Innovation announcement with vertical differentiation

JOURNALOF

EconomicBehavior & Organization

Journal of Economic Behavior and Organization Vol. 28 (1995) 399-408 ”

ELSEVIER

Innovation announcement with vertical differentiation Jim Y. Jin Science Center Berlin, Research Area N, Reichpietschufer

SO, 10785 Berlin, Germany

Received 10 January 1994; revised 10 August 1994

The paper studies the timing of innovation announcement in a vertically differentiated industry. The high quality firm introduces new products when they become profitable. The

new products can be announced quality firm knows the outcome announcement policy, however, the distribution of innovation competition. incompatible

It is shown that an early announcement with the interest of the innovative firm.

JEL classification: Keywords:

early or late. Under an early announcement policy the low of innovation when choosing its own quality. Under a late the low quality firm can only choose its quality based on outcomes. The quality decisions are followed by price policy

is socially

desirable

but

D82; L15

Vertical differentiation; Quality-price game; Innovation announcement

1. Introduction The paper studies the timing of innovation announcement in a vertically differentiated industry. The high quality firm improves its product quality. An early announcement allows the low quality firm to upgrade its quality according to the outcome of the high quality firm’s innovation. If the innovative firm delays the announcement, however the low quality firm can only adjust its quality based on its expectations. It is shown that a late announcement policy increases the innovative firm’s expected profit, but decreases the expected consumers surplus 0167-2681/95/$09.50

0 1995 Elsevier Science B.V. AI1 rights reserved

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J.Y. Jin / J. of Economic Behavior & Org. 28 (1995) 399-408

and social welfare. Hence the early announcement policy is socially desirable but not self-enforcing. In the contemporary economy firms constantly raise product qualities. The pace of quality improvement is often random even if the R&D expenditure is fixed. New products need to be introduced into the market. Empirical studies have shown that product innovation announcement generally increases firms’ stock values (Chancy et al., 1991). As marketing is concerned, early announcement gives the product more access to consumers and increases its demand. Nevertheless, not all firms announce new products as soon as they can. Among other considerations, a usual concern is competition from rivals (Eliashberg and Robertson, 1988). Given this conflict, innovative firms may announce new products early or late. In this paper we consider the cases where a firm commits to an early or a late announcement policy in a quality-price game. An early announcement policy allows the rival to adjust its quality with the knowledge of the outcome of innovation. A late announcement policy, however, only allows the low quality firm to know the innovative firm’s quality before price setting, but not before quality setting. The commitment to an announcement policy could be enforced by the market, instead of an institution such as a trade association. For instance, under late announcement more intensive market promotion is needed. It requires a marketing strategy different from one under early announcement. Changing marketing strategies is costly. An irregular announcement policy also causes unnecessary speculation in the stock market and makes a firm’s stock riskier. Thus, a firm should have an incentive to stick to a consistent announcement policy. The innovative firm either announces its innovation early or late. The timing of the announcement chosen by the innovative firm may not be in the best interest of consumers and the society. There can be a policy concern whether to encourage or discourage early announcement of product innovation. The problem of committed announcement comes close to the information sharing literature (Novshek and Sonnenschein, 1982; Vives, 1984; Gal-Or, 1985; Gal-Or, 1986; Li, 1985; Sakai, 1985). In these models firms commit to information sharing through a trade association. It has been shown that firms with substitute products have incentives to reveal common or private demand uncertainty before price competition, but no incentive to reveal private cost uncertainty. Information sharing before quality setting has not been studied. The previous results have little to say. It is not clear whether innovation uncertainty should be characterized as demand or cost uncertainty, and common or private uncertainty. Directly it only affects one firm’s cost function, as we will see, but indirectly it affects both firms’ demand. One crucial factor determining information sharing incentives in the previous models is whether firms’ reaction curves are downward or upward sloping. It does not apply to our case. In fact the low quality firm’s reaction curve is upward sloping but the high quality firm’s reaction curve is flat. These features make information exchange before quality decisions an interesting question.

J. Y. Jin /J. of Economic Behavior & Org. 28 (I 995) 399-408

401

The next section introduces the model. Section 3 solves the quality-price game. Section 4 evaluates the impact of early and late announcement policies on profits. Section 5 examines the welfare effect. The last section concludes the paper. 2. The model We consider a two stage quality-price game in a vertically differentiated industry. Before the game starts, the innovative firm commits to an early announcement policy or a late announcement policy. In the first stage the product innovation is realized and announced if so decided at the beginning. Then firms choose qualities. In the second stage firms set prices knowing qualities. We will evaluate firms’ expected profits and the social welfare under early and late announcement policies to see which policy will be chosen and whether it is socially optimal. Our vertical differentiation model follows Gabszewicz and Thisse (19791, Shaked and Sutton (19821, particularly Tirole (1989). There are two firms. Firm 1 produces the high quality product and firm 2 produces the low quality product. Let vi be firm i’s quality and pi be its price, we have vi > v2. Infinite number of consumers are indexed by 8, which is evenly distributed within [O,l]. Consumer 8 gains surplus 8vi - pi when he purchases a product from firm i. A higher value of 8 represents a higher preference on the quality. Each consumer purchases at most one product. No purchase occurs if the surplus is negative. Firms’ marginal costs are constant in quantities but increasing in qualities. When firms choose qualities, the marginal costs are also determined. Firm l’s marginal cost ci(vi) = (Yvi (a < 1) for vi I v and ci(vi) > vi for vi > v. Without innovation R&D, v keeps its initial value v’. With R&D the value of v stochastically increases. The value of v is realized before firms choose qualities. A higher v enables firm 1 to produce a higher quality product with a marginal cost LYvl. We need not specify the distribution of v, only assume that it is a common knowledge. Firm 2 can copy firm l’s technology from the existing products by reversed engineering. When it chooses its quality, it has the same cost function as firm 1 does up to v’. Thus, its cost function can be written as c,(v,) = ov2 for v2 I v” and c,(v,> > v2 for v2 > v’. In the quality setting game, only the linear cost function ci(vi> = CY vi is relevant. Firms will never choose qualities beyond the domain of the linear function. When firm 1 chooses vi > v, it bears a marginal cost c1 > vi. If firm 1 can make a non-negative profit, i.e. pi 2 cl, one has pi > vl. It implies 8v, - pi < 0 for all 8. So firm 1 can not sell any product. Similarly, if firm 2 chooses v2 > v”, then c2 > v2. We have p2 > v2 and Bv, - p2 < 0. Firm 2 can sell nothing. Thus firm 1 would never choose a quality higher than v and firm 2 would never choose a quality higher than v’. To ensure an interior solution, assume that v” is sufficiently high so that in equilibrium it is not a binding constraint for firm 2.

J.Y. Jin /J. of Economic Behavior & Org. 28 (1995) 399-408

402

If early announcement is committed, both firms know v while choosing qualities. Under a late announcement policy, though, the quality setting game is played with asymmetric information. However, under either early or late announcement, qualities are commonly known when firms set prices.

3. Quality-price equilibrium Let us start with the last stage price game. A consumer

8 prefenrs_fitntn l’s 1 1 product to firm 2’s if and only if Bv, - pi > Ov, - p2, i.e. 8 > 8’ = ;. He VI

-

v7

gets a positive surplus from firm 2’s product if and only if Bv, - p2 > 6, or 6 > 8” = I?.

If firm 2 can sell any product,

there must exist some

13> 0 such that

v2 8~2 > p2 and f3v, - p2 > Ov, - pi. These two inequalities imply 13’> 8”. Hence consumers with c92 0’ purchase from firm 1, consumers with 0 E [ 6”, 13’) purchase from firm 2 and those with 19< 13” buy nothing. Thus the demand functions for firm 1 and firm 2 are

x,+!KE,

x2=--Vl

Substituting

-

vz

the demand

Pl - P2

P2

Vl

v2

(1)

-v2

and marginal

.

costs ci = (Yvi into profit

functions

xi(pi - ci), we get rzT1= (I-~)(p,-av,)and~2=(~-~)(p2 - (Yv2). One can solve the Nash equilibrium 2( 1 + oL)Vi - (2 - cX)v2 ) Pl = Vl

4v,

- v2

p =V2(I+3a)v,-v2 2 4v, - v2

These price strategies imply the following

nTTI=4(I-o)

2 (v1 - v21v: (4v,_v,2) ’

prices as

equilibrium

572=(1-a)

(2)

.

profits

2 (vi - v2)v1v2 (4v,_vz) .

(3)

The high quality firm makes a higher profit (not include the cost of innovation). an1 Both firms’ profits are decreasing in (Y. One can check that r > 0 and 1

a7r2 c > 0. Both profits rise with firm l’s quality. It is expected since a higher vi 1

raises demand and relaxes competition with more product differentiation. One also an1 finds that c < 0. Firm l’s profit decreases with v2 given vi because less product differemiation

leads to more intensive

competition.

J. I’. Jin /J. of Economic Behavior & Org. 28 (I 995) 399-408

Then we consider the subgame perfect equilibrium Firms

choose

qualities

to maximize

the profits

for the qy:y

in (3). As $

403

setting game. > 0, firm l’s

optimal quality yields a corner solution. It always chooses the highest possible quality, v, regardless of early or late announcement. The low quality firm’s quality decisions. however, are different in the two cases. The first order condition

* PVI -

av2

av,=v1(v,

%) =

v2)3

-

a27T2 0

gives

the

optimal

solution

since

-

av;

=

sv, + 7v, -2v;

4 < 0. Under an early announcement

policy, firm 2 knows v and

(4v1 - v2) hence knows vr. The equilibrium

4v quality strategies are vr = v and v2 = 7.

Under a late announcement policy, firm 2 does not know v and has to choose a fixed VT based on the distribution of v. The following first order condition gives the optimal value of v; : E( ‘1;v-T:j::lj

=o.

(4)

Now VT does not depend on the realization of v. We can show that v; is lower than the expected value of v2 under early announcement, $E(v). Hence we get Proposition 1. While firm 1 always chooses the highest possible quality, its early announcement policy encourages firm 2 to choose a higher quality on average. Proof E(~-v~)=~E(v2(4v,~~~~~~~rl’jj.

Since (4v - v; )” > Fv,*

if and only if 4v > 7~; ,

V2

(4v-7v;)(4v-v;)3 ) > ~v;E(‘4vv;v$)=O.

E v2 (

(4v -v$v” -v;>o.

11

On average late announcement yields more product differentiation and less competition. Firm 2 behaves like a risk averse firm: when facing uncertainty it becomes less aggressive on average.

J.Y.Jin / J. of Economic Behavior & Org. 28 (1995) 399-408

404

We can also compare firms’ demand under early and late announcement policies. Substituting firms’ price strategies (2) into the demand functions Cl), one gets firms’ demand functions as follows: 2( 1 - o)vr x1 =

4v, - v2 ’

(1 x2=

o)vr 4v,-v, *

Firm l’s demand is always twice as4pge announcement policy, vr = v and v2 = 7, =

7(1 -o) 12

7(1-o) and x2 =

24 7(1 -cX)

(9

as firm 2’s. Under an early the sales are constant with x1

’ ’

They are independent of the value of v. The

1 + 701 consumers never purchase any The rest of 8 8 ’ product. As time goes by, the market coverage remains constant even though v keeps increasing. 2(I - o)v and x Under a late announcement policy, the sales are x1 = 2 4v-v; (1 -o)v The market share ratio remains 2 to 1, but the market coverage is = 4v - v; * no longer constant. It of v, given v;. The expected market coverage is

market coverage is 3(1 expected sales if 6 >

Early announcement gives firms higher Since this is indeed the case, we get

Proposition 2. Early announcement increases both firms ’ expected sales. Proof

Since (4v - VT)”

>2

ifandonlyif4v>7v;,E

Proposition 1 and Proposition 2 show that firm 2’s expected quality and both firms’ expected sales are distorted by early or late announcement. On the contrary,

J.Y. Jin / J. of Economic Behavior & Org. 28 (1995) 399-408

405

information sharing before quantity or price competition does not affect the expected quantity, price or demand. It changes expected profits and consumer surplus only through the variance and covariance of quantities or prices. This is because the demand in the previous models is linear in quantities or prices while in our quality setting game, it is not so.

4. Impact on profits The next question is how announcement policies affect profits. Substituting the equilibrium quality strategies under early announcement into profit functions (3), we obtain the equilibrium profits 711= $(l

- cX)2v, IT2 = $(l

- o)‘v.

(6) Both firms’ profits linearly increase with v. The expected total profit is f
,(v-v;>v’ ~1=4(1-~)

(4v_v;)2’

,(v-v2*)w; 7r2=(1---)

(4v_v;)2

*

(7)

The expected total profit is (4v+$)(v-v;) (~-cx)~E

v

(4v-v;)2 i i* The difference between two expected total profits is (l-c~)~E

f -

v(4v + v;)(v

-vJ)

(4v-v;)2 1 i . We will show that it is negative. So the total profit is lower under an early announcement policy. Since an early announcement policy provides the low quality firm better information with no effect on the high quality firm’s decision, it must benefit firm 2. Hence firm l’s profit must fall more than firm 2’s profit rises. Therefore we get Proposition 3. An early announcement policy hurts the high quality firm more than it benefits the low quality firm. Proof E ” _ v(4v+v;)(v-v;) 6

(4v - v; )’ v(8v2 + 2w; - v; ‘)

406

J.Y. Jin / J.

ofEconomic Behavior & Org. 28 (1995) 399-408

(4) implies 4v - 7v; E 2~5; i

(4v -v;>’

4v > 7v;,

4v, - 7v; E v(8v2 - v; ‘) (4v, _ v; )3 i v(4v + vl)(v

HenceE

94 > ~vv;

=O.As8v2-vV2*2

>

5%

if andonlyif

E

1

-v;>

s -

< 0. II (4v - v;)” i This result suggests that the high quality firm has no incentive to adapt an early announcement policy, even if a side payment is allowed. Thus a late announcement policy will be chosen.

5. Welfare effect We now examine the welfare effect of announcement policies. The total consumer surplus is the sum of the surplus of consumers who purchase either the high quality product or the low quality product. Adding this to the total profit one gets the social welfare. It can be written as SW

= /‘v,(

0 - o)dt3 + Lrvz( 8 - o)dt3

=~~~0.5(1-8’~)-~(1-*)j+v~{0.5(e~*-e~~*)-~~(e~-e~)} =v,xl(l-a-o.5x,) +v2x2(1-a-xX1-0.5x2). (8) Substituting

the equilibrium

welfare as a function

announcement

demand given by (5) into (8), one gets the social vl( 12v: - VIVZ- 2v;) of qualities, +* (4v, _ v2)2 . Under late

its expected value is +
Under

early announcement the expected social welfare is &(l - (w)*E(v). We now prove that the latter is bigger. Proof.

J.Y. Jin / J.

ofEconomic Behavior & Org. 28 (1995) 399-408

407

(4) implies 28v;E

(

4v, - 7v;

v2

= 0. Further, 32v2 + 5~; 2 > yvv;

if and only if

(4v, - v; )” 4v, - 7v;

4v-7v,*

>O.HenceE

v(32v2+5v;*) (4v, - v; )’

i >+;E(v2(4v:+;a]=0.

12v2 - w; ThereforeE

- 2v; *

Ev - v i

> 0. II (4v -v;>”

We already know that the total profit is lower under early announcement. Therefore consumers must be better off more than the firms are worse off. In addition, early announcement reduces uncertainty faced by consumers and may also lower firms’ marketing expenditures. All of these suggest Proposition 4. An early announcement policy is socially desirable. The main reason is also due to less product differentiation. It induces more intensive competition and brings prices down. Lower prices not only give consumers more surplus, but also increase the number of consumers who purchase products. Since an early announcement policy is socially desirable, but not self-enforcing, there might be a need for government intervention to implement mandatory early announcement in such a vertically differentiated industry.

6. Concluding remark In the model we assumed that the innovative firm commits to either an early announcement or late announcement policy. As a matter of fact, one can alternatively let the firm announce any value of v subject to a continuous cost of misreporting. This would give a separating equilibrium. The low quality firm can always infer the true value of v. The outcome is then essentially the same as the case of early announcement. If the cost of misreporting does not exist, the innovative firm, preferring v2 as low as possible, will always claim the lowest value of v, which is v’. This will result in a pooling equilibrium. The low quality firm can only make its quality decision based on the distribution of v. It corresponds to the case of late announcement. Hence the cases of early and late announcements can represent the situations where the innovative firm’s cost of misreporting is significant or negligible. As we mentioned earlier, a cost of

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J.Y. Jin /J.

of Economic Behauior & Org. 28 (1995) 399-408

misreporting may come from the stock market or consumers reaction. Future research may include the stock market or consumers explicitly as reacting to the announcement. It may provide some justification about a cost of misreporting and explain how it works. Another assumption in this paper is that only one firm innovates products. There are many cases, for example in the computer industry, where more than one firms conduct R&D and innovation announcements are used strategically for pre-emption. It has different, though relevant aspects from this paper and may be better studied in a horizontal rather than vertical differentiation model. We are trying here to focus our attention on competition from a technical follower. Nevertheless the topic of innovation announcement with more than one innovators is quite interesting and worthwhile to pursue later.

Acknowledgements I would like to thank an anonymous referee, Dan Kovenock, John Weinberg, Yukiko Hirao, Murgie Krishnan and especially Bill Novshek for their comments and suggestions. The responsibility for remaining errors is mine.

References Chaney, P., T. Devinney and R. Winer, 1991, The impact of new product introductions on the market value of firms, Journal of Business 64, 573-610. Eliashberg, J. and T. Robertson, 1988, New product preannouncing behaviour: A market signalling study, Journal of Marketing Research 25, 282-292. Gal-Or, E., 1985, Information sharing in oligopoly, Econometrica 53, 329-343. Gal-Or, E., 1986, Information transmission - Cournot and Bertrand equilibria, Review of Economic Studies 53, 85-92. Gabszewicz, J. and F. Thisse, 1979, Price competition, quality and income disparities, Journal of Economic Theory 20, 340-359. Li, L., 1985, Cournot oligopoly with information sharing, Rand Journal of Economics 16, 521-536. Novshek, W. and H. Sonnenschein, 1982, Fulfilled expectations Cournot duopoly with information acquisition and release, Bell Journal of Economics 13, 214-218. Sakai, Y., 1985, The value of information in a simple duopoly model, Journal of Economic Theory 36, 36-54. Shaked A. and J. Sutton, 1982, Relaxing price competition through product differentiation, Review of Economic Studies 49, 3-13. Tirole, J., 1989, The theory of industrial organization, The MIT Press. Vives, X., 1984, Duopoly information equilibrium, Coumot and Bertrand, Journal of Economic Theory 34, 71-94.