A road map to new product success: warranty, advertisement and price

Abstract

In today’s hyper-competitive marketplace, new product introduction is commonly viewed as a vehicle for profitably growing businesses, yet market success remains rare and new innovative products fail at stunning rates. Current corporate thinking identifies a number of potential reasons, one of which lies in the poor execution of marketing-mix strategies. In this paper, we analyze how best to structure the marketing strategy of a company to foster and leverage his innovative new product with a focus on three variables—namely warranty duration, advertising spending and selling price—and attempt to provide a theoretical explanation for factors that affect optimal trajectories of these variables over time. We also conduct a detailed numerical study in order to test which market- and product-related factors have the most influence on and best explain the company’s new product introduction strategy, and illustrate the associated profit impacts. Our analysis proposes a time-variant threshold on advertising spending that structures the company’s marketing strategy over time. Secondly, we point out that warranty duration and price collectively follow the pattern of the diffusion curve of the new product, but reach their maximum levels before the new product matures. We also provide guidance about the effect of such market- and product-related factors as referral power, failure rates and effectiveness of advertising spending on a company’s new product introduction strategy.

Appendices

Appendix A: Proof of Lemma 1

The proof is by contradiction. Suppose that $H_{WW}+\,\omega _WH_{PW}>0$. Then, $H_{WW} > -\omega _WH_{PW}$, and multiplying both sides of the inequality by $H_{PP}$ results in the following inequality;

$$\begin{aligned} H_{{ PP}}H_{WW} < -\omega _WH_{{ PP}}H_{PW}, \end{aligned}$$

where the direction of the inequality changes as $H_{{ PP}}<0$. Recall from the second-order conditions provided in (13) that $H_{{ PP}}H_{WW}>H_{PW}^2$. Thus,

$$\begin{aligned} H_{PW}^2< H_{{ PP}}H_{WW} < -\omega _WH_{{ PP}}H_{PW}, \end{aligned}$$

meaning that $H_{PW}^2< -\omega _WH_{{ PP}}H_{PW}$ and $H_{PW}\left( H_{PW}+\omega _WH_{{ PP}}\right) < 0$. Since $H_{PW}>0$, the value of $\left( H_{PW}+\omega _WH_{{ PP}}\right)$ must be less than $0$ and this is a contradiction. The proof follows. $\square$

Appendix B: Proof of Proposition 1

In (18), the optimal advertising trajectory is defined by

$$\begin{aligned} \dot{A} = \left( \frac{1}{H_{AA}}\right) F\left( -r\lambda G_A+G_Q-GG_{AQ}/G_A\right) . \end{aligned}$$

(20)

Since $H_{AA}<0$ and $F>0$, the sign of $\dot{A}$ is determined by $\left( -r\lambda G_A+G_Q-GG_{AQ}/G_A\right)$. That is, if

$$\begin{aligned} -r \lambda G_A + G_Q - \frac{GG_{AQ}}{G_A} > 0, \end{aligned}$$

(21)

then $\dot{A} <0$, and $\dot{A}>0$ otherwise. Recall that $G$ is given by $\left( Q_M-Q\left( t\right) \right) \left( \alpha +\beta \ln A(t)+\right.$ $\left. \alpha _2 Q(t)\right)$, and substituting this into (21) results in

$$\begin{aligned} A(t) > \frac{r\beta \lambda }{\alpha _2}. \end{aligned}$$

(22)

Let $\bar{A}$ represent $r\beta \lambda /\alpha _2$. Then, at any time $t$, $\dot{A} < 0$ if $A(t) > \bar{A}$, $\dot{A}=0$ if $A(t) = \bar{A}$ and $\dot{A}>0$ if $A(t) < \bar{A}$. The proof follows. $\square$

Appendix C: Proof of Proposition 2

The concave trajectory followed collectively by warranty duration and price over time is obtained from (6), (16), (17), (18), Lemma 1 and Proposition 1 through retracing similar steps taken in the proof of Proposition 1.

Regarding the time $t$ at which both variables attain their maximum, note that the time derivatives of warranty duration and price must be equal to $0$ at $t$. In other words, $r\lambda F_P+F^2G_Q$ must be equal to $0$ on the basis of expressions in (16), (17) and (18). Substituting sales rate function in (6) for the terms in this equality leads to the following condition:

$$\begin{aligned}&k_1\left( \frac{\left( W(t)+k_2\right) ^b}{P(t)^{-a}}\right) \left[ -\frac{r\lambda a}{P(t)}+k_1\left( W(t)+k_2\right) ^bP(t)^{-a}\left( -\alpha -\beta \ln A(t)\right. \right. \nonumber \\&\left. \left. \quad +\,\,\alpha _2\left( Q_M-2Q(t)\right) \right. \!)\right] = 0 \end{aligned}$$

(23)

Notice that the second term in the brackets is the explicit representation of $q_Q$ and the multiplier in front of the brackets is positive. Then, the condition provided in (23) can be restated in a simpler form so that $P(t) = {r\lambda a}/{q_Q}$, and the proof follows. $\square$

Appendix D: Tables for numerical analysis

See Tables 3, 4, 5 and 6.

Table 3 Sensitivity to failure rate ($\kappa$)

Table 4 Sensitivity to advertising effectiveness ($\beta$)

Table 5 Sensitivity to word of mouth effectiveness ($\alpha _2$)

Table 6 Sensitivity to price elasticity ($a$)