consumer choice between gasoline and sugarcane...

“100%”

“33%”

Alberto Salvo, Northwestern University

May 2011, Iowa State

(joint with Cristian Huse, Stockholm)

Consumer Choice Between Gasoline and Sugarcane Ethanol

• Central policy aim: wean economies off fossil fuels (particularly oil derivatives)• Diversify energy sources• Curb emissions• Sustain growth

• Private road transport: large and growing sector• Gasoline-powered engine set to lose share• Alternative energy sources: electricity, biofuels

• How will motorists substitute away from century-old gasoline??• Price incentives required at pump or plug?• Research is scarce: RP studies cannot be conducted• Except Brazil: Gasoline × Alternative (Sugarcane Ethanol)

Motivation

Alternative hypotheses & Preview

An example (lab measurements)Fiat Palio ELX (Flex), 2 doors, 1.0 –8V, manual transm., AC, hydraulic steering, city driving cycle:Ethanol (E100): ke = 6.9 km/liter Gasoline (E22): kg = 9.9 km/liter

$/km Ethanol = $/km Gasoline

ke/kg≈.7

Ethanol preferencee.g., “green” types,

“home bias”

Ethanol aversione.g., “conventional” types, “range anxiety”

FIND: Observed + unobserved consumer heterogeneity:+20% E v. G in $/km → 20% E+20% G v. E in $/km → 20% G

State dependencee.g., short-run habit, inattentive, unwilling or unable to compare prices

Null: Perfect substitutes

• A natural experiment• Our opportune survey• Brief descriptive stats

• Empirical demand

• Demand estimates• Probits, Multinomial probits• Price sensitivity of “median” motorist• Elasticity matrices for subgroups: aged +65y• WTP for “greenness” and to relieve “range anxiety”

• A counterfactual• Planning the energy mix

• (Time permitting) Consumer “inattention” ×“tastes”

Outline of talk

Oil, World Price (WTI) Sugar, World Price (ISA)

Gasoline "C", Retail Price São Paulo city Ethanol, Retail Price São Paulo city

World prices × local prices, 2000-2010World prices*WTI R$/bbl &ISA R$ cents/lb

Prices at the pump in the city of São Paulo*R$/liter

2003, 2006 and...2010: The pump price of Ethanol peaks when the world price of Sugar peaks

* Constant prices in Brazilian Real (R$), base Mar/10. Sources: EIA, ISO, IBGE (IPCA), Bacen

Sugar (ISA)

Oil (WTI)

Ethanol (E100)

Gasoline (regular, E20-25)

World/local sugar/ethanol markets: Arbitrage

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

900,000

Demand responds: Market-level data

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

Fuel shipments to stations,Total Brazil*m3 / monthGasoline (E20-25)

Ethanol (E100)

Gasoline (E20-25)

Ethanol (E100)

FFVs introduced

Market-level study:- Consumer heterogeneity?- Poor data (e.g., FFV fleet size and usage)

Early 2010:Fuel mix shifts Ethanol→ Gasoline→ Ethanol

Fuel shipments to stations,State of São Paulo*m3 / month

* Source: ANP

• Consumer “inattention” × “tastes”

Outline of talk

Variation in relative per-liter prices, pe/pg5

-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 -6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 -6-5-4-3-2-10 1 2 3 4 5 6 7 8 9

Belo Horizonte Curitiba Porto Alegre

Recife Rio de Janeiro Sao Paulo

pe_rel_pg_p5 pe_rel_pg_p25

pe_rel_pg_p75 pe_rel_pg_p95

Number of weeks prior to (negative) or after (positive) week of January 25 2010

Graphs by city

Percentiles of the distribution across stations surveyed by the regulator in each city

Evolution of the relative price of ethanol in the weeks about the week of January 25 2010

5th, 25th, 75th, 95th percentiles of distribution of Ethanol-to-regular-Gasoline price ratio over 1st Qtr 2010 in 6 main cities (source: ANP)

Week of11 Jan 2010

Week of25 Jan

Week of29 Mar2010

Vertical lines:9 city-weeks in our survey

Approximate parity ratio, pe /pg = 70%

• 6 cities: SP, CTB, REC, RJ, BH, POA• 9 city-weeks (3 weeks) in Jan and Mar 2010• 2160 FFV motorists in 180 retail fueling stations

• 12 motorists/station: pass filter & agree to interview• Private use (exclude cab and corporate use)• Week days + Saturday, rush + off-peak hours• Branded stations (29% BR, 27% Shell, 19% Ipiranga...)

• Instructed field representative to:• (Quietly) observe motorist’s choice (revealed preference)• E × G regular (plus, if available: G midgrade, G premium)• (Only then) approach motorist for short interview (“stated”

preference)• E.g.: Main reason(s) behind fuel choice (“spontaneous”

response); Car usage (km/week); Schooling

Survey design

Fueling stations visited

São Paulo

Curitiba

Rio de Janeiro

Porto Alegre

Belo Horizonte

Recife

Outline of talk

Station-level data (selected)Variable January visits

Mean (N,Std.Dev.)March visitsMean (N,Std.Dev.)

Total visitsMean (N,Std.Dev.)

Ethanol price, pe (R$/liter) SP1 1.89 (20,.12)

SP2 1.88 (20,.14)

CTB 1.91 (20,.06)

REC 1.89 (20,.04)

RJ 2.18 (20,.15)

BH 2.06 (20,.11)

POA 2.32 (20,.10)

SP 1.46 (20,.14)

CTB 1.33 (20,.06)

Per-liter ethanol-to-regular-gasoline price ratio, pe/pg (%)

SP1 74% (20,3%)

SP2 75% (20,3%)

CTB 75% (20,2%)

REC 75% (20,2%)

RJ 81% (20,4%)

BH 85% (20,3%)

POA 90% (20,4%)

SP 59% (20,4%)

CTB 58% (20,2%)

Midgrade gasoline markup over regular (%)

104% (164,3%)

Number of nozzles 13 (180,6)

E:4,G:5,midgrG:3

Duration of station visit (hours)

2.5 (180,1.0)

Price variation:Opportunity

Motorist-level data (selected)

22 liters (< half tank)

Median: 1 visit/week

rice r

tive to

asolin

e in %

0 .2 .4 .6 .8 1Ethanol's share of the aggregate energy embedded in the 12 FFV motorists’ purchases

rice r

tive to

asolin

e in %

0 .2 .4 .6 .8 1Share of FFV motorists who chose ethanol as their main energy source

Station visits in January 2010 Station visits in March 2010 Station visits in January 2010 Station visits in March 2010

Fuel choices aggregated to station level

Horizontal axis: “Unweighted” Ethanol share:

Vertical axis: pe/pg (per-liter prices)

Horizontal axis: “Weighted” Ethanol share:

asolin

rice r

el econ

0 .2 .4 .6 .8 1Empirical choice probability for ethanol

Controlling for “parity” differences across models

Choosing Ethanol when Gasoline is cheaper per km (i.e., where pei/kei > pgi/kgi)Vertical axis: 1 ppt bins:

E.g.: Motorist in Belo Horizonte in January, drove a VW Gol 1.0:88.2% ― 69.9% ≈ 18% → Enters the 18 ppt bin

(Equivalently:pei/kei ≈ 0.28 R$/kmpgi/kgi ≈ 0.22 R$/km0.06 R$/km, or 21%, discount represents624 R$ per year)

Choosing Gasoline when Ethanol is cheaper per km(i.e., where pei/kei < pgi/kgi)

pei/pgi― kei/kgi

Horizontal axis: Proportion of motorists in bin who chose ethanol as their dominant source of kilometers

Outline of talk

Discrete choice specifications

• Binary choice models:

• Probit:• Logit:

Note 2: Relying on the moderate (within-route) price dispersion and consumers’ professed station loyalty, we ignore any substitution across stations

• Multinomial response models (multinomial probits):• Motorist i chooses fuel with maximal utility

and thus (to state one choice probability):

Note 1: Standard errors clustered at the station visit level

Multinomial probit marginal effects (other results omitted)

Age > 65y →

“Environmental.”→

Invoke engine →

Pricey car→

Heavy user→

“Home bias”

40<Age< 65y →

Considerable “unobserved” consumer heterogen.

.146 .196 .246 .296 .346 .396Energy-adjusted ethanol price in R$/km

Energy-adjusted gasoline prices held constant at 0.246 R$/km regular and 0.256 R$/km midgrade

Fuel choice probabilities for median motorist in specification without city fixed effects

inal effe

Effect on the probability of choosing ethanol from raising the ethanol price by 0.01 R$/km

Ethanol

Regulargasoline

Midgradegasoline

Parity: pe /pg= 70%

pe /pg= 80%

pe /pg= 90%

pe /pg= 60%

pe /pg= 50%

Parity: pe /pg= 70%

pe /pg= 80%

pe /pg= 90%

pe /pg= 60%

pe /pg= 50%

Estimated marginal effect on ethanol and 95% confidence interval

• The “median” motorist’s price responsiveness• Male, 25-40y, some college, neither uses car heavily nor drives a pricey

model, invokes neither the environment, the engine nor range• Varying the ethanol price holding gasoline prices constant

• Baseline specification excluding city fixed effects (to conservatively reduce price range for switching)

“Observed” heterogeneity: Hypothetical extremes

• “Ethanol fan”: Younger (<25y), some college, resides in Curitiba (capital of

ethanol-producing state), spontaneously invokes the environment

• “Gasoline fan”: Older (>65y), no more than primary, resides in Porto Alegre

(ethanol importer), heavy commuter, drives expensive model, invokes engine

• Baseline specification (hereafter)

Fuel choice probabilities for ethanol fan

Ethanol

Regulargasoline

Midgradegasoline

Parity: pe /pg≈ 70%

pe /pg≈ 80%

pe /pg≈ 90%

pe /pg≈ 60%

pe /pg≈ 50%

Fuel choice probabilities for gasoline fan

Ethanol

Regulargasoline

Midgradegasoline

pe /pg≈ 80%

pe /pg≈ 90%

pe /pg≈ 60%

pe /pg≈ 50%

Price elasticity matrices: Effect of age

• Evaluated at the median of regressors:

Recall per-liter pe/pg:74% 74%

Willingness to pay for “greenness”

• Median motorist in each of 3 cities with varying home bias• Horizontal shifts provide natural measures for:

• “Greenness”: Switch environ.-invoking reason on/off: .12 R$/km (.10 $/mi)0

Ethanol choice probabilities for median motorists with and without environmental concerns

Ethanol

pe /pg≈ 80%

pe /pg≈ 90%

pe /pg≈ 60%

pe /pg≈ 50%

Curitiba

Rio de Janeiro

Porto Alegre

A counterfactual: Planning the energy mix

• A planner in the Amazonian state of Pará (pop 7.6m, 2/3 urban)• Nation’s highest state sales tax on ethanol: 28% ICMS (v. 12% SP)• Consider a plan to wean PA motorists (FFVs 45%) off gasoline• Different scenarios, common message: Uptake of ethanol would

remain limited• Qualifier: Ignores long run changes (preferences, behavior, information)

Consumer “inattention” versus “tastes”

• Restrict sample to: “Observably-average” motorists facing sufficiently unequal prices across G and E• In such markets, which observable characteristics help explain the choice

of the dear fuel over a cheaper close substitute?

Binary probit marginal effects: Choice of dear fuel

Larger stake, better informed? →

“Information diffusion effect”→

“Magnitude effect” →

Conscious of habit playing a role→

• Controls for gender, age, education and car price included but not significant

• Direct & transparent empirical strategy uncovers substantial consumer heterogeneity in the choice among century-old gasoline and a less-established alternative motor fuel

• Likely to generalize to other markets---and perhaps even in a magnified way• This setting: G & E similarly distributed, comparably priced and

billed, almost identically consumed• Gasoline v. Alternative: Comparison can be less transparent!

• Observed heterogeneity• E.g., “Green” consumers do exist (not Prius status-seekers),

Consumer’s age, Confusion about engine aspects

• Unobserved heterogeneity• Salience-raising policy considerations

Takeaways

P R E Ç O G A S O L I N A

R$/litro 2.00 2.02 2.04 2.06 2.08 2.10 2.12 2.14 2.16 2.18 2.20 2.22 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38 2.40 2.42 2.44 2.46 2.48 2.50 2.52 2.54 2.56 2.58 2.60 2.62 2.64 2.66 2.68 2.70 2.72 2.74 2.76 2.78 2.80 2.82 2.84 2.86 2.88 2.90 2.92 2.94 2.96 2.98 3.00

P 1.20 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.54 0.54 0.53 0.53 0.52 0.52 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.48 0.48 0.48 0.47 0.47 0.47 0.46 0.46 0.45 0.45 0.45 0.44 0.44 0.44 0.43 0.43 0.43 0.43 0.42 0.42 0.42 0.41 0.41 0.41 0.41 0.40 0.40

R 1.22 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.56 0.56 0.55 0.55 0.54 0.54 0.54 0.53 0.53 0.52 0.52 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.48 0.48 0.48 0.47 0.47 0.47 0.46 0.46 0.46 0.45 0.45 0.45 0.44 0.44 0.44 0.43 0.43 0.43 0.42 0.42 0.42 0.41 0.41 0.41 0.41

E 1.24 0.62 0.61 0.61 0.60 0.60 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.54 0.54 0.53 0.53 0.53 0.52 0.52 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.48 0.48 0.48 0.47 0.47 0.47 0.46 0.46 0.46 0.45 0.45 0.45 0.44 0.44 0.44 0.43 0.43 0.43 0.42 0.42 0.42 0.42 0.41

Ç 1.26 0.63 0.62 0.62 0.61 0.61 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.54 0.54 0.53 0.53 0.53 0.52 0.52 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.48 0.48 0.48 0.47 0.47 0.47 0.46 0.46 0.46 0.45 0.45 0.45 0.44 0.44 0.44 0.43 0.43 0.43 0.43 0.42 0.42

O 1.28 0.64 0.63 0.63 0.62 0.62 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.54 0.54 0.53 0.53 0.52 0.52 0.52 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.48 0.48 0.48 0.47 0.47 0.47 0.46 0.46 0.46 0.45 0.45 0.45 0.44 0.44 0.44 0.44 0.43 0.43 0.43

1.30 0.65 0.64 0.64 0.63 0.63 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.54 0.54 0.53 0.53 0.52 0.52 0.52 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.49 0.48 0.48 0.47 0.47 0.47 0.46 0.46 0.46 0.45 0.45 0.45 0.45 0.44 0.44 0.44 0.43

E 1.32 0.66 0.65 0.65 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.55 0.54 0.54 0.53 0.53 0.52 0.52 0.52 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.49 0.48 0.48 0.47 0.47 0.47 0.46 0.46 0.46 0.46 0.45 0.45 0.45 0.44 0.44

T 1.34 0.67 0.66 0.66 0.65 0.64 0.64 0.63 0.63 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.54 0.54 0.54 0.53 0.53 0.52 0.52 0.52 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.49 0.48 0.48 0.48 0.47 0.47 0.47 0.46 0.46 0.46 0.45 0.45 0.45

A 1.36 0.68 0.67 0.67 0.66 0.65 0.65 0.64 0.64 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.54 0.54 0.54 0.53 0.53 0.52 0.52 0.52 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.49 0.48 0.48 0.48 0.47 0.47 0.47 0.46 0.46 0.46 0.45

N 1.38 0.69 0.68 0.68 0.67 0.66 0.66 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.59 0.59 0.58 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.54 0.54 0.53 0.53 0.53 0.52 0.52 0.51 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.49 0.48 0.48 0.48 0.47 0.47 0.47 0.46 0.46

O 1.40 0.70 0.69 0.69 0.68 0.67 0.67 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.56 0.55 0.55 0.54 0.54 0.53 0.53 0.53 0.52 0.52 0.51 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.49 0.48 0.48 0.48 0.47 0.47 0.47

L 1.42 0.71 0.70 0.70 0.69 0.68 0.68 0.67 0.66 0.66 0.65 0.65 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.55 0.54 0.54 0.53 0.53 0.53 0.52 0.52 0.51 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.49 0.48 0.48 0.48 0.47

1.44 0.72 0.71 0.71 0.70 0.69 0.69 0.68 0.67 0.67 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.55 0.54 0.54 0.53 0.53 0.53 0.52 0.52 0.51 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.49 0.48 0.48

1.46 0.73 0.72 0.72 0.71 0.70 0.70 0.69 0.68 0.68 0.67 0.66 0.66 0.65 0.65 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.57 0.56 0.56 0.55 0.55 0.54 0.54 0.54 0.53 0.53 0.53 0.52 0.52 0.51 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.49

1.48 0.74 0.73 0.73 0.72 0.71 0.70 0.70 0.69 0.69 0.68 0.67 0.67 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.56 0.55 0.55 0.54 0.54 0.54 0.53 0.53 0.52 0.52 0.52 0.51 0.51 0.51 0.50 0.50 0.50 0.49

1.50 0.75 0.74 0.74 0.73 0.72 0.71 0.71 0.70 0.69 0.69 0.68 0.68 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.61 0.61 0.60 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.56 0.55 0.55 0.54 0.54 0.54 0.53 0.53 0.52 0.52 0.52 0.51 0.51 0.51 0.50 0.50

1.52 0.76 0.75 0.75 0.74 0.73 0.72 0.72 0.71 0.70 0.70 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.55 0.54 0.54 0.54 0.53 0.53 0.52 0.52 0.52 0.51 0.51 0.51

1.54 0.77 0.76 0.75 0.75 0.74 0.73 0.73 0.72 0.71 0.71 0.70 0.69 0.69 0.68 0.68 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.57 0.56 0.56 0.55 0.55 0.55 0.54 0.54 0.53 0.53 0.53 0.52 0.52 0.52 0.51

1.56 0.78 0.77 0.76 0.76 0.75 0.74 0.74 0.73 0.72 0.72 0.71 0.70 0.70 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.57 0.56 0.56 0.55 0.55 0.55 0.54 0.54 0.53 0.53 0.53 0.52 0.52

1.58 0.79 0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.73 0.72 0.72 0.71 0.71 0.70 0.69 0.69 0.68 0.68 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.56 0.55 0.55 0.54 0.54 0.54 0.53 0.53 0.53

1.60 0.80 0.79 0.78 0.78 0.77 0.76 0.75 0.75 0.74 0.73 0.73 0.72 0.71 0.71 0.70 0.70 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.63 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.58 0.57 0.57 0.56 0.56 0.56 0.55 0.55 0.54 0.54 0.54 0.53

1.62 0.81 0.80 0.79 0.79 0.78 0.77 0.76 0.76 0.75 0.74 0.74 0.73 0.72 0.72 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.57 0.56 0.56 0.55 0.55 0.55 0.54 0.54

1.64 0.82 0.81 0.80 0.80 0.79 0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.73 0.73 0.72 0.71 0.71 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.59 0.58 0.58 0.57 0.57 0.57 0.56 0.56 0.55 0.55 0.55

1.66 0.83 0.82 0.81 0.81 0.80 0.79 0.78 0.78 0.77 0.76 0.75 0.75 0.74 0.73 0.73 0.72 0.72 0.71 0.70 0.70 0.69 0.69 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.58 0.57 0.57 0.56 0.56 0.56 0.55

1.68 0.84 0.83 0.82 0.82 0.81 0.80 0.79 0.79 0.78 0.77 0.76 0.76 0.75 0.74 0.74 0.73 0.72 0.72 0.71 0.71 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.60 0.59 0.59 0.58 0.58 0.58 0.57 0.57 0.56 0.56

1.70 0.85 0.84 0.83 0.83 0.82 0.81 0.80 0.79 0.79 0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.73 0.73 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.59 0.58 0.58 0.57 0.57 0.57

1.72 0.86 0.85 0.84 0.83 0.83 0.82 0.81 0.80 0.80 0.79 0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.74 0.73 0.72 0.72 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.61 0.60 0.60 0.59 0.59 0.59 0.58 0.58 0.57

1.74 0.87 0.86 0.85 0.84 0.84 0.83 0.82 0.81 0.81 0.80 0.79 0.78 0.78 0.77 0.76 0.76 0.75 0.74 0.74 0.73 0.73 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.60 0.59 0.59 0.58 0.58

1.76 0.88 0.87 0.86 0.85 0.85 0.84 0.83 0.82 0.81 0.81 0.80 0.79 0.79 0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.73 0.73 0.72 0.72 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.59

1.78 0.89 0.88 0.87 0.86 0.86 0.85 0.84 0.83 0.82 0.82 0.81 0.80 0.79 0.79 0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.74 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.61 0.60 0.60 0.59

1.80 0.90 0.89 0.88 0.87 0.87 0.86 0.85 0.84 0.83 0.83 0.82 0.81 0.80 0.80 0.79 0.78 0.78 0.77 0.76 0.76 0.75 0.74 0.74 0.73 0.73 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60

1.82 0.91 0.90 0.89 0.88 0.88 0.87 0.86 0.85 0.84 0.83 0.83 0.82 0.81 0.81 0.80 0.79 0.78 0.78 0.77 0.76 0.76 0.75 0.75 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.61

1.84 0.92 0.91 0.90 0.89 0.88 0.88 0.87 0.86 0.85 0.84 0.84 0.83 0.82 0.81 0.81 0.80 0.79 0.79 0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.74 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.63 0.62 0.62 0.61

1.86 0.93 0.92 0.91 0.90 0.89 0.89 0.88 0.87 0.86 0.85 0.85 0.84 0.83 0.82 0.82 0.81 0.80 0.79 0.79 0.78 0.78 0.77 0.76 0.76 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62

1.88 0.94 0.93 0.92 0.91 0.90 0.90 0.89 0.88 0.87 0.86 0.85 0.85 0.84 0.83 0.82 0.82 0.81 0.80 0.80 0.79 0.78 0.78 0.77 0.76 0.76 0.75 0.75 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.64 0.63 0.63

1.90 0.95 0.94 0.93 0.92 0.91 0.90 0.90 0.89 0.88 0.87 0.86 0.86 0.85 0.84 0.83 0.83 0.82 0.81 0.81 0.80 0.79 0.79 0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.74 0.73 0.73 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.66 0.65 0.65 0.64 0.64 0.63

1.92 0.96 0.95 0.94 0.93 0.92 0.91 0.91 0.90 0.89 0.88 0.87 0.86 0.86 0.85 0.84 0.83 0.83 0.82 0.81 0.81 0.80 0.79 0.79 0.78 0.77 0.77 0.76 0.76 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64

1.94 0.97 0.96 0.95 0.94 0.93 0.92 0.92 0.91 0.90 0.89 0.88 0.87 0.87 0.86 0.85 0.84 0.84 0.83 0.82 0.82 0.81 0.80 0.80 0.79 0.78 0.78 0.77 0.76 0.76 0.75 0.75 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.66 0.65 0.65

1.96 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.92 0.91 0.90 0.89 0.88 0.88 0.87 0.86 0.85 0.84 0.84 0.83 0.82 0.82 0.81 0.80 0.80 0.79 0.78 0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65

1.98 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.93 0.92 0.91 0.90 0.89 0.88 0.88 0.87 0.86 0.85 0.85 0.84 0.83 0.83 0.82 0.81 0.80 0.80 0.79 0.79 0.78 0.77 0.77 0.76 0.76 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66

2.00 1.00 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.93 0.92 0.91 0.90 0.89 0.88 0.88 0.87 0.86 0.85 0.85 0.84 0.83 0.83 0.82 0.81 0.81 0.80 0.79 0.79 0.78 0.78 0.77 0.76 0.76 0.75 0.75 0.74 0.74 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.68 0.67 0.67

2.02 1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.94 0.94 0.93 0.92 0.91 0.90 0.89 0.89 0.88 0.87 0.86 0.86 0.85 0.84 0.83 0.83 0.82 0.81 0.81 0.80 0.80 0.79 0.78 0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67

2.04 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.94 0.94 0.93 0.92 0.91 0.90 0.89 0.89 0.88 0.87 0.86 0.86 0.85 0.84 0.84 0.83 0.82 0.82 0.81 0.80 0.80 0.79 0.78 0.78 0.77 0.77 0.76 0.76 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68

2.06 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.94 0.94 0.93 0.92 0.91 0.90 0.90 0.89 0.88 0.87 0.87 0.86 0.85 0.84 0.84 0.83 0.82 0.82 0.81 0.80 0.80 0.79 0.79 0.78 0.77 0.77 0.76 0.76 0.75 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.69

2.08 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.95 0.94 0.93 0.92 0.91 0.90 0.90 0.89 0.88 0.87 0.87 0.86 0.85 0.85 0.84 0.83 0.83 0.82 0.81 0.81 0.80 0.79 0.79 0.78 0.78 0.77 0.76 0.76 0.75 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69

2.10 1.05 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.95 0.94 0.93 0.92 0.91 0.91 0.90 0.89 0.88 0.88 0.87 0.86 0.85 0.85 0.84 0.83 0.83 0.82 0.81 0.81 0.80 0.80 0.79 0.78 0.78 0.77 0.77 0.76 0.76 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.70

2.12 1.06 1.05 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.95 0.94 0.93 0.92 0.91 0.91 0.90 0.89 0.88 0.88 0.87 0.86 0.85 0.85 0.84 0.83 0.83 0.82 0.82 0.81 0.80 0.80 0.79 0.79 0.78 0.77 0.77 0.76 0.76 0.75 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71 0.71

2.14 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.96 0.95 0.94 0.93 0.92 0.91 0.91 0.90 0.89 0.88 0.88 0.87 0.86 0.86 0.85 0.84 0.84 0.83 0.82 0.82 0.81 0.80 0.80 0.79 0.79 0.78 0.78 0.77 0.76 0.76 0.75 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71

2.16 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.96 0.95 0.94 0.93 0.92 0.92 0.91 0.90 0.89 0.89 0.88 0.87 0.86 0.86 0.85 0.84 0.84 0.83 0.82 0.82 0.81 0.81 0.80 0.79 0.79 0.78 0.78 0.77 0.77 0.76 0.76 0.75 0.74 0.74 0.73 0.73 0.72 0.72

2.18 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.96 0.95 0.94 0.93 0.92 0.92 0.91 0.90 0.89 0.89 0.88 0.87 0.87 0.86 0.85 0.84 0.84 0.83 0.83 0.82 0.81 0.81 0.80 0.80 0.79 0.78 0.78 0.77 0.77 0.76 0.76 0.75 0.75 0.74 0.74 0.73 0.73

2.20 1.10 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.96 0.95 0.94 0.93 0.92 0.92 0.91 0.90 0.89 0.89 0.88 0.87 0.87 0.86 0.85 0.85 0.84 0.83 0.83 0.82 0.81 0.81 0.80 0.80 0.79 0.79 0.78 0.77 0.77 0.76 0.76 0.75 0.75 0.74 0.74 0.73

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