## Introduction

^{1}TVC and TR can normally be directly observed in most datasets. In this paper, we consider the degree of robustness of this strategy concerning the degree of violation of the constant MC assumption. To this end, we rely on a controlled Monte Carlo experimental environment. We start by defining the degree of violation of the constant MC assumption by using the proportion of firms in the industry that have a constant marginal cost (β). This means that 1–β proportion of firms do not have a constant marginal cost. A higher β in a sample implies a relatively less severe violation of the constant MC assumption, whereas β = 0 means a complete violation. Using a Monte Carlo experiment, we derive the probability that a β-degree violation of the constant MC assumption would not lead to statistically significant differences between the estimates of ρ in the treatment and control groups as a function of β. This probability can be defined as the power of the constant MC assumption.

## Economic Framework and Identification Strategy

_{i}(q

_{i}) with the marginal cost of production being MC

_{i}(q

_{i}). Note that both functions are indexed by i, indicating the heterogeneity among firms. Firms set prices of their products to maximize profits, as follows:

_{i}= c

_{i}. Given this restriction, a firm’s optimal total revenue (TR) is \({TR}_{i}=\frac{1}{\rho }{\rho }^{\frac{1}{1-\rho }}\Phi {c}_{i}^{\frac{1}{\rho -1}}\) and its total variable cost (TVC) is \({TVC}_{i}={\rho }^{\frac{1}{1-\rho }}\Phi {c}_{i}^{\frac{1}{\rho -1}}\). Accordingly, there exists a relationship between TVC and TR, implied by firm profit maximization behavior, as follows:

_{i}= 0, as follows:

_{i}= TC

_{i}(0).

## The Experiment

### Data Generating Process

### Experimental Setup

## Findings

_{1}, c

_{2}, d > = < {0.2, 0.5, 0.9}, 1, fc ~ U(0.01, 0.1), b ~ U(0.5, 1), c

_{1}~ U(0, 1), c

_{2}~ U(-0.1, 1), d ~ U(0.01, 0.1) > , where c

_{1}and c

_{2}, respectively, are the values of parameter c in the cost functions of linear and quadratic MC firms. In Scenario 1, we do not allow the parameter c to be negative because a negative value of c often results in no solution to the first order conditions. In addition, the law of diminishing return requires c to be positive. Similarly, in Scenario 2, d is positive. Nevertheless, we do allow for c to be negative in Scenario 2 (which implies that firms have decreasing MC over certain range of output).

### Scenario 1

### Scenario 2

## Estimation Using Real Data

^{2}The dataset covers five four-digit industries: instant noodles and other convenient food manufacturing (252 firms), textile and garment manufacturing (6568 firms), cosmetics manufacturing (225 firms), household kitchen appliances manufacturing (306 firms), and computer manufacturing (85 firms). Table 1 presents the estimation results. Notably, the point estimates of ρ and the implied elasticities of substitution appear reasonable and broadly align with estimates in existing studies (for example, see Aw et al. 2011; Das et al. 2007; and Sun 2023).

[1] | [2] | [3] | [4] | [5] | |
---|---|---|---|---|---|

\(\rho \) | 0.741*** | 0.793*** | 0.809*** | 0.872*** | 0.890*** |

(0.00615) | (0.00195) | (0.00400) | (0.00636) | (0.0172) | |

Elasticity | 3.855*** | 4.841*** | 5.239*** | 7.794*** | 9.108*** |

(0.0914) | (0.0456) | (0.110) | (0.386) | (1.425) | |

N | 252 | 6,568 | 225 | 306 | 85 |

R ^{2} | 0.983 | 0.962 | 0.995 | 0.984 | 0.970 |