# Is It Better for a Publisher to Release an Audiobook after Its E-Book Version?

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Literature Related to Digital Products

#### 2.2. Literature Related to the Book Industry

#### 2.3. Our Contributions to the Related Literature

## 3. Model Development

#### 3.1. Notation and Assumptions

#### 3.2. Demand Analysis for E-Book and Audiobook in SR Model

#### 3.3. Demand Analysis for E-Book and Audiobook in LR Model

- (1)
- If ${p}_{{e}_{2}}\le \delta {p}_{{e}_{1}}$, there are$${D}_{{e}_{2}}=\left\{\begin{array}{ccc}\hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& (1-\lambda )({p}_{{e}_{1}}-\frac{{p}_{{e}_{2}}}{\delta})+\lambda (1-\frac{{p}_{{e}_{2}}}{\delta})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\ge {p}_{{e}_{2}}+\delta ({\theta}_{H}-1)\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& (1-\lambda )({p}_{{e}_{1}}-\frac{{p}_{{e}_{2}}}{\delta})+\lambda ({\overline{v}}_{{H}_{2}}-\frac{{p}_{{e}_{2}}}{\delta})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{\theta}_{H}{p}_{{e}_{2}}\le {p}_{a}\le {p}_{{e}_{2}}+\delta ({\theta}_{H}-1)\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& (1-\lambda )({p}_{{e}_{1}}-\frac{{p}_{{e}_{2}}}{\delta})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{\theta}_{L}{p}_{{e}_{2}}\le {p}_{a}\le {\theta}_{H}{p}_{{e}_{2}}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& (1-\lambda )({p}_{{e}_{1}}-{\overline{v}}_{{L}_{2}})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{{e}_{2}}-\delta (1-{\theta}_{L}){p}_{{e}_{1}}\le {p}_{a}\le {\theta}_{L}{p}_{{e}_{2}}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& 0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\le {p}_{{e}_{2}}-\delta (1-{\theta}_{L}){p}_{{e}_{1}}\hfill \end{array}\right.$$$${D}_{a}=\left\{\begin{array}{ccc}\hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& 0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\ge {p}_{{e}_{2}}+\delta ({\theta}_{H}-1)\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& \lambda (1-{\overline{v}}_{{H}_{2}})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{\theta}_{H}{p}_{{e}_{2}}\le {p}_{a}\le {p}_{{e}_{2}}+\delta ({\theta}_{H}-1)\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& \lambda (1-\frac{{p}_{a}}{\delta {\theta}_{H}})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{\theta}_{L}{p}_{{e}_{2}}\le {p}_{a}\le {\theta}_{H}{p}_{{e}_{2}}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& (1-\lambda )({\overline{v}}_{{L}_{2}}-\frac{{p}_{a}}{\delta {\theta}_{L}})+\lambda (1-\frac{{p}_{a}}{\delta {\theta}_{H}})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{{e}_{2}}-\delta (1-{\theta}_{L}){p}_{{e}_{1}}\le {p}_{a}\le {\theta}_{L}{p}_{{e}_{2}}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& (1-\lambda )({p}_{{e}_{1}}-\frac{{p}_{a}}{\delta {\theta}_{L}})+\lambda (1-\frac{{p}_{a}}{\delta {\theta}_{H}})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\le {p}_{{e}_{2}}-\delta (1-{\theta}_{L}){p}_{{e}_{1}}\hfill \end{array}\right.$$
- (2)
- If $\delta {p}_{{e}_{1}}\le {p}_{{e}_{2}}\le \delta $, there are$${D}_{{e}_{2}}=\left\{\begin{array}{ccc}\hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& \lambda (1-\frac{{p}_{{e}_{2}}}{\delta})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\ge {p}_{{e}_{2}}+\delta ({\theta}_{H}-1)\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& \lambda ({\overline{v}}_{{H}_{2}}-\frac{{p}_{{e}_{2}}}{\delta})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{\theta}_{H}{p}_{{e}_{2}}\le {p}_{a}\le {p}_{{e}_{2}}+\delta ({\theta}_{H}-1)\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& 0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\le {\theta}_{H}{p}_{{e}_{2}}\hfill \end{array}\right.$$$${D}_{a}=\left\{\begin{array}{ccc}\hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& 0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\ge {p}_{{e}_{2}}+\delta ({\theta}_{H}-1)\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& \lambda (1-{\overline{v}}_{{H}_{2}})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{\theta}_{H}{p}_{{e}_{2}}\le {p}_{a}\le {p}_{{e}_{2}}+\delta ({\theta}_{H}-1)\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& \lambda (1-\frac{{p}_{a}}{\delta {\theta}_{H}})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\delta {\theta}_{L}{p}_{{e}_{1}}\le {p}_{a}\le {\theta}_{H}{p}_{{e}_{2}}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& (1-\lambda )({p}_{{e}_{1}}-\frac{{p}_{a}}{\delta {\theta}_{L}})+\lambda (1-\frac{{p}_{a}}{\delta {\theta}_{H}})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\le \delta {\theta}_{L}{p}_{{e}_{1}}\hfill \end{array}\right.$$
- (3)
- If $\delta \le {p}_{{e}_{2}}\le \frac{{\theta}_{H}}{{\theta}_{L}}\delta $, there are:$${D}_{{e}_{2}}=0$$$${D}_{a}=\left\{\begin{array}{ccc}\hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& 0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\ge \delta {\theta}_{H}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& \lambda (1-\frac{{p}_{a}}{\delta {\theta}_{H}})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\delta {\theta}_{L}{p}_{{e}_{1}}\le {p}_{a}\le \delta {\theta}_{H}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& (1-\lambda )({p}_{{e}_{1}}-\frac{{p}_{a}}{\delta {\theta}_{L}})+\lambda (1-\frac{{p}_{a}}{\delta {\theta}_{H}})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\le \delta {\theta}_{L}{p}_{{e}_{1}}\hfill \end{array}\right.$$
- (4)
- If ${p}_{{e}_{2}}\ge \frac{{\theta}_{H}}{{\theta}_{L}}\delta $, there are$${D}_{{e}_{2}}=0$$$${D}_{a}=\left\{\begin{array}{ccc}\hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& 0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\ge \delta {\theta}_{H}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \phantom{\rule{1.em}{0ex}}& \lambda (1-\frac{{p}_{a}}{\delta {\theta}_{H}})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{p}_{a}\le \delta {\theta}_{H}\hfill \end{array}\right.$$

## 4. Strategy Analysis of Publisher

#### 4.1. Publisher’s Optimal Pricing Strategy under SR Model

**Theorem 1.**

#### 4.2. Publisher’s Optimal Pricing Strategy under LR Model

**Lemma 1.**

**Lemma 2.**

- (1)
- If $\lambda \ge \frac{{\theta}_{L}}{4{\theta}_{H}-3{\theta}_{L}-\delta {\theta}_{H}{\theta}_{L}}$, there are ${{p}_{{e}_{1}}}^{*}=\frac{1}{2}$, ${{p}_{{e}_{2}}}^{*}=\frac{\delta}{2}$, ${{p}_{a}}^{*}=\frac{\delta {\theta}_{H}}{2}$, ${{D}_{e}}^{*}=\frac{1-\lambda}{2}$, ${{D}_{a}}^{*}=\frac{\lambda}{2}$, ${\pi}^{*}=\frac{1-\lambda +\delta \lambda {\theta}_{H}}{4}.$
- (2)
- If $\lambda \le \frac{{\theta}_{L}}{4{\theta}_{H}-3{\theta}_{L}-\delta {\theta}_{H}{\theta}_{L}}$, there are ${{p}_{{e}_{1}}}^{*}=\frac{2\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)+\delta \lambda {\theta}_{H}{\theta}_{L}}{4\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-(1-\lambda )\delta {\theta}_{H}{\theta}_{L}}$, ${{p}_{{e}_{2}}}^{*}$ can be any value in the interval $[\delta {{p}_{{e}_{1}}}^{*},\delta ]$, ${{p}_{a}}^{*}=\frac{\delta (1+\lambda ){\theta}_{H}{\theta}_{L}}{4\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-(1-\lambda )\delta {\theta}_{H}{\theta}_{L}}$, ${{D}_{e}}^{*}=\frac{(1-\lambda )(2\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)+\delta \lambda {\theta}_{H}{\theta}_{L})2\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-\delta {\theta}_{H}{\theta}_{L}}{{(4\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-(1-\lambda )\delta {\theta}_{H}{\theta}_{L})}^{2}}$, ${{D}_{a}}^{*}=\frac{(1+\lambda )((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L})}{4\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-(1-\lambda )\delta {\theta}_{H}{\theta}_{L}}$, ${\pi}^{*}=\frac{(1-\lambda )\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)+\delta \lambda {\theta}_{H}{\theta}_{L}}{4\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-\delta (1-\lambda ){\theta}_{H}{\theta}_{L}}$.

**Lemma 3.**

- (1)
- If $\lambda \ge \frac{{\theta}_{L}}{4{\theta}_{H}-3{\theta}_{L}-\delta {\theta}_{H}{\theta}_{L}}$, there are ${{p}_{{e}_{1}}}^{*}=\frac{1}{2}$, ${{p}_{{e}_{2}}}^{*}$ can be any value in the interval $[\delta ,\frac{{\theta}_{H}}{{\theta}_{L}}\delta ]$, ${{p}_{a}}^{*}=\frac{\delta {\theta}_{H}}{2}$, ${{D}_{e}}^{*}=\frac{1-\lambda}{2}$, ${{D}_{a}}^{*}=\frac{\lambda}{2}$, ${\pi}^{*}=\frac{1-\lambda +\delta \lambda {\theta}_{H}}{4}$;
- (2)
- If $\lambda \le \frac{{\theta}_{L}}{4{\theta}_{H}-3{\theta}_{L}-\delta {\theta}_{H}{\theta}_{L}}$, there are ${{p}_{{e}_{1}}}^{*}=\frac{2\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)+\delta \lambda {\theta}_{H}{\theta}_{L}}{4\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-(1-\lambda )\delta {\theta}_{H}{\theta}_{L}}$, ${{p}_{{e}_{2}}}^{*}$ can be any value in the interval $[\delta ,\frac{{\theta}_{H}}{{\theta}_{L}}\delta ]$, ${{p}_{a}}^{*}=\frac{\delta (1+\lambda ){\theta}_{H}{\theta}_{L}}{4\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-(1-\lambda )\delta {\theta}_{H}{\theta}_{L}}$, ${{D}_{e}}^{*}=\frac{(1-\lambda )(2\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)+\delta \lambda {\theta}_{H}{\theta}_{L})2\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-\delta {\theta}_{H}{\theta}_{L}}{{(4\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-(1-\lambda )\delta {\theta}_{H}{\theta}_{L})}^{2}}$, ${{D}_{a}}^{*}=\frac{(1+\lambda )((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L})}{4\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-(1-\lambda )\delta {\theta}_{H}{\theta}_{L}}$, ${\pi}^{*}=\frac{(1-\lambda )\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)+\delta \lambda {\theta}_{H}{\theta}_{L}}{4\left((1-\lambda ){\theta}_{H}+\lambda {\theta}_{L}\right)-\delta (1-\lambda ){\theta}_{H}{\theta}_{L}}$.

**Lemma 4.**

**Theorem 2.**

#### 4.3. Publisher’s Optimal Choice

**Theorem 3.**

- 1.
- If $\delta \le {\delta}_{1}$, releasing a book in its audible and e-book versions simultaneously is the optimal choice of the publisher. The corresponding optimal pricing for the books, the demand for the e-book and the audiobook, and the publisher’s optimal profit are, respectively, as follows:$${{p}_{e}}^{*}=\frac{1}{2},{{p}_{a}}^{*}=\frac{{\theta}_{H}}{2},{{D}_{e}}^{*}=\frac{1-\lambda}{2},{{D}_{a}}^{*}=\frac{\lambda}{2},{\pi}^{*}=\frac{1+\lambda ({\theta}_{H}-1)}{4};$$
- 2.
- If $\delta \ge {\delta}_{1}$, releasing a book in its audible version after its e-book version is the optimal choice of the publisher. The corresponding optimal pricing for the books, the demand for the e-book and the audiobook, and the publisher’s optimal profit are, respectively, as follows:$$\begin{array}{c}{{p}_{{e}_{1}}}^{*}=\frac{2+\delta \lambda}{4-\delta (1-\lambda )},{{p}_{{e}_{2}}}^{*}=\frac{\delta (1+\lambda )}{4-\delta (1-\lambda )},{{p}_{a}}^{*}=\frac{\delta \left({\theta}_{H}(4-\delta (1-\lambda ))-(1-\lambda )(2-\delta )\right)}{2(4-\delta (1-\lambda \left)\right)},\hfill \\ {{D}_{e}}^{*}=\frac{(1-\lambda )(6-\delta (2-\lambda \left)\right)}{2(4-\delta (1-\lambda \left)\right)},{{D}_{a}}^{*}=\frac{\lambda}{2},{\pi}^{*}=\frac{\delta \lambda \left({\theta}_{H}(4-\delta (1-\lambda ))+\delta (1-\lambda )\right)+4(1-\lambda )}{4(4-\delta (1-\lambda \left)\right)}.\hfill \end{array}$$

## 5. Numerical Analysis

#### 5.1. Effects of Discount Factor

#### 5.2. Effects of Percentage of High-Value Consumers

- 1.
- The consumer surplus in the SR model is higher than that in the LR model. This result is the same as that in Section 5.1.
- 2.
- When $\delta =0.1,0.5$, $C{S}_{L}$ and $S{W}_{L}$ both decrease with $\lambda $; when $\delta =1$, $C{S}_{L}$ and $S{W}_{L}$ both increase with $\lambda $. In addition, $C{S}_{S}$ and $S{W}_{S}$ both increase with $\lambda $.This result shows that in the LR model, as the percentage of high-value consumers increases, the consumer surplus and the social welfare will both decrease if the consumers’ patience is not strong enough; but if the consumers have enough patience, both the firm and consumers can benefit. In the SR model, the firm and consumers can both benefit from a higher percentage of high-value consumers.
- 3.
- When $\delta =0.1$, the social welfare in the SR model is higher than that in the LR model if $\lambda \ge 0.007$; otherwise, if $\lambda \le 0.007$, the social welfare in the LR model is higher. When $\delta =0.5$, the social welfare in the SR model is higher than that in the LR model if $\lambda \ge 0.074$; otherwise, if $\lambda \le 0.074$, the social welfare in the LR model is higher. When $\delta =1$, the social welfare in the LR model is higher than that in the SR model.From Figure 2, we can see that in the LR model, the patience of the consumers helps to improve the social welfare. But, the percentage of high-value consumers hurts the social welfare when the patience of the consumers is not strong enough. Thus, as the patience of the consumers increases, the condition for the percentage of high-value consumers, under which the social welfare is higher in the LR model, will be less strict.

#### 5.3. Effects of High-Value Consumers’ Acceptance Level of Audiobook

- 1.
- ${\pi}_{L}$ and ${\pi}_{S}$ both increase with ${\theta}_{H}$. As the above analysis shows, a higher acceptance level results in a higher price of the audiobook, thus the publisher can obtain more profit from the audiobook. Therefore, he can obtain more total profits.
- 2.
- When $\delta =0.1,0.5$, ${\pi}_{L}\le {\pi}_{S}$; when $\delta =1$, ${\pi}_{L}\ge {\pi}_{S}$. From the above analysis, it can be seen that a stronger patience of the consumers helps the monopolist to choose the LR model. When the consumers are less patient, the monopolist prefers the SR model. But when the patience of the consumers is strong enough, the monopolist prefers the LR model. This result agrees with Theorem 3.

**Figure 6.**Publisher’s profit relations with high-value consumers’ acceptance level for audiobook in two models when $\delta =0.1,0.5,1$.

- 1.
- The consumer surplus in the SR model is higher than that in the LR model. This result is the same as those in Section 5.1 and Section 5.2. This means that no matter how these three factors ($\delta ,\lambda ,{\theta}_{H}$) change, this result always holds.
- 2.
- $C{S}_{L}$ and $S{W}_{L}$, $C{S}_{S}$ and $S{W}_{S}$ all increase with ${\theta}_{H}$.This result shows that as the acceptance level of high-value consumers increases, the consumers can obtain more surplus. Further, as shown in Theorem 2, the publisher’s profit will also rise with the acceptance level. Thus, a higher acceptance level will result in higher social welfare.
- 3.
- When $\delta =0.1,0.5$, the social welfare in the SR model is higher than that in the LR model; when $\delta =1$, the social welfare in the LR model is higher than that in the SR model.

## 6. Discussion

**Finding 1.**

**Finding 2.**

**Finding 3.**

**Finding 4.**

**Finding 5.**

## 7. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Derivation of Demand for the E-Book and the Audiobook under the SR Model

## Appendix B. Derivation of Demand for the E-Book and the Audiobook in the Second Stage under LR Model

**Remark A1.**

**Remark A2.**

**Remark A3.**

**Remark A4.**

## Appendix C

**Proof of Theorem 1.**

## Appendix D

**Proof of Lemma 1.**

## Appendix E

**Proof of Lemma 2.**

## Appendix F

**Proof of Lemma 3.**

## Appendix G

**Proof of Lemma 4.**

## Appendix H

**Proof of Theorem 2.**

## Appendix I

**Proof of Theorem 3.**

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**Figure 3.**Consumer surplus relations with percentage of high-value consumers in two models as well as social welfare when $\delta =0.1$.

**Figure 4.**Consumer surplus relations with percentage of high-value consumers in two models as well as social welfare when $\delta =0.5$.

**Figure 5.**Consumer surplus relations with percentage of high-value consumers in two models as well as social welfare when $\delta =1$.

**Figure 7.**Consumer surplus relations with high-value consumers’ acceptance level for audiobook in two models as well as social welfare when $\delta =0.1$.

**Figure 8.**Consumer surplus relations with high-value consumers’ acceptance level for audiobook in two models as well as social welfare when $\delta =0.5$.

**Figure 9.**Consumer surplus relations with high-value consumers’ acceptance level for audiobook in two models as well as social welfare when $\delta =1$.

**Figure 10.**First example of book retail price on Amazon.com (screenshot was taken on 28 November 2020).

**Figure 11.**Second example of book retail price on Amazon.com (screenshot was taken on 28 November 2020).

**Figure 12.**Third example of book retail price on Amazon.com (screenshot was taken on 28 November 2020).

$\mathit{v}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Consumer’s valuation of the e-book. |

${\theta}_{H}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | High-value consumers’ acceptable level for the audiobook. |

${\theta}_{L}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Low-value consumers’ acceptable level for the audiobook. |

$\lambda \phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Percentage of high-value consumers. |

$SR\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | The model where publisher releases the audiobook and the e-book simultaneously. |

$LR\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | The model where publisher releases the audiobook after the e-book. |

${p}_{e}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Retail price of the e-book under the SR model. |

${p}_{{e}_{i}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Retail price of the e-book in stage i under the LR model, $i=1,2$. |

${p}_{a}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Retail price of the audiobook. |

${u}_{e}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Consumer’s utility if she buys the e-book under the SR model. |

${u}_{{a}_{L}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Low-value consumer’s utility if she buys the audiobook. |

${u}_{{a}_{H}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | High-value consumer’s utility if she buys the audiobook. |

${u}_{{e}_{i}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Consumer’s utility if she buys the e-book in stage i under the LR model, $i=1,2$. |

$\delta \phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Discount factor of the e-book under the LR model. |

${\overline{v}}_{H}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Valuation threshold of high-value consumer who is indifferent between buying the audiobook and the e-book under SR model. |

${\overline{v}}_{L}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Valuation threshold of low-value consumer who is indifferent between buying the audiobook and the e-book under the SR model. |

${\overline{v}}_{{H}_{2}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Valuation threshold of high-value consumer who is indifferent between buying the audiobook and the e-book in the second stage under LR model. |

${\overline{v}}_{{L}_{2}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Valuation threshold of low-value consumer who is indifferent between buying the audiobook and the e-book in the second stage under the LR model. |

${D}_{e}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Demand for the e-book under the SR model. |

${D}_{{e}_{i}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Demand for the e-book in stage i under the LR model, $i=1,2$. |

${D}_{a}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Demand for the audiobook. |

$\pi \phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}$ | Total profit of the publisher. |

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## Share and Cite

**MDPI and ACS Style**

Zhang, L.
Is It Better for a Publisher to Release an Audiobook after Its E-Book Version? *Systems* **2024**, *12*, 33.
https://doi.org/10.3390/systems12010033

**AMA Style**

Zhang L.
Is It Better for a Publisher to Release an Audiobook after Its E-Book Version? *Systems*. 2024; 12(1):33.
https://doi.org/10.3390/systems12010033

**Chicago/Turabian Style**

Zhang, Linlan.
2024. "Is It Better for a Publisher to Release an Audiobook after Its E-Book Version?" *Systems* 12, no. 1: 33.
https://doi.org/10.3390/systems12010033