
▪ Adjusted Gross Income (AGI)
✔
▪ Total Income from all sources
▪ Exemptions
✔
▪ How tax system redistributes income to make distribution more equitable.
▪ Taxable income
✔ ▪ Fixed amount that a taxpayer can deduct from taxable income to reduce tax liability eg. Medical, tuition f
▪ Tax expenditures
✔ ▪ Percentage of additional dollar of taxable income that is paid in taxes.
▪ Amount of money that taxpayers can subtract directly from the taxes they owe Eg. child care.
▪ Amount withheld from Y- Taxes owed
▪ Amount out of a total income of person that does not attract taxability Eg. HRA, LTA
▪ Equity
✔
▪ Amount of income left after subtracting exemptions and deductions from adjusted gross income.
▪ Marginal Tax rate
✔
▪ = Total tax payment/ Gross income
▪ Average Tax rate
✔ ▪ Gross Income- Deductions
▪ Statutory tax rate
✔
▪ Legally imposed rate; Percentage of tax paid as a percentage of taxable Income
▪ Average tax rate: Share of income that they pay in taxes; Also
called effective tax rate.
Average Tax Rate= Total taxes paid/ Total Y (Gross Y) * 100
▪ Marginal tax rate: Tax rate imposed on their last dollar of
income.
Marginal Tax rate= Δ in Tax paid/ Δ in Total taxable Y *100
▪
In most cases, Average tax rates < marginal rate.
▪ Statutory Tax Rate = Total taxes/ Taxable Income* 100
Marginal Tax Rate= 12%
Average Tax rate= 7.9%
#2. Jonas and his brothers inform you they know they
paid 10% taxes on their first $10,275, which is
$1,027.5. Jonas says he was charged $2,967 and made
$35,000 in total. What did the government tax him?
#1. Josh has gross income of $1,90000 and taxable income (after
deduction adjustments & exemptions) it is $1,70,000 (no tax
credits). Calculate Marginal, Average & Statutory Tax Rates.
US Income Tax Slab Rates
Income Less than $18,450: 10¢ per dollar
For the next $56,450: 15¢ per dollar
For the next $76,300: 25¢ per dollar
For the next $79,250: 28¢ per dollar
For the next $181,050: 33¢ per dollar
For the next $53,350: 35¢ per dollar
Above $ 464,850: 39.6¢ per dollar
•
Marginal Tax rate is 28%
•
Total tax bill = ($18,450 * 0.1) + ($56,450 * 0.15) + ($76,300 *
0.25) + ($18,800 * 0.28) = $34,651.50
Taxable Income = $35000- $10,275= $24,725; Taxes paid =$2967
•
Marginal Tax rate= $ 2967/ $ 24725= 12%
•
Average tax rate = $34,651.50/$190,000 (Gross income) = 18%
•
Statutory Tax Rate = Total taxes/ Taxable Income= 34,651.50/
1,70,000= 20.3%
Average Tax rates = Total taxes paid/ Total Income
Total Taxes paid= $ 2967 + $ 1027.5= $ 3994.5
•
•
Marginal Tax rate = Δ in taxes paid/ Δ in taxable income
Average Tax rate= $ 3994.5/ $ 35000 * 100= 11.41%
A. Ability to Pay Approach
▪ Vertical Equity: People with more resources should
pay a higher tax.
▪ Horizontal equity: People with similar amount of
income and assets should pay same amount of taxes
irrespective of their life style choices.
▪ Concept of Tax Neutrality: Similar treatment to people
earning in the same income group by imposing the same
level of tax; Not happening due to deductions, tax credits,
incentives, and loopholes.
B. Benefit Approach: Tax burden should be
equivalent to the benefits received from the public
sector.
▪ E.g State Property taxes in US fund maintenance of
local public parks, road cleaning, street lights; Petrol
taxes for road maintenance etc.
Reality, Equality, Equity & Justice Difference: Can you spot?
▪ Progressive Tax system: Effective average tax rates ↑ with income.
▪ Eg. Individuals pay 10% tax if income is $10,000 & 30% if
income is $100,000.
▪ Proportional Tax system: All taxpayers pay same proportion of
their income in taxes; Uniform effective average tax rates.
▪ Eg. 10% income taxes whether they earn $10,000 or $100,000;
Kazakhstan (10%), Madagascar (20%)
▪ Regressive Tax system: Effective average rates ↓ with income.
▪ Eg. Tax payers pay 15% income tax at an income of $10,000 &
10% with an income of $100,000.
▪ Eg. Gas tax, Payroll tax
India’s Income Tax Structure
#1. Suppose that income tax in a certain nation is computed according the following tax brackets.
▪ 10% for income up to $9325
▪ 15% for income between $9326 to $37950
▪ 25% for income $37951 to $91,900
▪ 28% for income between $ 91,901 to $1,91,650
▪ 33% for income between $ 1,91,651 to $ 416,700
▪ 35% for income between $ 416,701 to $ 418,400
▪ 39.60% for income between $ 418,401 or more
A & B are two individual who live in this nation and their annual income is $62000 and $ 1,20,000 respectively. Compute their marginal and average tax
rates.
Individual A with a salary of $ 62000
Taxable income/ bracket
10% for income up to $9325
$9325
Tax Liability
.10 *9325= $ 932.5
Individual B with a salary of $ 1,20,000
Taxable income per bracket
Tax Liability
$9325
.10 *9325= 932.5
15% for income between $9326 to $37950
37950-9325= $ 28625
.15 *28625= $ 4293.75
37950-9325= $ 28625
.15 *28625= $ 4293.75
25% for income $37951 to $91,900
62000-37950= $ 24050
.25 * 24050= $ 6012.5
91,900- 37950= $53950
.25 * 53950= $ 1348.75
28% for income between $ 91,901 to $1,91,650
N.A
-
1,20000- 91900= $28100
.28* 28100= $7868
33% for income between $ 1,91,651 to $ 416,700
N.A
-
N.A
-
35% for income between $ 416,701 to $ 418,400
N.A
-
N.A
-
39.60% for income between $ 418,401 or more
N.A
-
N.A
-
$62000
$ 11238.75
$1,20,000
$14,443
Marginal Tax= 25%
Average Tax=11238.75/
62000*100= 18.12 %
Marginal Tax= 28%
Average Tax=14443/
1,20,000*100= 12.03 %
Total
Tax Rates
▪ Income Tax base (amount of assets/ income that can be taxed) is smaller than
total Y due to Exemptions, deductions & credits
▪ Haig Simons Approach developed by 2 US economists- Robert M. Haig &
Henry C Simons in 1920s.
▪ Haig-Simons “Taxable Income/ Resources” Definition: Individual’s ability
to pay taxes depends on their potential annual consumption (= Total annual
consumption + ↑ in stock of wealth) e.g. Employer funded health insurance,
compensation etc.
▪ Ensures Vertical Equity: Those who have more pay higher taxes; Nontaxed sources are taxed like employer provided health insurance.
▪ Ensures Horizontal equity: Same amt of tax regardless of the form in
which they choose to receive /spend their resources.
Appropriate Business Deductions
•Legal Fees & Insurance
•Business interest
•Advertising and marketing
•Business use of car
•Salaries & benefits
•Bad Debt
•Business Casualty Losses
•Charitable donations
•
•
•
▪ Goal of Tax base design: Difficulty in Adopting Haig Simons Approach
1. Defining a person’s power to consume/ability to pay: Desired Vs
Undesired consumption (Repairs, Fire damages, Casualty losses, Necessary Vs
Un-necessary Medical Expenditures (10%); State and local tax payments.
2. Dealing with expenditures associated with earning a living and not
personal consumption: eg. Business Lunches, Meals & Drinks
•
•
•
Inappropriate Business Deductions
Private Expenditure incurred by Jewish
Rabbi; for inviting congregation members for
his son’s bar mitzvah
Business expense for selling drugs; IRS
disallowed due to lack of documentation
Dinah Shore Ruling: Dresses worn for
entertainment as business expense
Cost of bribing foreign officials
Cat food costs claimed by junkyard owner; to
keep property snake and rat free to attract
customers
Body oil expenses by a body builder
CHARITABLE GIVING & 2. HOUSING EXPENDITURES
I.
Charitable Giving: Public Good→ Positive Externalities & Under provided
For Example: Building shelters for homeless
a. Government Provision: Subsidize homeless shelter
b. Tax Subsidies: Subsidize charitable giving relative to other Consumption
▪ Example: Suppose Ellie has a choice: $4 cup of coffee or to donate $4
▪ No tax on donation but if spent on consumption →required to pay income tax on that dollar @ tax rate λ: Assuming λ = 50%
▪ To consume coffee Ellie needs to earn $8 i.e. 4/(1- λ) but for donation only $4; $ 2 for other consumption & only $1 for charity
▪ Relative price of charitable consumption < Other consumption
▪ For Charitable Spending: Government Spending or Tax subsidy?
▪ Government Spending: Crowding out of private charity spending
▪ Tax Subsidy: Crowding In→ Substitution Effect (↓ relative price of charitable giving) & Real Y effect (Feels richer with ↓ taxes)
▪ Marginal vs. Infra Marginal Effect
▪ Marginal Impact: Changes in behavior the government hopes to encourage through the tax incentive i.e. ↑ in charity.
▪ Inframarginal Impact: Tax breaks deduction i.e. lost revenue from those giving charity anyways
▪ Cost Efficient Tax breaks have higher marginal rather than infra-marginal effects.
▪ Trade Offs Between Direct Spending vs tax subsidies:
▪ Direct Spending: ↑ Charitable Funding + ↓ Private Spending for charitable purposes
▪ Tax Subsidies: ↑ Private Spending + subsidizes existing giving (Infra marginal effect)
▪ Thumb Rule: Mathematically expressed → Tax break should be used instead of direct spending by govts
If ↑ in charity per dollar of Tax Break > 1 - ↓ in charity per dollar of Govt. Spending
▪ Evidence: Studies indicate that a 1% ↓ in the relative price of charitable giving leads to 1% ↑ in charitable giving.
▪ Elasticity of charitable giving wrt subsidy = –1; Marginal Effect of tax (↑ in charity) = Infra-marginal Effect (Lost
tax revenue from existing giving )
▪ Direct Government spending per dollar delivers only 30¢ – 90¢ in new spending due to some private crowding out.
▪ Tax subsidies: Up-side: Government respects citizen’s preferences & Efficient provisioning by private sector
▪ Down side: Hard to detect if citizens are actually making contributions
Home Ownership vs. Renting: Social benefits
•
↑ stake in society + Democracy- vote for
long-run investments instead of short-run
transfers.
•
Greater Incentives to maintain & take care of
neighborhoods/ towns→ higher K value of
neighboring
house(positive
financial
externality)
•
Greater political
connections
•
Greater citizen
development
activism
welfare
and
+
social
country’s
2. Home Ownership: Positive Externalities
▪ For Example: Looking for a house→ Rent of $1,000/ month or $1,00,000 purchase price; EMI on house loan→ $1000/ month; Given tax rate
=50% & monthly Y= $4000
▪ Under Haig-Simons approach: (Regular Y + Net consumption value/ Imputed rental value of living in the house) - the cost to you of
doing so ($1,000)→ tax burden unaffected whether property brought or rented.
▪ Current U.S. tax system allows EMI deductions on home loans only & not rental payment deductions from their taxable income.
▪ Evidence: Little evidence of ↑ in home ownership per se – argument weak on positive externality grounds
▪ Tax subsidy doesn’t appear to ↑ homeownership but does ↑ housing expenditures; Elasticity of spending wrt tax subsidies is approx= 1.
▪ Tax subsidy is inducing individuals to spend more on houses that they would have bought anyway, even without the tax subsidy.
▪ Housing Subsidies: Tax Deductions or Tax Credits?
▪ Tax Deductions/ Tax Subsidy: EMI’s on home loans can be deducted from taxable income; Subsidizes all spending partially
▪ Benefit: Lowers the price of home buying versus other expenditures to $(1- t), where t is the marginal income tax rate.
▪ Tax credits: Reduction in tax liability by the amount of EMIs ; Subsidizes some spending fully (up to tax credits) and some not at all
▪ Benefit: If an individual’s home loan expenditure < Tax credits → Lowers the price of home buying to zero.
▪ Tax Credits vs Tax Deductions: Which policy to adopt on Efficiency grounds?
Unclear!
▪ Tax Credits: Incentive to give up to tax credit level (Subsidizes spending fully up to the tax credit & then none at all); For
example: with $1,000 worth of tax credits→ those giving < $1,000 in charity have a strong incentive to ↑ up to the $1,000
level because it is free; For charitable donations > $1000- no subsidy at all.
▪ Tax Deductions: Incentive to give even beyond the $1,000 limit (Subsidizes all spending partially)
▪ Policy Efficiency depends on
1. Nature of the demand for the subsidized good: For certain goods, individuals demand is elastic (more responsive) to
price changes→ Tax credits effective as they cause a larger ↓ in relative price.
2. Minimal behavior levels vs Higher Target levels: Tax deductions effective to achieve higher target level but for under
provided public goods with +ve externalities (health insurance, charitable donations)→ Target not as important as people’s will
is.
▪ Tax Credits vs Tax Deductions: Which policy to adopt on Equity grounds? Tax Credits ensure vertical equity!
▪ Tax Credits: Progressive→ Available equally to all Y groups →% share of tax credits to Y are lower for high Y groups &
higher for low Y groups→ ↑ vertical equity; If refundable with or without paying any taxes→ Progressivity is lost!
▪ Tax Deductions: Regressive →Deductions ↑ with Y levels + tax rates— Higher deduction possible for high Y groups as
compared to low Y groups→↓ vertical equity
▪ Impact of a Tax: Refers to the Initial stage of tax burden.
▪ Shifting of Tax Burden: Passing of money burden through sale and purchase transaction; Can be shifted Forward (to
Consumer), Backward (to FOP), Single point Shifting (Directly from manufacturer to consumer) or multipoint (From
producer to wholesaler to retailer to consumer).
▪ Tax Incidence: Refers to the ultimate resting place of the tax; Not possible to shift the burden thereafter; Relates more
to changes in prices rather than quantities
▪ Statutory incidence: The burden of a tax borne by the party that sends the cheque to the government.
▪ Economic incidence: Burden measured by change in resources of the economic agent (producer/ consumer) as a result
of taxation; Difference between Individual available resources before and after tax after sharing of the tax burden.
Impact
Incidence
Initial burden
Ultimate burden
Felt at the point of tax imposition
At the point of final source from which
money is received
Falls on those who have first responsibility Falls on those who finally pay for the tax
of paying it to the govt
Impact can be shifted
Incidence cannot be shifted
▪ Tax Wedge: The difference between Demand Price & Supply Price of a good.
▪ Demand Price (Price paid by consumer):Maximum price that buyers are willing and able to pay for the
new equilibrium quantity.
▪ Supply Price (Price received by seller): Minimum price that sellers are willing and able to accept for the
new equilibrium quantity.
▪ Burden of a Tax: The immediate Impact of a tax
▪ Real Burden: Loss of welfare, sacrifice, fall in real income/ consumption/ Investment
▪ Monetary Burden: Money value of the tax
Consumer tax burden = (Post-tax price - pre-tax price) + per-unit tax payment if paid by consumers
Producer tax burden = (Pre-tax price - post-tax price) + per-unit tax payment if paid by producers
Rule 1: The statutory burden of a tax does not describe who really bears the tax.
Rule 2:
The side of the market on which the tax is imposed is irrelevant to the
distribution of tax burden.
Rule 3: Parties with inelastic supply or demand bear taxes; parties with elastic supply
or demand avoid them.
RULE 1: THE STATUTORY BURDEN OF A TAX DOES NOT DESCRIBE WHO REALLY BEARS THE TAX.
Example: Market for Gasoline
▪ Equilibrium Before Tax: Point A
▪ P₁=$1.50
▪ Q₁ = 100 units
Pre-tax Equilibrium
Post tax Equilibrium
▪ Equilibrium after Producer’ s tax of 50¢ per gallon: Point D
▪ After Tax→↓ in SS from S₁ to S₂ due to ↑ in MC & ↑ in price
from P₁ to P₃
▪ P₃ = $1.80
Q₃ = 90 units
▪ Tax Wedge= 50¢ DD Price= $1.80
Consumer
Burden
SS Price= $1.30
▪ Thus proved: Statutory Tax burden imposed on Seller= 50¢
▪ Consumer’s Burden= (P₃ – P₁)+ 0 = ($1.80 – $1.50) = $0.30
▪ Higher burden of tax borne by consumer: 30¢
▪ Producer’s Burden= (P₁ – P₃) + 0.50 = (1.50 – 1.80) + 0.50=
$0.20
▪ Producers Burden much less than the tax amount: 20¢
Seller
Burden
RULE 2: THE SIDE OF THE MARKET ON WHICH THE TAX IS IMPOSED IS IRRELEVANT TO THE DISTRIBUTION OF THE TAX
BURDEN
▪ Equilibrium Before Tax: Point A
Example: Market for Gasoline
▪ P₁=$1.50
▪ Q₁ = 100 units
▪ Equilibrium after Consumer Tax of 50¢ per gallon(Cheque
collected at the pump when they come to buy gas): Point D
▪ After tax @ Price P₁ - earlier 100 units demanded (Pt A)and now
only 80 units (Pt C) →↓ in DD at every price level ( Shift from D₁
to D₂) → Excess SS equivalent to CA → producers ↓ price to sell
excess SS → New Equilibrium at D
▪ New Equi Price P₃ = $1.30
Q₃ = 90 units
▪ Tax Wedge= 50¢
DD Price= $1.80
SS Price= $1.30
▪ Consumer’s Burden: 30¢
Producers Burden: 20¢
▪ Consumer’s Burden: (P₃ – P₁)+ $0.50 = $1.30 – $1.50 + $0.50 =
$0.30
▪ Producer’s Burden= (P₁ – P₃) + 0 = ($1.50 – $1.30) + 0= $0.20
▪ Thus proved irrespective of the
side of the market the tax is
imposed: Distribution of Tax burden is same → consumers pay
more.
Consumer
Burden
Seller
Burden
Gross & After Tax Prices:
Gross price: Price paid/ rec’d by the party not paying the tax to the govt;
Same as Market Price
After Tax Price: Price paid/ rec’d by the party paying the tax to the govt;
Could be less than tax amount if producers pay or higher than tax amount if
consumers pay
• With Producer Gas Tax: Gross Price paid by Consumer =$1.80 ; After
tax price rec’d by seller= $1.80- 0.50= $1.30
• With Consumer Gas Tax: Gross Price rec’d by Seller = $1.30;
After tax price paid by consumers= $1.30 + $0.50= $1.80
RULE 3: PARTIES WITH INELASTIC SUPPLY OR DEMAND BEAR TAXES; PARTIES WITH ELASTIC
SUPPLY OR DEMAND AVOID THEM
Perfectly Inelastic Demand for Gasoline
Demand Elasticities: With Producer Gas Tax of of 50¢ per gallon
A. Perfectly Inelastic Demand: Entire Burden on Consumers
▪ Consumer burden= [Post-tax price (P₂) - pre-tax price (P₁)] + Consumer tax payments
Consumer
Burden
= ($2.00 - $1.50) + 0 = $0.50
▪ Producer burden= [Pre-tax price (P₁) - Post-tax price (P₂)] + Producer tax payments
=( $1.50 - $2.00) + $0.50= $0
B. Perfectly Elastic Demand: Entire Burden on Producers
Perfectly Elastic Demand for Gasoline
▪ Consumer Burden= [post-tax price (P₁)- pre-tax price (P₁)]+ Consumer tax payments
= ($1.50 - $1.50) + 0 = $0
▪ Producer burden=[Pre-tax price (P₁)- Post-tax price (P₁) ]+ Producer tax payments
= ($1.50 - $1.50) + $0.50= $0.50
▪ Price Burden more Important than Quantity Burden in calculating Tax Incidence:
▪ Despite consumer bearing no tax burden- Qty of gas consumed↓→ not taken into
account as at the prevailing price the consumer is indifferent to consuming gas or some
other substitute/ good.
Seller
Burden
A. Tax on Steel Producers: Inelastic Supply
A. Relatively Inelastic Supply: Steel Production with producer Tax of 50¢ / unit of Steel
Production: More Burden on Producers
▪ Equilibrium Before Tax: Point A
Equilibrium Price P₁
Consumer Burden
Seller Burden
Quantity Q₁
▪ With tax due to inelastic SS→not possible to ↓ SS due to fixed K investment →Smaller
↑ in prices→ More burden on producers
▪ Equilibrium After Tax: Point B
Equilibrium Price P₂
Quantity Q₂
B. Relatively Elastic Supply: Tax on Sidewalk Vendors selling watches, scarfs of 50¢
/unit of Good sold: More Burden on Consumers
▪ Equilibrium Before Tax: Point A
Equilibrium Price P₁
B. Tax on Sidewalk Vendors: Elastic Supply
Quantity Q₁
▪ With tax due to Elastic SS→↓ SS is more→ Larger ↑ in prices & ↓ in quantities sold →
More burden on consumer as sellers burden is offset by larger ↑ in prices due to tax
▪ Equilibrium After Tax: Point B
Equilibrium Price P₂
Quantity Q₂
Consumer Burden
Seller Burden
▪ Thus proven Rule 3 of Tax Incidence: Elastic factors avoid taxes, while inelastic
factors bear them.
FACTOR MARKET
▪ Example: Market for Labor
▪ Consumers of Labor: Firms
▪ Producers of Labor: Individuals
Equilibrium Before Tax: Point A
Market Wage Rate W₁=$7.25
Labor hours supplied = H₁
A. Producer Tax levied on Labor: Payroll Tax of $1/ hr worked → ↓ in Labor SS
▪ After Tax Equilibrium @ Pt B : ↓ in SS from S₁ to S₂ → W₂ wages= $7.75 & H₂ labor hours.
▪ Tax incidence as per DD/SS Elasticities: If elasticities are equal- Burden shared Equally (50 ¢)
Equilibrium/ Firm wage/ Gross Market wages ↑= $7.75/ hr
▪ Workers Take home pay/ after tax wages↓ = $6.75 / hr
▪ As per Second Rule: What matters for tax incidence is not who pays for it but how much is
the tax wedge and the elasticities of dd & SS.
B. Consumer Tax levied on Firms: $1/ labor hr consumed → ↓ in Labor DD
▪ After Tax Equilibrium @ Pt C : ↓ in DD from D₁ to D₂ → W₃ wages= $6.75 & H₂ labor hours
▪ Equal elasticities hence equal sharing of the burden: 50 ¢ each
Tax on workers
Firm
Burden
Worker
Burden
Tax on Firms
Firm Burden
Worker
Burden
Equilibrium/ Gross Market Wages ↓= $6.75/ hr
Workers Take home wages/ after tax wages ↓= $6.75 / hr (50¢ lower than earlier wages $7.25)
After Tax Wages paid by Firm ↑: $7.75 / hr
LABOR MARKET WITH MINIMUM WAGES
Market For Labor
▪ Equilibrium Before Tax: Point A
▪ Market Wage Rate W₁=$7.25
▪ Labor hours supplied = H₁
Fixed Minimum Wage Rate; WM =$7.25/ hr
A. Producer Tax levied on Labor: Payroll Tax of $1/ hr worked → ↓ in Labor SS
→No Effect of Minimum Wages → Equal sharing of burden (50 ¢ each)
▪ After Tax Equilibrium @ Pt B
Wages W₂= $7.75 & H₂ labor hours.
▪ Equilibrium/ Firm wages/ Gross Market wages↑= $7.75/ hr
▪ Workers Take home pay/ after tax wages↓ = $6.75 / hr
Tax on workers
Firm Burden
Minimum wage
Worker
Burden
▪ B. Consumer Tax levied on Firms: $1/ labor hr consumed → ↓ in Labor DD→
Entire Burden on the Firm ($1)
▪ With Minimum Wage Stipulation → Equilibrium wages cannot fall to $6.75 (Pt. C)→
New After Tax Equilibrium @ Pt C’ with wages WM= $7.25 & H₃ labor hours.
▪ After Tax Wages paid by Firm↑: $ 8.25/ labor hr consumed
▪ Workers Take home wage (same): $7.25 /labor hr supplied
Tax on Firms
Firm
Burde
n
Minimum wage
IMPERFECT MARKETS
▪ Pre- Tax Equilibrium under Monopoly (MC=MR): Pt A
▪ Equilibrium quantity Q₁ & P₁ price
Monopoly Market
▪ Can fix qty or price @ Q₁ qty- consumers willing to pay P₁ only; If price fixed to P₂→Q₁
Qty demanded
▪ Post Tax Equilibrium after a Consumer Tax: Pt B
▪ Tax on consumer→↓ in DD from D₁ to D₂ & MR from MR₁ to MR₂ → Equilibrium
established ((S₁) MC= MR₂) →Equilibrium price ↓ to P₂ & & quantity to Q₂ respectively.
▪ Monopolist shares Consumer Tax Burden: Fall in equilibrium price from P₁ to P₂
Tax on Consumers
▪ Rules of Tax Incidence apply under Monopoly conditions too; No matter which
side of the market tax is imposed→ some burden shared by monopolist despite its
market power.
▪ Balanced budget Incidence: Tax incidence analysis that takes into account both
who bears the burden and those who benefit from the tax.
▪ Taxes result in DWL to society but also generate govt revenue for higher public expenditure
for general welfare.
Example: Restaurant Tax on all Meals
▪ General Vs Partial Equilibrium:
▪ Partial equilibrium: Tax incidence analysis in one market in isolation
▪ General equilibrium: Tax incidence analysis of a tax in one market & its effect
in several related markets
▪ Example: $1 Tax on all restaurant meals (Perfectly Elastic Demand) in Lexington
Town, MA→ Full burden of tax on restaurant owner
▪ Pre- Tax Equilibrium: Pt A
Equilibrium Price P₁= $20 & Qty Q₁ = 1000
▪ With $1 tax →↓ in SS of restaurant meals from S₁ to S₂ →↓ equilibrium qty +
Price remains the same
▪ Post Tax Equilibrium: Pt B
New Equilibrium Price P₁ = $20 & Qty = 950
Restaura
nt owner
Burden
Restaurant Tax: Spill Over Incidence in Labor & K Market
▪ Spill Over Incidence of Tax in Labor (Elastic Labor SS) & Financial K Markets
(Inelastic K SS) in Lexington Town → No burden on workers & Full burden on
K owners
▪ Labor Market: Given elastic labor SS → ↓ in labor DD from D₁ to D₂→ no
change in wages→ Workers bear no burden of tax
▪ K Market: Given inelastic SS of K → ↓ in demand of K from D₁ to D₂→ ↓ in
ROR by full amount of tax r₂ → Capital owners bear full burden of tax
▪ Thus with a restaurant meal tax in Lexington town→ it is the K owners or
investors of Lexington Restaurant who will bear the burden in the form of a lower
return on their investment.
Investors
Burden
FOLLOWING THE TAX BURDEN
▪ Issues to Consider in General Equilibrium Analysis:
1. Effect of Time Period on Tax Incidence: Short Run (Inelastic DD/SS) vs Long Run (Elastic DD/SS)
2. Effect of Tax Scope on Tax Incidence: Share of the product in the product market [Elastic DD for meals in
Lexington town (presence of substitutes) vs inelastic dd for meals in all of Massachusetts (absence of substitutes)]
▪ In the SR- with inelastic dd of restaurants meals in MA(lesser substitutes)- Some burden borne by consumers
while the rest shared between workers & capitalist/ investor depending on their elasticity.
3. Spill over Between Product Markets: In case of consumer restaurant meal tax: ↓ DD for restaurant meals
▪ Income Effect: Consumers have lower incomes and may therefore purchase fewer units of all goods.
▪ Substitution Effect: ↑ DD for movies, concerts (substitute goods), ↓ DD for baby sitters (since they are less likely to go
out)
▪ Complementary Effect: ↓ DD for valet parking services (complementary service)
▪ To know tax incidence: We need know changes in market price (ΔP) due to imposition of tax: In case of Consumer Tax;
▪ For Consumers: Total Price change= ΔP (Change in mkt price) + τ (Greek symbol tau denoting tax amount)
▪ For Producers: Total Price Change = ΔP (Reduction in mkt price)
▪ For Consumer Tax: 3 Steps to calculate Tax Incidence
▪ Step 1: Knowing DD & SS side Elasticity formula; With Elasticity denoted by Greek alphabet Eta η
ηd = ΔQ/ (ΔP + τ ) * P/Q
ηs = ΔQ/ ΔP * P/Q
and
▪ Step 2: Rearrange the 2 expression so that they can be set equal to ΔQ/Q
ΔQ/Q = ηd * (ΔP + τ)/ P = ηs * ΔP/P
▪ Step 3: Equating the 2 expressions to solve for change in price formula (ΔP ) as a function of tax
For Consumer‘s Tax: ΔP = [ηd / (ηs –ηd)] * τ
ηd * (ΔP + τ)/ P = ηs * ΔP/P
Applying same logic For Producer’s Tax: ΔP = [ηs / (ηs –ηd )] * τ
→ ηd ΔP + ηd τ = ηs ΔP → ηs ΔP - ηd ΔP = ηd τ → ΔP (ηs - ηd ) = ηd τ
For Inelastic demand(ηd = 0): No change in mkt price→ Consumer bears the entire tax burden
For perfectly elastic Demand (ηd=∞): Price ↓ by full amount of tax→ Consumer pays no tax burden
or
▪ Monopoly Equilibrium where MC= MR
▪ Perfect Competition: DD=SS or MC= MR
▪ Total Revenue= Price * Qty
▪ Marginal Revenue: ∆ TR /∆ Q or a applying first order differential
▪ Marginal Cost: ∆ TC /∆ Q or a applying first order differential
▪ With consumer tax: Pc= Ps + Tax ; Affects DD Function (↑ Price + ↓ DD)
▪ With Producer’s tax= Ps = Pc – Tax ; Affects SS Function (↑ Cost + ↓ SS )
▪ Consumer Tax Burden = [post-tax price (P₁)- pre-tax price (P₁)] + Consumer tax payment
▪ Producer Tax Burden =[Pre-tax price (P₁)- Post-tax price (P₁)] + Producer tax payment
# 1. A Monopoly firm has a cost function C= 12 + q² & DD function: p= 24 – q. Who will bear the higher tax burden in case of (a)
Monopolist Tax of $4/ unit sold (b) consumer tax of $4/unit
Solution: Pre- Tax Equilibrium: MC= MR
Given TC Function: C= 12 + q²
To calculate MR: TR Function= P * Q= (24-q) *q=24q - q²
MC= 2q (derivative of cost fn wrt qty)
MR= 24-2q (derivative of revenue fn wrt qty).
Equating MC= MR; 2q= 24-2q=6 units & Solving for price p= 24-6= $18
(a) With the Govt imposing a tax on Monopolist of $4/ unit sold: New Cost Function C= 12 + q² +4q; MC= 2q+ 4
Equating MC= MR; 2q + 4= 24-2q=5 units
Solving for price p= 24-5= $ 19
▪ Monopolist tax = $4 [$1 Consumer burden + $3 monopolist burden]
After Tax price received by the monopolist= (Equilibrium price) $19 - $4 tax= $ 15
Given MR =24-2q
(b) With Consumer Tax of $4/ unit: New DD (AR) Function p = 24 - q - 4 = 20-q →TR= P * Q = (20-q) * q= 20q- q²
MC= 2q
Equating MC= MR; 20-2q = 2q; 4q= 20; q =5 units
Solving for price p= 20-5= $ 15
▪ Consumer Tax= $4 [$1 Consumer Burden + $3 Monopolist burden]
▪ After Tax price to consumer= (Equilibrium price) $15 + $ 4 tax= $ 19
MR= 20-2q Given
Consider the supply of copper is fixed in La La Land Qs= 4. The demand for copper is given by Qd= 10-2P where p is
the price per tonne and Qd is quantity demanded. The government imposes a tax of $ 2 per tonne on the consumer.
(i) What is the price paid by the consumer before and after the tax is imposed?
(ii) What is the price received by producers?
(iii) How much tax revenue is raised by the government?
Solution:
(i) Pre- Tax Equilibrium Price: Qd= Qs= 10-2P= 4; P= $3
Qty= 10-2(3)= 4 units
(ii) Post Tax Equilibrium Price: With $2/ton on consumers of copper; Pc= Ps + Tax
=10-2 (Ps + $2)= 4; 10-2Ps= 8; Ps= $1
▪ Post Tax: Price Paid by Consumers= $3 ($1 + $2 tax)
Qty= 10-2(1+2)= 4 units
Price Received by producers=$1
▪ Consumer Burden= New Price paid – Old price paid= (1-3) + $2 = $0
▪ Producer Burden= Old price rec’d- New Price rec’d= (3-1) + 0= $2
(iii) Total Tax Revenue= P* Q= 2* 4= $8
Consider a competitive market with demand given by Pc = 100 − 2Q and supply given by PS = 10 + Q.
a) Find competitive equilibrium price and quantity.
b) Suppose government introduces as per unit tax producer tax t= $15. Find the quantity traded in the market
after tax
c)Find the price paid by consumers and price received by producers after tax. Show your results on a diagram
Solution:
a) Pre- Tax Equilibrium: DD= SS; 100 − 2Q = 10 + Q; Q = 30 units
P = 100-2(30)= $ 40
b) Post Tax Equilibrium: With Seller tax: Ps + Tax = Pc
▪ At Equilibrium DD = SS; (10 + Q + 15) = 100 − 2Q ; 25 + Q= 100-2Q; 3Q= 75; Q= 25 Price= 100- 2(25); P= $ 50
c) Price paid by consumers after tax= $50; Consumer Burden= (50-40) + 0= $10
Price received by Producers after tax= $50 − $15 (tax) = $ 35; Producer Burden = (40-50) + 15= $5
If demand and supply for a product is given by Qd= 120-4P and Qs= 60+2P. If the government imposes a seller
tax of Rs 6 per unit of output, calculate burden of tax on consumers and producers?
Solution:
Pre- Tax Equilibrium Price: 120-4P= 60 + 2P; 6P= 60; P= Rs 10
Q=120-4(10); Q= 80 units
Post Tax Equilibrium: With Seller Tax of $ 6/ unit; Price sellers receive (Ps) = Price consumer’s pay (Pc) – Tax
▪ @ Equilibrium: DD= SS= 120 - 4Pc = 60 + 2(Pc - 6) = 120 - 4Pc = 60 + 2Pc – 12= 120 - 4Pc = 48 + 2Pc ; 6Pc = 120- 48; Pc= Rs 12
▪ Quantity Q= 120-4 (12)= 72 units
▪ Consumer burden= [12 - 10] + 0 = Rs 2 ; Price consumers pay =Rs 12
▪ Producer burden= [10 - 12] + 6 = Rs 4 ; Price sellers receive= Rs 6
# The Demand for tickets for a cricket match is Qd= 400-10P and the supply of the tickets is Qs=15P. The govt
imposes a per-ticket tax of $4 on consumers. Calculate (i) Price paid by the consumers after tax (ii) Gross
After tax price received by the ticket seller and (iii) Consumer & Seller Burden
Solution:
Pre- Tax Equilibrium Price: 400-10P= 15P; 25P= 400; P= $ 16 Q=400-10(16); Q= 240 units
Post Tax Equilibrium: With Consumer Tax: Pc= Ps + Tax
▪ At Equilibrium DD= SS= 400-10Pc= 15Ps; 400-10(Ps +4)= 15Ps ; 400 - 10Ps – 40= 15Ps ; 360= 25Ps ; Ps = $ 14.4
▪ Pc= Ps + Tax ($4)= 14.4 + 4= $ 18.4
Quantity= 400-10(18.4)= 400-184= 216 units
▪ Consumer burden= [14.4 - 16] + 4 = $2.4 ; Price paid by consumers after tax= $18.4
▪ Producer burden= [16 - 14.4] + 0 = $1.6 ; Gross After tax price received by sellers = $ 14.4
Lynda Inc is a monopolist whose cost of production is given by C= 12+q². Demand for Lynda Inc. is p= 24-q.
(i) What price will monopolist charge and what profits will the monopolist earn?
(ii) How will the monopolist price and profits change if a tax of Rs 4 is imposed on the suppliers of the product?