CRC Economics 1

CRC Economics 2

ExercisesEcon 304

Chapter 12

CRC Economics 3

Do you know …

how to analyze a tax system? the different tax systems? why the current tax system is

discouraging saving? what a marriage tax is?

CRC Economics 4

1a. How to analyze a tax system?

Given the following tax table

Answer the questions below.

$50,000 20%

$50,000 40%

Amount below

Amount over

Tax Rates

IncomeY

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Questions to answer

$50,000 20%

$50,000 40%

Amount below

Amount over

Tax Rates

IncomeY

Suppose that Y = $75,000. How much are total taxes (T)?

Total taxes (T) = Tax on income below $50,000 +Tax on income over $50,000

T = ($50,000*20%) + ($25,000*40%) = $20,000

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Questions to answer

$50,000 20%

$50,000 40%

Amount below

Amount over

Tax Rates

IncomeY

How much is the average tax rate (atr)?

atr = T / Y

atr = $20,000 / $75,000 = 27%i.e. on the average, the tax payment is 27 cents per dollar.

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Questions to answer

$50,000 20%

$50,000 40%

Amount below

Amount over

Tax Rates

IncomeY

How much is the marginal tax rate (mtr)?

mtr = T / Y

mtr = $10,000 / $25,000 = 40%i.e. the extra tax is 40 cents per extra dollar

on income over $50,000.

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Questions to answer

$50,000 20%

$50,000 40%

Amount below

Amount over

Tax Rates

IncomeY

Does this tax system increase or reduce efficiency?

The higher the mtr, the less efficient a tax system is.People have to pay more tax on extra income, they work less.

mtr = 40% > atr = 27%.This tax system reduces efficiency.

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Questions to answer

$50,000 20%

$50,000 40%

Amount below

Amount over

Tax Rates

IncomeY

Does this tax system increase or reduce equity?

The higher the mtr, the more tax is collected. The government has more money to help the poor.

mtr = 40% > atr = 27%.This tax system increases equity.

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1b. How to analyze a tax system?

Given the following tax table, where LS = lump sum

Answer the questions below.

$4,000All levels

IncomeY

LS Taxes

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Questions to answer

$4,000All levels

IncomeY

LS Taxes

Y$20,000

$40,000

T$4,000

$4,000

atr20%

10%

mtr0%

0%

Given two levels of income Y, fill in the blank boxes below.

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Questions to answer

$4,000All levels

IncomeY

LS Taxes

Y$20,000

$40,000

T$4,000

$4,000

atr20%

10%

mtr0%

0%

Does this tax system increase or reduce efficiency?

This tax system increases efficiency. In fact, it is the mostefficient system, because mtr = 0%

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Questions to answer

$4,000All levels

IncomeY

LS Taxes

Y$20,000

$40,000

T$4,000

$4,000

atr20%

10%

mtr0%

0%Does this tax system increase or reduce equity?

This tax system reduces equity. In fact, it is the leastequitable system, because (1) the poor pay the same tax as the rich, and (2) the government will not have enough

tax revenues to help the poor.

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2. Different tax systems

Given the following tax table

Answer the questions below.

Tax atr (%) Tax atr (%) Tax atr (%)$12,500 25% $15,000 30% $10,000 20%

$25,000 25% $25,000 25% $25,000 25%

$50,000 25% $40,000 20% $60,000 30%

Income$50,000

$100,000

$200,000

Y Proportional Regressive Progressive

Tax System

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Questions to answer

Tax atr (%) Tax atr (%) Tax atr (%)$12,500 25% $15,000 30% $10,000 20%

$25,000 25% $25,000 25% $25,000 25%

$50,000 25% $40,000 20% $60,000 30%

Income$50,000

$100,000

$200,000

Y Proportional Regressive Progressive

Tax System

What are the atr’s under the proportional tax system?

25% , 25%, and 25%.

What does that imply?

Under the proportional tax system, the same tax rate applies toall income levels.

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Questions to answer

Tax atr (%) Tax atr (%) Tax atr (%)$12,500 25% $15,000 30% $10,000 20%

$25,000 25% $25,000 25% $25,000 25%

$50,000 25% $40,000 20% $60,000 30%

Income$50,000

$100,000

$200,000

Y Proportional Regressive Progressive

Tax System

What are the atr’s under the regressive tax system?

30% , 25%, and 20%.

What does that imply?

Under the regressive tax system, the tax rate falls asincome rises.

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Questions to answer

Tax atr (%) Tax atr (%) Tax atr (%)$12,500 25% $15,000 30% $10,000 20%

$25,000 25% $25,000 25% $25,000 25%

$50,000 25% $40,000 20% $60,000 30%

Income$50,000

$100,000

$200,000

Y Proportional Regressive Progressive

Tax System

What are the atr’s under the progressive tax system?

20% , 25%, and 30%.

What does that imply?

Under the progressive tax system, the tax rate rises asincome rises.

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Questions to answer

Tax atr (%) Tax atr (%) Tax atr (%)$12,500 25% $15,000 30% $10,000 20%

$25,000 25% $25,000 25% $25,000 25%

$50,000 25% $40,000 20% $60,000 30%

Income$50,000

$100,000

$200,000

Y Proportional Regressive Progressive

Tax System

Which system increases efficiency the most?

The regressive system.

Which system increases equity the most?

The progressive system.

What is the U.S. income tax system, proportional, regressive, orprogressive?

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3. Why does the current U.S. income tax system discourage saving?

Given the following tax table

Answer the questions below.

Age Saving i(%)

25 $100 8% 0% 25%

65 $2,172 $1,029

8% 6%

Tax rate

Effective i(%)

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Questions to answer

Age Saving i(%)

25 $100 8% 0% 25%

65 $2,172 $1,029

8% 6%

Tax rate

Effective i(%)

Suppose that there is no income tax on saving, what is the futurevalue of $100 saving for 40 years (65-25) at 8% return per year?

FV = PV(1+i) n = $100(1+8%)40 = $2,172

How much is the effective rate of interest (i)?

i = 8%

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Questions to answer

Age Saving i(%)

25 $100 8% 0% 25%

65 $2,172 $1,029

8% 6%

Tax rate

Effective i(%)Suppose that the tax rate on saving is 25%, what is the future

value of $100 saving for 40 years (65-25) at 8% return per year?

FV = PV(1+i) n = $100(1+8%(1-25%))40 = $1,029

How much is the effective rate of interest (i)?

i = 6%

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Questions to answer

What does that imply?

The current U.S. tax system taxes the returns on saving, thus reducing the effective rate of interest and reducing people’s incentive

to save.

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Questions to answer

What if we remove that tax and replace it with a consumption tax?

Then people will have more money at the end. They have the incentive to save more.

This will be good for the economy in the long run. As more money is saved, more money will be invested.

That means the U.S. economy will have more meansto produce more goods and services.

The economy will grow more.

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3. What is a marriage tax? Given the following tax table

Answer the questions below.

Income t(%)

$10,000 0%

$10,000 25%

Sam Sally Total S&S Tax

$0 $100,000 $100,000 $100,000

$0 $22,500 $22,500 $22,500 $0

John Joan Total J&J Tax

$50,000 $50,000 $100,000 $100,000

$10,000 $10,000 $20,000 $22,500 $2,500Tax

MarriageBefore After

Income

Couple 1

Tax

Couple 2

Income

Less than

Above

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Questions to answer Income t(%)

$10,000 0%

$10,000 25%

Sam Sally Total S&S Tax

$0 $100,000 $100,000 $100,000

$0 $22,500 $22,500 $22,500 $0

John Joan Total J&J Tax

$50,000 $50,000 $100,000 $100,000

$10,000 $10,000 $20,000 $22,500 $2,500Tax

MarriageBefore After

Income

Couple 1

Tax

Couple 2

Income

Less than

Above

How much is the tax paid by Sam & Sally before marriage?After marriage?

Before marriage T = $90,000 * 25% = $22,500.After marriage T = $22,500.

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Questions to answer Income t(%)

$10,000 0%

$10,000 25%

Sam Sally Total S&S Tax

$0 $100,000 $100,000 $100,000

$0 $22,500 $22,500 $22,500 $0

John Joan Total J&J Tax

$50,000 $50,000 $100,000 $100,000

$10,000 $10,000 $20,000 $22,500 $2,500Tax

MarriageBefore After

Income

Couple 1

Tax

Couple 2

Income

Less than

Above

How much is the tax paid by John & Joan before marriage?After marriage?

Before marriage T = $80,000 * 25% = $20,000.After marriage T = $22,500.

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Questions to answer What happens?

Sam, who does not work, and Sally pay the sameamount of tax both before and after marriage.

John and Joan, both working, by getting married, pay more tax.

The tax law penalizes married couples, who both work, with a marriage tax.

Was there any changes in the tax law about the issue?

The tax law was changed to include some adjustmentsto the issue of marriage tax.

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Now you know …

how to analyze a tax system. the different tax systems. why the current tax system is

discouraging saving. what a marriage tax is.

CRC Economics 29