Hydrogen Market Penetration: Further Refinements on the Strategy for Research

HYDROGEN MARKET P E N E T R A T I O N :

FURTHER R E F I N E M E N T S ON T H E STRATEGY FOR RESEARCH Jean-Pierre P o n s s a r d

September 1 9 7 4

R e s e a r c h M e m o r a n d a a r e informal p u b l i c a t i o n s r e l a t i n g t o ongoing o r projected areas of re- search a t I I A S A . T h e v i e w s expressed a r e t h o s e of t h e a u t h o r , and do n o t n e c e s s a r i l y r e f l e c t t h o s e of I I A S A .

Hydrogen Market P e n e t r a t i o n :

F u r t h e r R e f i n e m e n t s on t h e S t r a t e g y f o r R e s e a r c h J e a n - P i e r r e P o n s s a r d *

1. I n t r o d u c t i o n

A t i t s e a r l y s t a g e a r e s e a r c h and d e v e l o p m e n t program i s a r i s k y v e n t u r e . Numerous a l t e r n a t i v e a p p r o a c h e s h a v e t o b e t e s t e d i n o r d e r t o d e t e r m i n e a s u c c e s s f u l o n e , i f a n y . C l e a r - l y e n t h u s i a s m and e v e n s t u b b o r n n e s s w i l l p l a y a s i g n i f i c a n t r o l e , h u t economic c o n s i d e r a t i o n s may a l s o h e l p t o e f f i c i e n t l y a l l o c a t e t h e e f f o r t , a n d , i n p a r t i c u l a r , t o s p e c i f y a somewhat

" r e a s o n a b l e " t i m e - c o s t t r a d e o f f f o r t h e c o m p l e t i o n of t h e p r o j - e c t . " R e a s o n a b l e " c a n o n l y b e p r o p e r l y d e f i n e d o n c e t h e main f e a t u r e s of t h e s i t u a t i o n h a v e b e e n q u a n t i f i e d a n d r e l a t e d t o e a c h o t h e r w i t h i n a model. Then l o g i c a l a n a l y s i s o f t h e model

may be u s e d t o p r o v i d e g u i d e l i n e s f o r a c t i o n . 1 The o b j e c t i v e o f t h i s p a p e r i s t o b r i e f l y r e v i e w t h e a n a l - ^I y s i s of a s a m p l i n g p r o c e s s which a p p e a r s t o b e u s e d as a model

i

i n t h e r e s e a r c h and d e v e l o p m e n t l i t e r a t u r e (see Manne-Marchetti

I

[ 3 ] and a l s o S c h e r e r [5] )

.

T h i s s a m p l i n g p r o c e s s may b e s i m p l y d e s c r i b e d by a s e t of f i v e a s s u m p t i o n s :

( i ) e a c h a p p r o a c h w i l l e i t h e r r e s u l t i n t o a f a i l u r e ,

I

w i t h s u b j e c t i v e p r o b a b i l i t y p (0 < p < 1)

,

^{o r a}

*on l e a v e f r o m t h e C e n t r e d l E n s e i g n e m e n t s u p 6 r i e u r du Management P u b l i c , 94112, A r c u e i l , and from Groupe d e G e s t i o n d e s O r g a n i s a t i o n s E c o l e P o l y t e c h n i q u e , 75005, P a r i s , F r a n c e ; r e s e a r c h s c h o l a r a t t h e I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d S y s t e m s A n a l y s i s , L a x e n b u r g , A u s t r i a .

s u c c e s s , w i t h s u b j e c t i v e p r o b a b i l i t y 1

-

^{p ;}

( i i ) a l l a p p r o a c h e s a r e s t o c h a s t i c a l l y i n d e p e n d e n t ; ( i i i ) one o r more s u c c e s s f u l a p p r o a c h e s y i e l d a g l o b a l

b e n e f i t b ( t a k e n a s u n i t y ) ;

( i v ) a l l a p p r o a c h e s have t h e same c o s t c ( e x p r e s s e d i n p e r c e n t a g e o f t h e b e n e f i t ) ; and

( v ) a l l a p p r o a c h e s r e q u i r e t h e same amount of t i m e ( t a k e n a s u n i t y ) t o y i e l d any r e s u l t .

The r e v i e w of t h i s model w i l l be made a l o n g two l i n e s of i n - q u i r y : f i r s t , t h e c h o i c e of t h e d e c i s i o n c r i t e r i o n and i n p a r t i c u l a r t h e s i g n i f i c a n c e of r i s l c a v e r s i o n ; s e c o n d , t h e r o l e of d i s c o u n t i n g i n s e q u e n t i a l s a m p l i n g . The r e s u l t of t h e a n a l - y s i s w i l l show t h a t t h e o p t i m a l sample s i z e may v a r y w i d e l y i f t h e p a r a m e t e r s of t h e problem happen t o be i n a c e r t a i n r a n g e . T h i s w i l l c a l l f o r a v e r y c a r e f u l model s p e c i f i c a t i o n whenever it is s u s p e c t e d t h a t s u c h v a l u e s a r e r e l e v a n t .

B e f o r e ~ u r n i n g t o t h e a n a l y s i s l e t u s d e f i n e some n o t a t i o n . x = number of p a r a l l e l a p p r o a c h e s ,

i = d i s c o u n t r a t e between two s u c c e s s i v e p e r i o d s , i? = d i s c o u n t f a c t o r between two s u c c e s s i v e p e r i o d s

= l / ( l + i ) ,

p = p r o b a b i l i t y of f a i l u r e of any a p p r o a c h , q = p r o b a b i l i t y of s u c c e s s o f any a p p r o a c h ,

= 1

-

p ,

c = c o s t of any a p p r o a c h e x p r e s s e d i n p e r c e n t a g e of t h e g l o b a l b e n e f i t a s s o c i a t e d w i t h one o r more s u c c e s s f u l a p p r o a c h e s ,

pX =

overall probability of failure in one time period,

1

-

^{pX =}

probability that at least one approach is a suc-

cess in one time period,

f(x)

=

expected benefit in one time period,

=

1 -

pX

- ^{cx, and}

g(x)

=

discounted expected benefit with an infinite horizon

=

f (x)/(l - ^fJpX).

2.

The Choice of the Decision Criterion

In the last ten years, decision under uncertainty has been the object of a considerable amount of theoretical and empirical research (Raif f a

[4]

, Edwards [ l ]

)

. Whereas simple criteria such as maximization of expected benefit have been under critical scrutiny, behavioral considerations such as

"aversion towards risk" have led to the more general utility maximization theory.

In this section we wish to investigate the implications

of explicitly introducing risk considerations into the model. I ~

To somewhat enhance the results and simplify the analysis, we shall restrict our attention to the one time period decision problem. Now, is this decision problem a risky venture at all?

Let us pour out some numbers. The cost of one approach c may

be assumed small relative to the benefit, say c

=

,001. Under

any criteria one should not start more than 1000 approaches,

and by starting 100 one has used only 10% of the benefit asso-

ciated with success. Now if the probability of success of any

approach p is larger than .l, by starting 100 approaches the overall probability of success will be more than 1 - ^{(-9) 100}

%

- .99997! This is not what we would call a risky venture.

On the other hand if q is of the same order of magnitude as c, say 5c, this number would only be 1 - ^{(.995) loo}

^%

- .4. The prospect seems much dimmer and the attitude toward risk becomes cruclal. Should one use up 90% of the potential benefit to obtain what is left of it (a mere lo%, but this might still be a large sum of money) with a reasonable probability of success

(now 1 - ^(.995) 2 .989), or just forget about the whole matter? This is the question we wish to answer from a theoret- ical point of view. As

a

utility function for the benefit w expressed in money terms, we shall take

U(W)

=

(1 - e-PW)/p ,

in which

p

is a parameter related to the decision maker's risk aversion. Note that for

0 =

0, u(w)

=

w. It will be conven- ient to use as a reference point the certainty equivalent r of the lottery

(0

with probability 1/2 and I with probability 2 Then

p

and r are related by the following table:

As an illustration, if

p =

1.8, the decision maker would be

indifferent between receiving

(i) an amount r

= .3

with probability 1,

(ii) an amount

0

with probability 1/2 or 1 with probabil- ity 1/2.

Hence, the smaller r (or p) the more risk averse the decision maker. This class of utility functions is widely used in de- cision analysis. (This key underlying assumption is the following: Suppose that your present wealth is W. You are offered a risky venture that you are prepared to accept. Now if your present wealth were modified by a positive or negative amount AW, would you still be prepared to accept the venture?

If the answer is yes, whatever the value of AW, then it may be shown that the utility function belongs to the class described above.

Under the utility maximization assumption the decision problem becomes

Max [u (f (x)

I ]

x integer

probability utility probability utility - - [ ^of I.[ ^of I+[ ^of ].Irf ^]

failure - ^{cx success} - ^cx

After some manipulations this problem may be equivalently written as

Max

₍

-

^CX

- ^; 1 ^Log rp ^{x + e-"(1 -}

^pX)])

^.

x integer

The r e s u l t s a r e summarized i n T a b l e 1.

3 . The Role of D i s c o u n t i n g i n S e q u e n t i a l Sampling

I f s e q u e n t i a l sampling i s a l l o w e d , t h a t i s , w a i t i n g one t i m e p e r i o d t o s e e t h e r e s u l t s of t h e a p p r o a c h e s b e f o r e u n d e r - t a k i n g any new o n e s , t h e n t h e r e i s a b a s i c t r a d e o f f between t h e a r r i v a l d a t e of t h e f i r s t s u c c e s s and t h e amount o f R & D e x p e n d i t u r e s s p e n t i n p a r a l l e l a p p r o a c h e s . More p r e c i s e l y , s i n c e more t h a n one s u c c e s s i s r e d u n d a n t , e n g a g i n g i n t o p a r a l l e l a p p r o a c h e s m i g h t l e a d t o s p e n d i n g money u n n e c e s s a r i l y and n o t e n g a g i n g i n t o p a r a l l e l a p p r o a c h e s might l e a d t o a w a s t e of t i m e b e f o r e o b t a i n i n g t h e f i r s t s u c c e s s . T h i s t r a d e o f f i s

t h e o r e t i c a l l y r e s o l v e d by comparing f u t u r e s t r e a m s of money i n t e r m s of - t h e i r d i s c o u n t e d p r e s e n t v a l u e s (Koopmans [ 2 ] ) . A c o n s t a n t d i s c o u n t r a t e i s somehow e q u i v a l e n t t o a n i m p a t i e n t b e h a v i o r which d o e s n o t depend on t h e c u r r e n t w e a l t h o f t h e d e c i s i o n maker. The more i m p a t i e n t t h e l a r g e r t h e d i s c o u n t r a t e ( t h e s m a l l e r t h e d i s c o u n t f a c t o r )

.

I n t h i s s e c t i o n we want t o s t u d y n u m e r i c a l l y t h e relation^

s h i p between d i s c o u n t i n g and e x p e c t e d a r r i v a l d a t e of t h e f i r s t s u c c e s s w i t h i n t h e s a m p l i n g model d e s c r i b e d i n t h e i n t r o d u c t i o n .

T h i s problem may be f o r m u l a t e d a s f o l l o w s :

Max [g(x)]

x i n t e g e r

g ( x ) = (1

-

^pX

^-

c x ) / ( l

-

^{B ~ ~}

.

⁾

L e t x* be t h e o p t i m a l s i z e , t h e n t h e e x p e c t e d a r r i v a l d a t e of

t h e f i r s t s u c c e s s T* i s s u c h t h a t

x* x*

T* = l ( 1

-

p )

+

2 p X * ( 1

-

p ⁾

+

^--•

₊

_{n p} ^nx* ( 1

-

pX*)

+

^{- 9 .}

= 1/(1

-

pX*)

.

T h e n u m e r i c a l r e s u l t s a r e s u m m a r i z e d i n T a b l e 2 , a s s u m i n g c = -001 a n d p = .99.

T a b l e 2. Discounting in Sequential Sampling and Expected A r r i v a l Date of Success

R e f e r e n c e s

[I]

^{Edwards, W .} " B i b l i o g r a p h y : D e c i s i o n Making,"

E n g i n e e r i n g P s y c h o l o g y Group, U n i v e r s i t y o f M i c h i g a n , Ann A r b o r , M i c h i g a n , 1964.

[2] Koopmans, T.C. " S t a t i o n a r y O r d i n o l U t i l i t y a n d I m p a t i e n c e , " E c o n o m e t r i c a ,

28,

No. 2 ( 1 9 6 0 )

.

[3] Manne, A.S

.

a n d M a r c h e t t i , C

.

"Hydrogen: Mechanisms a n d S t r a t e g i e s o f Market P e n e t r a t i o n , " IIASA R e s e a r c h R e p o r t , RR-74-4, March 1974.

[4] R a i f f a , H . D e c i s i o n A n a l y s i s : I n t r o d u c t o r y L e c t u r e s o n C h o i c e s u n d e r U n c e r t a i n t y . Addison Wesley, 1968.

[5] S c h e r e r , F.M. "Time-Cost T r a d e o f f s i n U n c e r t a i n E m p i r i c a l R e s e a r c h P r o j e c t s

,"

N a v a l R e s e a r c h L o q i s t i c s Q u a r t e r l y , 12, No. 1 (March 1 9 6 6 ) .