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THE DEMAND FOR MARIJUANA, TOBACCO AND ALCOHOL

December 2008

by

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Kenneth W Clements

Yihui Lan

The University of Western Australia

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and

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Xueyan Zhao

Monash University

The Marijuana Market

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D

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Observed

Legalised (no tax)

Legalised (with tax)

Price

Quantity

Demanded

The Risk Premium

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Revenue

D

D

X

Y

Z

Observed

Legalised (with tax)

Price

Quantity

Demanded

Distribution of the Risk Premium

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Mean = 300%

Median = 277%

SD = 179%

Note: Truncated at 750%

Cross Effects

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Tax revenue

Marijuana tax

0

Alcohol

(Substitute for Marijuana)

Marijuana

(Price inelastic)

Tobacco

(Complement for Marijuana)

Information Needed

• Own-price elasticity of demand for Marijuana
• Cross-price elasticities:
• Tobacco w.r.t Marijuana
• Alcohol w.r.t Marijuana
• “Observed” expenditure on Marijuana
• All very uncertain!

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Elasticities I

• Start with preference independence

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• Leads to Frisch price elasticities (marginal utility of income constant) of the form:

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Kronecker delta

Income elasticity of i > 0

Elasticities I

• Consider n = 4 goods, Marijuana, Tobacco, Alcohol and Other. The 4x4 matrix of Frisch price elasticities is:

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Elasticities I

• Under preference independence, this matrix is diagonal:

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�Elasticities II

• Preference independence means all goods are unrelated
• But Marijuana and Tobacco are likely to be complements
• Modify PI by using the Frisch elasticities as a tool to organise our (fragmentary) prior information

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Elasticities II

• Frisch price elasticity of demand for Marijuana w.r.t. the price of Tobacco:

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Budget share of Marijuana (1) and Tobacco (2)

Elasticities II

• The correlation:

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Elasticities II

• Under preference dependence, which allows for complementarity between Marijuana and Tobacco, the Frisch matrix takes the form:

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Elasticities II

• Here:

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• This is a “minimal” movement away from preference independence, whilst maintaining the underlying structure of the matrix

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Data

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• Income Flexibility:

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• Correlation:

Uncertainty

• Budget shares, income elasticities, and all follow truncated normal distributions
• E.g.

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Price Elasticities

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The price elasticity of demand for all interesting goods is -1/2.

See next figure

THEOREM

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PRICE ELASTICITIES OF DEMAND

Source: Clements “Price Elasticities of Demand are Minus One-half.” Economics Letters, 2008.

Mean = -0.54

Standard error = 0.17

Stochastic Elasticities

• Derive the implied distributions of price elasticities via Monte Carlo simulations
• Examples:

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Mean = -0.65

SD = 0.39

Mean = 1.29

SD = 0.69

Legalising and Taxing Marijuana

• Log-change in price of Marijuana is

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• Suppose , same as Tobacco
• Suppose
• Change in price is

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• Price falls with legalisation as tax < risk premium

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Producer Tax rate

Risk premium

Impact on Consumption

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Note: Money income held constant

Impact on Consumption

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Note: Money income held constant

Marijuana

% Change in

consumption

Marijuana

Mean = 26%

SD = 16%

Impact on Consumption

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Note: Money income held constant

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-3

Marijuana

Tobacco

Alcohol

Vice

% Change in

consumption

Taxation Revenue

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$ per capita p.a.

Marijuana tax rate

(% of consumer price)

Taxation Revenue

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Note: Additional revenue is calculated from observed tax revenue of Tobacco ($324), � Alcohol ($360) and Total ($684).

Revenue Uncertainty

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Why the Singularity?

• In above, risk premium
• Uncertainty band vanishes when consumer tax (t) on Marijuana ≈ 70%

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Why the Singularity?

• Producer tax:

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• Change in price:

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• Change in consumption of i:

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Other Applications of Approach

• Limited information
• Other illicit products
• New goods
• CGE modelling?

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