Integumentary Perfections Curtis Baade Shamara Manora Agenda 1. - - PowerPoint PPT Presentation

Integumentary Perfections

Curtis Baade Shamara Manora

Agenda

• 1. The Skin
• 1. The Skin
• 1. The Skin
• 1. The Skin
• 2. Pro
• 2. Product Design

uct Design

• 2. Pro
• 2. Product Design

uct Design

• 3. Eco
• 3. Economic Analysis
• mic Analysis
• 3. Eco
• 3. Economic Analysis
• mic Analysis
• 4. Co
• 4. Conclusions

nclusions

• 4. Co
• 4. Conclusions

nclusions

The Skin

Skin Layers

The Skin The Skin

Semi-permeable barrier between body and environment Contains three layers: epidermis, dermis and subcutaneous

Source: http: Source: http://cancer.heal //cancer.healthcentersonli thcentersonline.com/skincancer/basalcellca e.com/skincancer/basalcellcarcinoma.cfm cinoma.cfm

Epidermis Epidermis

The outermost layer of the epidermis is the stratum corneum

Approximately 20 cell layers thick Location in which desquamation occurs

Desquamation is the shedding

• f the top layer of cells in the

stratum corneum Approximately 1 layer per day is released

Source Source: www.euce : www.eucerim.co.uk im.co.uk

Stratum Corneum Stratum Corneum

Contains hydrophilic cells (keratinocytes) surrounded by a hydrophobic lipid bilayer (lipid lamellae) Contains natural moisturizing factors (NMF) which are responsible for the absorption and retention of water.

www.ce www.cerave rave.com/barrie

• m/barrier.htm

tm

Effects on Skin Barrier Effects on Skin Barrier

Reduced or low water content in the Stratum Corneum results in a compromised barrier (chapping) This compromised barrier must be restored in order to prevent transepidermal water loss Compromised Barrier Compromised Barrier Intact Barrier Intact Barrier

Source Source: http: : http://www.cetaphil //www.cetaphil.com.au/ .com.au/importance_ portance_of_your_ski f_your_skin_more n_more.asp .asp

The Skin

Skin Disorders

Xerosis (Dry Skin)

Natural moisturizers Stratum Corneum are removed Caused by overexposure to water, sun, or cold weather Symptoms include dry, itchy skin

Source Source: Uni : University of Cal ersity of California, San F fornia, San Fransico, www.uscf ansico, www.uscf.e .edu du

Ichthyosis Vulgaris

Incurable, genetic disorder affecting production and/or desquamation of cells

Caused by

low water content in Stratum Corneum enzymatic reactions controlling desquamation are inhibited

Symptoms include dry, thickened, scaly skin

Source Source: Gen : Geneva Foundation for Me va Foundation for Medi dica cal Education and Research, www.gfmer.ch l Education and Research, www.gfmer.ch

The Skin

Treatment Therapy

Treatment Strategy Treatment Strategy

Three key steps to effectively effectively treat the disorders

Promote desquamation Deliver moisturizing agents to underlying skin Restore the skin’s lipid bilayer

Transdermal Diffusion

Percutaneous absorption mostly occurs via transcellular diffusion (Pathway 2) Other pathways are

Intercellular diffusion (Pathway 1) Diffusion through skin appendages (Pathway 2)

keratinocytes lipid lamellae appendage (follicle or sweat duct) 1 2 3

Source: A Geoscience Source: A Geoscience Approa Approach to M ch to Modeling Chemical deling Chemical Tra Transport Through the Skin sport Through the Skin

Moisturizer Formulation Moisturizer Formulation

The simplest vehicle for skin moisturizers are emulsions For lotions, oil-in-water emulsions are used

Water is the continuous phase Oil is the dispersed phase

Source: http: Source: http://www.pg.com/scie //www.pg.com/science/skinc nce/skincare/Skin_tws_101.htm re/Skin_tws_101.htm

Lotion Composition Lotion Composition

Lotions have active and inactive ingredients Ingredients are characterized by a combination of properties (e.g. effectiveness, smoothness, thickness, etc.)

Product Design

Lotion Composition

Product Regulations Product Regulations

Since skin moisturizers are considered cosmetic products, they do not have to adhere to FDA regulations Cosmetics are subject to restrictions on the concentration of certain ingredients determined by the Cosmetic Ingredient Review

Source Source: http : http: www.cfsan.f www.cfsan.fda.gov/~dms/cos-206 a.gov/~dms/cos-206.html

Lotion Composition

Replenish Skin’s Health Replenish Skin’s Health

HUMECTANTS EXFOLIANTS OCCLUSIVES EMOLLIENTS

Lotion Composition

Ot Other Lotion Prop r Lotion Propert erties es

SOLVENTS PRESERVATIVES THICKENERS FRAGRANCE BUFFERS EMULSIFIER COLOR

Product Design

Customer Satisfaction Assessment

Consumer Satisfaction Assessment Consumer Satisfaction Assessment

A model was developed to assess the consumer needs The model measures how satisfied the consumer is with the properties of the lotion Consumer rates lotion characteristics correlated to a physical properties

) 100 ( ) 1 ( ) 100 ( − = − = − = = ∑

• n

satisfacti property y property

• f

weight w

• n

satisfacti S y w S

i i i i i i

Source Source: http : http://ww //www.ou.

• u.edu/class/ch

/class/che-design/a-d esign/a-design/Pricing%2 sign/Pricing%20of%20Consume 0of%20Consumer%20Products. r%20Products.pdf

Consumer Surveys Consumer Surveys

Consumer surveys were used to determine the satisfaction

• f the consumer for each

property The consumers rated the lotion properties based upon extremes (i.e. very thin to very thick) Consumer ratings were then correlated to the physical properties of the lotion (surface tension, viscosity, etc.) to find consumer satisfaction

Consumer Satisfaction Assessment Consumer Satisfaction Assessment

Ordained surveys were completed to determine the best product and the importance of each property.

Please indicate your preference preference for each property on the indicated scale (S (Scale of

• f 1-X)

X). With 1 being your desired desired product, and the highest number (X) being your worst worst product. ______________________________________________________________________ ______________________________________________________________________

Thickness: Thickness: Thickness of the Lotion (Scale of 1-4) (Scale of 1-4) Extremely Thick:___ ___ Moderately Thick:___ ___ Moderately Thin:___ ___ Very Thin:___ ___ Durabil Durability: The ability for the lotion to wash off or rub off. The Lotion lasts for…(Scal (Scale of 1-7)

• f 1-7)

30 minutes:___ ___ 1hr:___ ___ 2hrs:___ ___ 3hrs:___ ___ 4hrs:___ ___ 5 hrs:___ ___ 6hrs:___ ___ Absorpti Absorption Rate:

• n Rate: How long it takes the moisturizing chemicals to officially absorb into the skin (Scale of 1-7)

(Scale of 1-7) 1min:___ ___ 2min:___ ___ 4min:___ ___ 5min:___ ___ 6min:___ ___ 8min:___ ___ 10min:___ ___

Survey Results Survey Results

Prop Property erty Weight of Property Weight of Property Effectiveness 24.36% Thickness 10.16% Durability 15.19% Absorption Rate 13.92% Smoothness 14.61% Greasiness 11.44% Spreadability 10.31%

Study Population: 48 Males, 50 Females, 2 Not Specified, Total = 100

Product Design

Property Correlations

Assessed Lotion Properties Assessed Lotion Properties

Text Text Text Text Thickness Effectiveness Durability Absorption Rate Spreadability Greasiness Smoothness Percutaneous Absorption of Ingredients Apparent Viscosity How easy lotion can be removed from skin Diffusion Time Skin Appearance and Feel Skin Appearance and Feel Spontaneity of the lotion to spread across the skin

Effectiveness

The effectiveness of a lotion is determined by how well the lotion can treat the skin problems associated with Xerosis and Ichthyosis Vulgaris.

Severely dry skin Thickened skin Dismantled lipid bilayer

Depends on percutaneous absorption modeled by

∑

∞ = −

⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ − − =

1

2 2 2

sin 1 2 1

n L R t n D sc sc

• w

w

sc sc sc

e L x n n L x C C

π

π π

Effectiveness Effectiveness

Amount of Active Ingredients vs. Skin Appearance y = -10x + 6 R2 = 1 1 2 3 4 5 0.1 0.2 0.3 0.4 0.5 Relative Concentration (C/Cw) Consumer Rating

Consu Consumer R Rating ting 1 No Skin Scales Present 2 Few Skin Scales Present 3 Some Skin Scales Present 4 Skin Moderately Scaly 5 Skin Very Scaly

Consumer Preferences: Adjusted Effectiveness

y = -0.2282x + 1.2699 R2 = 0.9914 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 1 2 3 4 5 Consumer Rating Consumer Satisfaction

Best Product: Best Product: Preference (1), Concentration (0.5)

Wetting

Wetting is an application of adsorption at a liquid-solid interface. Wetting is defined as the displacement of one fluid by another on a given surface. Durability and Spreadability depend on wetting properties For solid surfaces, like the skin, the contact angle of the liquid must determined using Young’s Equation

Source: The Handbook of Cosmetic S urce: The Handbook of Cosmetic Scien ience and Technolo e and Technology gy Ima Image Provided From: The Water Break Test e Provided From: The Water Break Test

angle contact emulsion

• f

tension surface skin

• f

tension surface emulsion skin

• f

tension surface

e s se e s se

= = = − = − = θ γ γ γ θ γ γ γ cos

Durability Durability

Durability is how easily the lotion rubs or washes off and depends on adhesional wetting The adhesional wetting is the ability of a fluid to adhere to a surface The adhesional wetting is quantified by the work of adhesion, Wa The work of adhesion is the reversible work required to separate the unit area of liquid from a surface

emulsion

• f

tension surface angle contact W

e e a

= = + = γ θ θ γ ) 1 (cos

Source Source: Surf : Surfactants and Interfacial Phenomena actants and Interfacial Phenomena

Durability Durability

Contact Angle vs. Durability

y = 0.0708x3 - 0.3338x2 + 0.0315x + 0.9996 R2 = 1

• 0.2

0.2 0.4 0.6 0.8 1 1.2 0.5 1 1.5 2 2.5 3 3.5 Contact Angle (Rad) Consum er Rating: Durability

4hrs 5 3 hrs 4 5hrs 6 Consu Consumer R Rating ting 1 30 min 2 1 hr 3 2 hrs 7 6hrs Consumer Preferences: Adjusted Durability

y = 0.3725Ln(x) + 0.2799 R2 = 0.9874 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00% 1 2 3 4 5 6 7 Consumer Rating: Durability Consumer Satisfaction

Best Product: Best Product: Preference (7), Contact Angle (0o)

Spreadability Spreadability

Spreadability is characterized by how easily the lotion spreads over the skin and depends on spreading wetting Spreading wetting is how well one fluid displaces another fluid on a given surface (The two fluids are air and lotion) and if the spreading is spontaneous Spontaneity depends on the free energy, the interfacial area and the surface tension The Spreading coefficient identifies the spontaneity of a fluid to spread

emulsion

• f

tension surface skin

• f

tension surface emulsion skin

• f

tension surface S

e s se e se s se

= = − = + − = γ γ γ γ γ γ ) (

Source Source: Comparison of surface f : Comparison of surface free en ee ener ergy gy bet between een r reco construc tructed ep epid iderm ermis an and in in s situ h human s skin in

Spreadability Spreadability

75% Spreading 5 93% Spreading 6 Consu Consumer R Rating ting 1 0% Spreading 2 7% Spreading 3 25% Spreading 4 50% Spreading 7 100% Spreading Consumer Preference vs. Contact Angle

y = -1.9099x + 7 R2 = 1 1 2 3 4 5 6 7 8 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 Contact Angle (Rad) Consumer Rating: Spreadability Consumer Preferences: Adjusted Spreadability y = 0.0025x4 - 0.0412x3 + 0.1875x2 - 0.1107x + 0.4399 R2 = 0.9996 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 1 2 3 4 5 6 7 Consumer Rating Consumer Satisfaction (%)

Best Product: Best Product: Preference (4.5), Contact Angle (72o)

Thickness Thickness

( )

( ) ( ) ( ) ( )( )

( )

phase continuous

• f

ity vis phase dispersed

• f

ity vis fraction volume the I cos / cos 3 / 1 ^ 1 1 10 1 25 1 10 1 4 11 84 10 4 5 . 5

7 3 4 3 10 7 2 7

= = − − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − − − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + = κ λ λ λ κ λ λ λ λ κ λ λ λ

Thickness is the viscosity and shear rate of the lotion Shear rate can be related to film thickness

( )

phase dispersed

• f

fraction volume I = + = φ φ λ η 1

Source Source: Evaluation of the : Evaluation of theoretical viscosity mode retical viscosity models ls for concentra for concentrated emulsions ed emulsions at low capil at low capillary number ary numbers

Viscosity vs. Shear Rate 1 10 100 1000 10000 0.0001 0.001 0.01 0.1 1 10 100 1000 Shear Rate (1/s) Visocosity (Poise)

thickness film the is dy velocity in change the is dv rate shear the is D where dy dv D =

Thickness Thickness

Shear Rate vs. Film Thickness

0.01 0.1 1 10 0.001 0.01 0.1 1 Film Thickness (cm) Shear Rate (1/s) Film Thickness vs. Thickness Perception 1 2 3 4 0.001 0.01 0.1 1

Film Thickness (cm) Consumer Rating (Thickness Perception)

Consu Consumer R Rating ting 1 Extremely Thick 2 Moderately Thick 3 Moderately Thin 4 Very Thin Consumer Preferences: Adjusted Thickness

y = 0.0733x3 - 0.8218x2 + 2.5355x - 1.3704 R2 = 1 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 1 2 3 4 Consumer Rating Consumer Satisfaction

Best Product: Best Product: Preference (2.3), Film Thickness (0.25cm)

Viscosity ity v. Sh

• v. Shear

ear Rate: h Rate: http:// ttp://www.rh .rheologysch choo

• ol.co

l.com

Smoothness Smoothness

Smoothness is based on how the skin feels after the lotion is applied. The skin becomes rough and chapped when the moisture level of the skin is below 10%. Smoothness is based on the amount of fatty oils present in the lotion. Smoothness is a function of the greasiness of the

• lotion. This correlation was found experimentally.
• ils

fatty

• f

ion concentrat the is G t coefficien friction skin the is smoothness the is S where G S 236 . ) 098 . 2 0174 . ( = + − = µ µ

Smoothness Smoothness

Consu Consumer R Rating ting 1 Very Smooth 2 Moderately Smooth 3 Moderately Rough 4 Very Rough

Consumer Rating vs. Smoothness

y = 246.98x5.5336 R2 = 0.9917 1 2 3 4 0.35 0.37 0.39 0.41 0.43 0.45 0.47 0.49 Smoothness Consum er Rating

Consumer Preferences: Adjusted Smoothness

y = -0.0514x2 - 0.0613x + 1.1276 R2 = 0.9916 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 1 2 3 4

Best Product: Best Product: Preference (1), Smoothness (0.37)

Absorption Rate Absorption Rate

The Absorption Rate is how long it takes the ingredients to absorb into the skin and is characterized by the steady state intercellular diffusion time

sc sc SC ss

D R L t

2

45 . =

surface the from corneum stratum to in nce dista L continuum corneum stratum phase the

• f

factor n retardatio R continuum corneum stratum phase

• f

t coefficien diffusion effective D time S S Diffusion t

sc sc sc ss

= − = − = = 3 3 .

Source: A Geoscience Source: A Geoscience Approach to Mode Approach to Modeling Chemical Tran ling Chemical Transport t sport throu rough Skin h Skin

Absorption Rate Absorption Rate

6min 5 5min 4 8min 6 Consu Consumer R Rating ting 1 1min 2 2min 3 4min 7 10min Consumer Preferences: Adjusted Absorption Rate

y = 0.0026x3 - 0.0449x2 + 0.1008x + 0.943 R2 = 0.9927 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00% 2 4 6 8 10 12 Absorption Rate (min) Consumer Satisfaction

Best Product: Best Product: Absorption Rate (1min-2min)

Greasiness Greasiness

The greasiness is characterized by the look/feel of the skin after the lotion is applied The greasiness can be determined by the amount of fatty oils present in the lotion Fatty oils leave the skin looking greasy/oily because of its high concentration of triglycerides or fatty acids If a lotion is too greasy the stratum corneum can become swollen and inflamed If the lotion does not have enough oils, the skin can remain rough and chapped.

Amount of Oils vs. Greasiness

y = -0.0003x3 + 0.016x2 - 0.3933x + 5.6 R2 = 1 1 2 3 4 5 10 15 20 25 30 35 Percentage of Fatty Oils Consumer Rating

Greasiness Greasiness

Very Dry 4 Consu Consumer R Rating ting 1 Very Greasy 2 Moderately Greasy 3 Moderately Dry

Consumer Preferences: Adjusted Greasiness y = -0.3122x2 + 1.6109x - 1.0568 R2 = 0.9936 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 1 2 3 4 Consumer Ratings Consumer Satisfaction

Best Product: Best Product: Preference (2.8), Greasiness (13% Fatty Oils)

Maximum Satisfaction Product Maximum Satisfaction Product

Lotion Lotion Prop Property erty Satisfaction Satisfaction Score Score Durability 87% Greasiness 95% Smoothness 74% Thickness 95% Effectiveness 100% Spreadability 99% Absorption Rate 82%

Product Satisfaction: 81% Product Satisfaction: 81% Competitor Satisfaction: 77% Competitor Satisfaction: 77% β= NPW= = NPW=

Product Design

Manufacturing

Manufacturing Procedure Manufacturing Procedure

Two separate phases make up lotion: aqueous and oil phases Must completely combine two phases Steps in lotion formation:

1) Heat and mix aqueous and oil phases separately 2) Combine both phases into one batch 3) Perform post treatment modifications (i.e. decrease particle size)

Process Flow Diagram Process Flow Diagram

Equipment Costs Equipment Costs

Equipment Equipment Cost Cost Storage Tanks $10,000 Water Phase Mixing Tank $8,000 Oil Phase Mixing Tank $4,000 Bath Sonicator $60,000 Homogenizer $11,000 2 Pumps $11,500 Colloid Mill $25,000 Total Cost Total Cost $129,500 $129,500

Source Source: Vari : Various Ven

• us Vendors
• rs

Plant Location Plant Location

Buckeye, AZ

37 miles from Phoenix, AZ Population: 25,406 Located within the southwest market Inexpensive property value High Productivity Low Labor costs

Source Source: http : http://ww //www.rlmart rlmartin.com/ in.com/phot photos/scenic/a s/scenic/ari rizo zona/d na/default. efault.htm tm

Competition Model Competition Model

( )

ρ ρ ρ

β α

1 1 2 1 1 1 2 1

d p d p Y p p d

−

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

2 1 1 2

p d p Y d − =

( ) ( )

ρ ρ

β α

2 1

d d S + =

2 1

d d D + = γ + = 1

1

D d

1 −

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

ρ ρ

β α γ Unsaturated Market

2 1

d d D + > Saturated Market

( ) 1

1 1 1

d a p profit − =

Target Market Target Market

91 Million People 14 Million People Affected 364 Thousand People with IV 1.5 Million People will buy Lotion 6 Million Bottles per year 500 Thousand Bottles per month

D Y

.5 * 500,000 * 12.13 $3,000,000 per month

Beta and TPC Beta and TPC

H2 = .75 = .75 H1max

max = .91

= .91

Beta Beta TPC TPC .82 $4.30/bottle .85 $4.80/bottle .9 $5.00/bottle .95 $5.50/bottle 1 $5.50/bottle

Summary of Parameters Summary of Parameters

15 $ 8 $ 13 . 12 $ 75 . 1 000 , 000 , 3 000 , 500

1 2

→ = = = = ≈ = p p Y D ρ α

Beta Beta TPC (a TPC (a1) .82 $4.30/bottle .85 $4.80/bottle .9 $5.00/bottle .95 $5.50/bottle 1 $5.50/bottle

Constant Prices Constant Prices

Price Response Price Response

( )

ρ ρ ρ

β α

1 1 2 1 1 1 2 1

d p d p Y p p d

−

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

2 1 1 2

p d p Y d − =

( ) ( )

1 1 1 1

d a p profit Max − =

( ) ( )

ρ ρ

β α

2 1

d d S + =

2 1

d d D + = γ + = 1

1

D d

1 −

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

ρ ρ

β α γ

Unsaturated Market

2 1

d d D + >

Saturated Market

( )

2 1

, 2 2 , 2 2 , 2 , 2 2 α α

β ϕ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − − =

• d

d d a p p p

Price Changes

1 2 3 4 5 6 7 8 9 10 10 11 11 12 12 Our price p1 p1 p2 p2 p3 p3 p4 p4 p5 p5 p6 p6 Their price p1 p2 p2 p3 p3 p4 p4 p5 p5 p6 p6 p7

Summary of Parameters Summary of Parameters

20 $ 7 $ 15 $ 8 $ 7 $ 13 . 12 $ 75 . 1 000 , 000 , 3 000 , 500

max 1 1 2 2

→ = → = = = = = ≈ =

p i

p p a p Y D ρ α

Beta Beta TPC (a TPC (a1) .82 $4.30/bottle .85 $4.80/bottle .9 $5.00/bottle .95 $5.50/bottle 1 $5.50/bottle

NPW NPW

Price Response Price Response

( )

ρ ρ ρ

β α

1 1 2 1 1 1 2 1

d p d p Y p p d

−

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

2 1 1 2

p d p Y d − =

( ) ( )

1 1 1 1

d a p profit Max − =

( ) ( )

ρ ρ

β α

2 1

d d S + =

2 1

d d D + = γ + = 1

1

D d

1 −

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

ρ ρ

β α γ

Unsaturated Market

2 1

d d D + >

Saturated Market

( ) ( )

2 2 2 2

d a p profit Max ′ − =

Price Changes

( )

ρ ρ ρ

β α

′ ′ − ′

′ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ′ − ′ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ′ ′ = ′

1 1 2 1 1 1 2 1

d p d p Y p p d

2 1 1 2

p d p Y d ′ − ′ = ′

2 1

d d D ′ + ′ > ′

Summary of Parameters Perfect Information Summary of Parameters Perfect Information

20 $ 7 $ 15 $ 8 $ 7 $ 20 $ 7 $ 13 . 12 $ 75 . 1 000 , 000 , 3 000 , 500

max 1 1 2 max 2 2

→ = → = = → = = = = ≈ =

p i p i

p p a p p Y D ρ α

Beta Beta TPC (a TPC (a1) .82 $4.30/bottle .85 $4.80/bottle .9 $5.00/bottle .95 $5.50/bottle 1 $5.50/bottle

NPW with Perfect Information NPW with Perfect Information

Summary of Parameters Imperfect Information Summary of Parameters Imperfect Information

7 $ 20 $ 7 $ 20 $ 7 $ 15 $ 8 $ 13 . 12 $ 75 . 1

2 max 1 max 2 1 2

= → = → = → = = = = a p p p p

p p i i

ρ α

Beta Beta TPC (a TPC (a1) .82 $4.30/bottle .85 $4.80/bottle .9 $5.00/bottle .95 $5.50/bottle 1 $5.50/bottle

000 , 000 , 3 $ 000 , 500 ≈ = Y D 000 , 600 , 3 $ 000 , 600 ≈ ′ = ′ Y D

NPW with Imperfect Information NPW with Imperfect Information

NPW with Imperfect Information NPW with Imperfect Information

Thanks for your time!

Any Question?