Market Size, Prices, and Purity

Jonathan P. Caulkins

Carnegie Mellon University Heinz College and

Qatar Campus

RAND, Drug Policy Research Center

2

Outline

• Estimating market size

• Fun with price & purity

• Other stuff on the supply side

• Concluding thought/comment on

Belgium and supply side

3

Estimating Market Size

Supply side methods

• Seizures * 10

• Production – seizures – consumption

elsewhere

Demand side methods

• # of users * consumption per user

• # of users * spending per user / price

4

Mr. Pareto’s Curse: You can only count

the users that do not matter (as much)

0

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

30,000,000

35,000,000

Users Days of Use (100s)

Past-Year but not Past Month

Past-Month 3.5 Times or Fewer

Past-Month 4-19 Times

Past-Month 20+ Times

5

Uncertainty Comes from Factors that

Have Not Been Studied

R1 PM: # of Users 16,752,428 NSDUH 2009

R2 PM: Days used in past year 156.3 NSDUH 2009 (Mean)

R3 PM: Joints per use day 2.5 NHSDA 1994 (Mean)

R4 PY: Number of users 11,967,200 NSDUH 2009 (Mean)

R5 PY: Days used in past year 29.8 NSDUH 2009 (Mean)

R6 PY: Joints per use day 1.25 0.5 * R3 (assumed)

R7 Grams per joint 0.43 Kilmer et al., 2010

R8 PM: Total grams 2,815,145,011 =R1 * R2 * R3 * R7

R9 PY: Total grams 191,748,950 =R4 * R5 * R6 * R7

R10 % underreporting 20% Various sources

Baseline Total 3,800 MT =(R8+R9) / (1 - R10)

Recent estimate of US marijuana consumption.

Supply (Price, Purity, and Availability)

Matters

• People used to think “Addicts will do anything to get their

fix” so elasticity of demand is 0.

• Once learned how to estimate price series, could show

that is not true.

6

2

7

US Cocaine and Heroin ED Mentions Inversely

Related to Prices

0

100

200

300

400

500

600

700

800

1981 1983 1985 1987 1989 1991 1993 1995

Pri

ce

pe

r P

ure

Gra

m &

ER

Me

nti

on

s/y

r 0.1*Heroin Price

Cocaine Price

Heroin ER Mentions/200

Cocaine ER Mentions/200

2

8

Price Raised to a Constant Elasticity Can

Explain Most Variation in ED Mentions

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

1978 1982 1986 1990 1994

Nu

mb

er

of

ED

Men

tio

ns p

er

Year

Cocaine Mentions Predicted by Price

Actual Cocaine Mentions

Heroin Mentions Predicted by Price

Actual Heroin Mentions

2

9

HS Seniors Marijuana Use Inversely

Correlated with Price

Trends in MJ Prices & MTF Annual Prevalence for HS Seniors

0

10

20

30

40

50

1980 1985 1990 1995 2000 2005

Pre

vale

nce (

%)

& P

rice (

$/g

ram

)

MJ Price/Gram

Annual Prevalence

Price Trend

Prevalence Trend

2

10

Key May Be Affordability,

Not Price Per Se

Mean Times Cannabis Used per Student, ESPAD (2003) Data, Nordic

Countries Excludedy = 0.0002x - 0.4373

R2 = 0.5287

0

1

2

3

4

5

6

7

8

9

$0 $10,000 $20,000 $30,000 $40,000GDP Per Capita

2

11

Disequilibrium Models & Detective Work

3

12

Heroin Overdoses in Victoria

0

50

100

150

200

250

300

350

400

450

500

1998 1999 2000 2001 2002 2003 2004 2005

Definite heroin OD

Likely heroin involvement

3

13

Little Change in “Raw” Price

Heroin price per gram, without purity adjustment (gram level)

$0

$50

$100

$150

$200

$250

$300

$350

$400

$450

$500

1998 1999 2000 2001 2002 2003 2004

Price per Raw Gram

(Interpolated from IDRS)

3

14

Big Change in Retail Heroin Purity

Average Heroin Purity (%) in VIC Seizures

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

1998 1999 2000 2001 2002 2003 2004

3

15

So Purity-Adjusted Price Soared

Heroin Price/ Gram, with & without Purity Adjustment (gram level)

$0

$500

$1,000

$1,500

$2,000

$2,500

$3,000

$3,500

$4,000

$4,500

1998 1999 2000 2001 2002 2003 2004

Price per Raw Gram

(Interpolated from IDRS)Price per Pure Gram

3

16

Which Can Explain Variation in

Ambulance Call-Outs

Compare Actual Total Monthly Ambulance Calls to What Would

Be Predicted Based on Price Trends from Mid 1999 On with a

Constant Elasticity Model (eta = -1.12)

0

100

200

300

400

500

600

700

1998 1999 2000 2001 2002 2003 2004 2005

Actual Total Ambulance Calls

Expected Total, from Price Trends

3

If Drought Was A Supply-Side Event,

Question is: “What Level?”

• Sub-national?

• Importation level?

• Source zone?

– SE Asia (Myanmar, etc.)

– SW Asia (Afghanistan, etc.)

17

3

Market Decline & Shock Were National,

not State Level Events

18

0

50

100

150

200

250

300

350

400

NSW Narcotics Arrests Correlate Extremely Well with VIC Heroin Purity

Heroin Use/Possession Arrests in NSW

VIC Heroin Purity (x4)

3

19

Similar Analysis for UK: Even Just Purity

Can Be Useful

3

Monthly Cocaine & Crack Purity in

London

20

0

10

20

30

40

50

60

70

80

90

100

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Avg Monthly Cocaine and Crack Purity in London Area

COCAINE

Crack

3

Weekly Amphetamine Series Shows

Abrupt Decline in Early 2000

21

0

5

10

15

20

25

30

0 52 104 156 208 260 312 364 416 468 520

Avg Amphetamine Purity, by Week (1997-Mid 2007)

3

22

Heroin Purity Series Also Suggestive of

(Later) Market Shock

London Heroin Purity Over Time (Mean +/- One SD)

0

10

20

30

40

50

60

70

80

1997 1999 2001 2003 2005 2007

Mean - 1 SD

Mean

Mean + 1 SD

3

23

Other Stuff on the Supply Side

• The wisdom of suitcases

• Cycle times & transience of batches

• Distribution (not just mean) of seizure

sizes in Australia

• Couriers’ wages

– (and existence of sacrificial sheep)

• Etc.

24

Supply-Chain Modeling

• Much like other distribution chains – Multi-layered network for heroin (and cocaine)

– Log-linear price-quantity relationship

– Price mark-ups may be slightly smaller

• And curiously stable across drugs

• Other comments – High cycle frequency (low inventory holding?)

– Importers are vertically integrated into domestic distribution

5

Typical Heroin Distribution

25

Transaction

Level Seller Buyer Amount

Price (per

transaction) Price/kg

4th Level

Wholesale Importer Respondent B

10-60 kg £437,500 £12,500

3rd Level

Wholesale

. Respondent B Respondent A

1 kg £15,000 £15,000

0.5 kg £8,000 £16,000

2nd Level

Wholesale Respondent A A's Customers

9 oz. £6,750 £27,000

1 oz. £900 £32,400

1st Level

Wholesale A's Customers Retail Sellers

0.5 oz. £625 £45,000

0.25 oz. £350 £50,400

0.125 oz. £187.50 £54,000

Retail Retail Sellers Users 1 gram £60 £60,000

0.1 gram £10 £100,000

5

Prices Follow Classic Log-Linear Model:

P = Q

26

y = 18709x0,8218

R² = 0,9972

y = 18709x-0,178

R² = 0,9444

£1

£10

£100

£1 000

£10 000

£100 000

£1 000 000

0,0001 0,001 0,01 0,1 1 10 100

Transaction Size (Kilograms)

Price

Price/kg

Power (Price)

5

Price-Quantity Exponent Fairly Stable

Across Substances

27

# of Cycles Average Min Max Std Dev.

Cannabis 5 0.817 0.674 0.966 0.116

Cannabis Resin 4 0.851 0.775 0.932 0.076

Cocaine 7 0.869 0.792 0.920 0.040

Crack 5 0.827 0.731 0.886 0.058

Ecstasy 6 0.754 0.547 0.937 0.129

Heroin 28 0.834 0.253 0.975 0.142

Heroin (w/o outlier) 27 0.855 0.620 0.975 0.086

5

Price-Quantity Exponent Larger in the

UK, Which Makes Sense

28

UK

Retail

Mid-Low

Level Mid-Level Top-Level

Cannabis 0.8170.72 imported

0.76 domestic 0.5730.802 0.783

Sinsemilla 0.850

Cannabis Resin 0.851

Hashish 0.770

Cocaine 0.869 0.830 0.716 0.751 0.787 0.813

Crack 0.827 0.790 0.731 0.661 0.833

Heroin 0.8340.83 brown

0.84 white 0.5310.718 0.764

US

Matrix Data

(Avg.)

Caulkins &

Padman (1993)

Arkes et al. (2004)

5

29

Modeling Suppliers as Businesses

• Project consequences of legalization – Production cost

– Distribution cost

– Price declines around the country

6

$30 $125 $260 $205

$1 075

$3 000

$-

$500

$1 000

$1 500

$2 000

$2 500

$3 000

$3 500

OUTDOORFARM

GREENHOUSE RESIDENTIALGROW-HOUSE

INDUSTRIALWAREHOUSE

DUTCHFACILITY

CURRENTWHOLESALE

Pro

du

cti

on

Co

st

per

lb.

Legal production and supply far cheaper

than illegal wholesale prices

Sources: Altered State? (RAND 2010), interview with medical marijuana cultivator, Kilmer (2012)

6

US MJ wholesale prices increase

systematically with distance from source

y = 0.4633x + 281.53R² = 0.4728

y = 0.3428x + 561.22R² = 0.454

$0

$200

$400

$600

$800

$1,000

$1,200

$1,400

$1,600

0 500 1000 1500 2000

Distance from Mexico (Miles)

STRIDE

Narcotics News

6

Trafficking legally produced MJ could lead to

price collapse across U.S. 6

33

Concluding Comment

• Belgium is affected by supply but

cannot affect (wholesale) supply

• Targeting retail supply

– Possible in theory

– Perilous in practice (at least for the US)