Value Creation out of Innovation and Resources

Abstract

Along with the development of modern technology, there have appeared unprecedented kinds of markets participated by traditional and nontraditional players. These new markets have simultaneously bought forward unparalleled challenges to the academic world and decision-making managers and entrepreneurs. To meet these challenges, this chapter, which is mainly based on (Forrest et al., to appear, Potentials of value creation and capture based on innovation, resources, strategic networks and blocks), explore potentials of value creation at the firm level from several diverse vantage points, and the next chapter looks at potentials of value capture at the firm level.

Appendix: Proof of Theorem 12.1

What is assumed in this theorem implies that the said market is in a state of mutual forbearance (Bernheim & Whinston, 1990). The incumbent firms alleviate their rivalries by partitioning the market according to their strengths so that they surrender dominance to their stronger competitors in marketplaces where they are less efficient (Li & Greenwood, 2004). The codependence of these firms gradually decreases the rates of market entry and exit (Fuentelsaz & Gómez, 2006; Yu & Cannella Jr., 2012), while reducing interfirm hostility (Haveman & Nonnemaker, 2000). Due to this state of mutual forbearance, let us consider the aggregate of the incumbent firms as one imaginary firm with α being its market share in percentage. So, β = 1 − α denotes the percentage size of the consumer surplus.

As detailed in Chap. 3, let us assume that there are n incumbent firms and that all relevant boundary conditions are normalized such that incumbent firms’ individual selling prices, production costs, loyal customers’ reservation values within the said market, lower and upper boundary conditions and magnitudes of loyal-customer bases are all, respectively, normalized to P_i (0 ≤ P_i, ≤ 1), 0, 1, 0, 1, and α/n, i = 1, 2, …, n.

Proof of 1) ⇒ 2). Assume that by randomizing its price over the interval from production cost to loyal customers’ reservation value, or [0,1] after applying normalization, a firm enters into the said market of n incumbent firms, which are collectively seen as one aggregate firm. So, the consumer surplus must satisfy β = 1 − α > 0.

Proof of 2) ⇒ 1). Assume that the consumer surplus satisfies β = 1 − α > 0. Firstly, let α₀ be a real number so that β = 1 − α > α₀ > 0 and α = ℓα₀, where ℓ is a natural number. Secondly, let us imagine that the aggregate firm is divided into ℓ many identical (imaginary) “firms,” named i, i = 1, 2, …, ℓ. Each of these firms provides consumers with an identical product and enjoys the market share α₀ = α/ℓ of loyal consumers. These firms compete over the switchers with adjustable prices. And thirdly, these ℓ imaginary firms do not have any symmetric pure strategy Nash equilibrium, for details see Chap. 3.

For the rest of this proof, it suffices to show that there is one firm that will be expected to profit by entering this market through uniformly randomizing its price strategy over the interval [0,1]. To this end, let F(P) be the price distribution of Firm j, one of the imaginary firms of the aggregate firm. The aggregate firm or equivalently each of the ℓ imaginary forms sets its price after considering the price of the entering firm and those of all other imaginary firms. Hence, the profits for Firm j from its loyal consumers is α₀P and those from its share of the switchers is ${\prod}_{i\ne j}^{\ell}\left(1-P\right)\left[1-F(P)\right]\beta P=\beta P\left(1-P\right){\left[1-F(P)\right]}^{\ell -1}$. Hence, the profit Π Firm j generates when the firm sells its product at price P is

$$ {\alpha}_0P+\beta P\left(1-P\right){\left[1-F(P)\right]}^{\ell -1} $$

and the objective of Firm j is to maximize the following by choosing its price distribution F(P)

$$ E\left(\Pi \right)=\underset{-\infty }{\overset{+\infty }{\int }}\left\{{\alpha}_0P+\upbeta P\left(1-P\right){\left[1-F(P)\right]}^{\ell -1}\right\} dF(P) $$

$$ =\underset{0}{\overset{1}{\int }}\left\{{\alpha}_0P+\beta P\left(1-P\right){\left[1-F(P)\right]}^{\ell -1}\right\} dF(P) $$

where E(Π) stands for Firm j’s expected profit for all possible prices. The reason why the upper and lower limits of the integral are changed respectively from +∞ and −∞ to 1 and 0 is because when P < 0 or when P > 1, the profits are zero.

The equilibrium indifference condition of Firm j is

$$ {\alpha}_0\times P+\beta \times P\left(1-P\right){\left[1-F(P)\right]}^{\ell -1}={\alpha}_0\times 1. $$

(12.1)

So, for the ℓ imaginary firms, solving Eq. (12.1) leads to their symmetric equilibrium pricing strategy as follows:

$$ F(P)=1-{\left(\frac{\alpha_0}{\beta P}\right)}^{\frac{1}{\ell -1}}. $$

(12.2)

From β > α₀, it follows that α₀/β < 1. So, for any Price P, satisfying 1 ≥ P ≥ α₀/β, Eq. (12.2) is well-defined as a probability distribution. This end implies that for the ℓ imaginary firms, or equivalently, the aggregate firm, the lowest allowed price is α₀/β.

To complete this proof, it suffices to show that the entrant actually expects to make profits in this new market. To this end because ${\mathit{\lim}}_{P\to {1}^{-}}F(P)=1-{\left({\alpha}_0/\beta \right)}^{1/\left(\ell -1\right)}\ne F(1)=1$, the cumulative price distribution function F(P) has a jump discontinuity at the reservation value P = 1, where the amount of jump is (α₀/β)^{1/(ℓ − 1)}. That is, F(P) has a mass point of size (α₀/β)^{1/(ℓ − 1)} at the reservation price P = 1. So, the expected profit of the entrant is the following:

$$ E\left(\Pi \right)=\underset{0}{\overset{\alpha_0/\beta }{\int }}\beta P dP+\underset{\alpha_0/\beta }{\overset{+\infty }{\int }}\beta P{\left[1-F(P)\right]}^{\ell } dP $$

(12.3)

$$ =\underset{0}{\overset{\alpha_0/\beta }{\int }}\beta P dP+\underset{\alpha_0/\beta }{\overset{1}{\int }}\beta P{\left[1-F(P)\right]}^{\ell } dP+\beta {\left(\frac{\alpha_0}{\beta}\right)}^{\ell /\left(\ell -1\right)} $$

(12.4)

where the first term in the right-hand side of Eq. (12.3) stands for the expected profit of the entrant when it charges the lowest price in the marketplace and captures the entire consumer surplus, and the second term is the entrant’s expected profit when it is in direct competition with the ℓ incumbent firms.

It can be readily shown that all the terms on the left-hand side of Eq. (12.4) are positive. So, it implies that if the consumer surplus β = 1 − α > 0, there will be at least one entrant into the said market to compete with the incumbent firms.