Commodity tax

Question 1

When does producer bear burden of tax?

Answer 1

• elasticity of demand = large

- elasticity of supply = small

Question 2

When does consumer bear burden of tax?

Answer 2

• elasticity of demand = small

- elasticity of supply = large

Question 3

When is DWL large?

Answer 3

1. both elasticities higher

2. tax rate higher

Question 4

1. If capital and labour are elastic in the long-run, which factor of production does the burden of taxation ultimately fall on (in perfect general equilibrium)?
2. Why?

Answer 4

1. Land

2. It’s the only inelastic factor of production

Question 5

Why is the social value of government revenue higher when taxes are higher?

Answer 5

1. Relaxing the revenue constraint by £1 means we can reduce taxes by £1
2. Because the DWL is proportional to the square of the tax rate, the gain in social welfare from reducing taxes by £1 is greater when taxes are high

Question 6

If relax revenue raising constraint by £1, why is it better to reduce taxes by £1, rather than give out £1 as lump-sum?

Answer 6

1. Reduces taxes by £1 and handing out £1 lump-sum benefit both increase income by £1
2. But, given that taxes distortionary, additional welfare benefit from reducing taxes (lower DWL)

Question 7

When does social marginal utility of consumption = social marginal utility of income?

Answer 7

If there are no income effects

Question 8

What problem is the inverse elasticity rule an answer to?

Answer 8

1. Simple version of single person Ramsey tax problem (1 person, independent goods)
   i. e. no cross-price or income effects

Question 9

What are the implications of the General Ramsey tax rule?

Answer 9

1. Optimal tax system reduces compensated demand for each good by same proportional rule
2. Substitutes – when taxing a good, tax its substitutes too (or you won’t reduce demand for each good by same proportional rule)
3. Complements – when taxing a good, take care over taxing its complements (potentially tax complements less)

Question 10

What is the only untaxed good in the Ramsey framework?

Answer 10

Leisure

Question 11

Why does Ramsey taxation imply the same disincentive for work as labour taxation?

Answer 11

1. Leisure = only untaxed good (i.e. most desirable, relatively)
2. If leisure the most desirable good, this means labour is the least desirable
3. Hence, same disincentive to work as labour taxation

Question 12

Corlett and Hague (1953) theorem

Answer 12

1. In 3 goods case (2 consumption goods and leisure), the good more complementary with leisure should be taxed more heavily
2. Reason - want to encourage work (i.e. discourage leisure)

Question 13

Implications of many person Ramsey rule?

Answer 13

1. Tax goods in inverse proportion to demand elasticities
2. Subsidise good if disproportionately demanded by people for whom social marginal utility of transfer is positive (high-gamma people)

Question 14

Key tax incidence conclusions to remember

Answer 14

1. Statutory incidence ≠ economic incidence
2. Equilibrium independent of who nominally ‘pays’ tax
3. More inelastic factors bear more of the tax

Question 15

Assumptions made for all versions of the single person Ramsey tax problem?

Answer 15

1. No income tax
2. No individualised lump-sum taxation
3. Producer prices fixed
4. Commodity taxes are linear

Question 16

Key assumption to derive simple non-general version of single person Ramsey rule?

Answer 16

No cross-price effects

Question 17

Why does general Ramsey rule recommend taxing complements of leisure?

Answer 17

1. Leisure the only untaxed good in Ramsey framework (i.e. relatively most desirable)
2. Hence same disincentive to work as labour taxation
3. So, to reduce compensated demand for each good (including leisure) by the same proportional rule, tax the complements of leisure
4. Taxing complements of leisure increases incentive to work

Question 18

1. What is the Diamond-Mirrlees (1971) production efficiency theorem?
2. Implications for design of commodity tax system?
3. Intuition for result?

Answer 18

1. Assume absence of:
   (i) Externalities
   (ii) Non-competitive behaviour
   (iii) Restrictions on tax instruments that can be used
   1b. Given assumptions, necessary (in Pareto sense) feature of optimal tax system = production decisions left undistorted
2. Implication – business transactions shouldn’t be taxed
3. Intuition – distorting product decisions reduces aggregate output

Question 19

Key limitation of the inverse elasticity rule?

Answer 19

Ignores cross-price effects

Question 20

Evidence that multiple VAT rates substantially increase reporting burden on businesses?

Answer 20

Cnossen (2003)

Question 21

1. Evidence that weak separability condition consistently empirically rejected?
2. How strong is this effect?
3. Implication/conclusion?

Answer 21

1. Crawford et al (2008)
2. Effects of hours worked on commodity demands = small
3. Gains from moving to ‘optimally differentiated’ commodity tax system might be small

Question 22

Implications of fact that DWL increases (approximately) with the square of the tax rate?

Answer 22

For efficiency:

1. Spread taxes across goods
2. Spread taxes across time

Question 23

Some favour capital taxation to hit the rich, but how might this burden ultimately fall back on labour to some extent?

Answer 23

1. Capital taxes decrease returns to capital, which may lower savings
2. If savings fall, then capital stock falls
3. Fall in capital stock will cause wages to decrease (hurting workers)

Question 24

1. What do theories of optimal taxation generally ignore?

2. Therefore, what should be kept in mind?

Answer 24

1. Incidence of taxation

2. Keep in mind general equilibrium effects (e.g. tax on capital may hurt labour)

Question 25

When is the social value of government revenue higher?

Answer 25

When R (revenue that needs to be raised) is higher

Question 26

Answer to simple version of single person Ramsey tax problem (1 person, independent goods)

Answer 26

Inverse elasticity rule

Question 27

Key implications of inverse elasticity rule

Answer 27

Optimal commodity taxation is:

1. Positive
2. Inversely proportional to elasticity of demand
3. Higher on all goods, if revenue-raising constraint R is higher

Question 28

What problem is the general Ramsey tax rule an answer to?

Answer 28

General version of single person Ramsey tax problem (1 person, cross-price and income effects)

Question 29

What does optimal commodity tax differentiation depend on?

Answer 29

1. Degree of concern for the poor (inequality aversion)

2. Differences in consumption patterns between rich and poor

Question 30

….. et al (…..)

1. Ending all zero and reduced rates (except housing/exports), whilst increasing all means-tested benefit/tax credit rates by …..% would:
   (i) leave poorest …..% better off (on average)
   (ii) raise extra £…..
2. Reason - …..

Answer 30

Crawford et al (2010)

1. Ending all zero and reduced rates (except housing/exports), whilst increasing all means-tested benefit/tax credit rates by 15% would:
   (i) leave poorest 30% better off (on average)
   (ii) raise extra £11 billion
2. Reason - income tax/transfers = better targeted instruments than commodity taxes

Question 31

Crawford et al (2010)

Answer 31

1. Ending all zero and reduced rates (except housing/exports), whilst increasing all means-tested benefit/tax credit rates by 15% would:
   (i) leave poorest 30% better off (on average)
   (ii) raise extra £11 billion
2. Reason - income tax/transfers = better targeted instruments than commodity taxes

Question 32

Evidence that the case for using differential VAT rates to help the less well-off is weak

Answer 32

Crawford et al (2010)

1. Ending all zero and reduced rates (except housing/exports), whilst increasing all means-tested benefit/tax credit rates by 15% would:
   (i) leave poorest 30% better off (on average)
   (ii) raise extra £11 billion
2. Reason - income tax/transfers = better targeted instruments than commodity taxes

Question 33

Cnossen (2003)

Answer 33

Evidence that multiple VAT rates substantially increase reporting burden on businesses

Question 34

Possible implication of ignoring cross-price effects in inverse elasticity rule

Answer 34

Increased tax on good w/low price elasticity could even fall in total tax revenue or more distortions

Question 35

What does weak separability between consumption and leisure condition mean?

Answer 35

All goods similarly complementary w/leisure

Question 36

Sufficient condition for uniform commodity taxation to be optimal?

Answer 36

1. Weak separability between consumption and leisure (all goods equally complementary with leisure)

Question 37

Crawford et al (2008)

1. Examples of goods that are complementary with leisure?
2. Examples that are complementary with work?

Answer 37

1. Complements w/leisure (higher tax):
   (i) Food
   (ii) Domestic energy
   (iii) Children’s clothing
   (iv) Public transport
2. Complements w/work (lower tax):
   (i) Alcohol
   (ii) Food eaten out of home
   (iii) Motor fuel

Question 38

Practical problems with differential commodity taxes

Answer 38

1. Cnossen (2003) – multiple VAT rates substantially increase reporting burden on businesses
2. Increased lobbying for preferential treatment

Question 39

1. Assume absence of:
   (i) Externalities
   (ii) Non-competitive behaviour
   (iii) Restrictions on tax instruments that can be used
   1b. Given assumptions, necessary (in Pareto sense) feature of optimal tax system = production decisions left undistorted
2. Implication – business transactions shouldn’t be taxed
3. Intuition – distorting product decisions reduces aggregate output

Answer 39

Diamond-Mirrlees (1971) production efficiency theorem

Question 40

Theorem to support idea that business transactions should not be taxed in optimal tax system?

Answer 40

Diamond-Mirrlees (1971) production efficiency theorem

1. Assume absence of:
   (i) Externalities
   (ii) Non-competitive behaviour
   (iii) Restrictions on tax instruments that can be used
   1b. Given assumptions, necessary (in Pareto sense) feature of optimal tax system = production decisions left undistorted
2. Implication – business transactions shouldn’t be taxed
3. Intuition – distorting product decisions reduces aggregate output