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In this paper, we will first give a general description of the model and we will further describe how optimal resource allocation is achieved. Next, we will look at the case when resource misallocation occurs and how this affects output and TFP. Lastly, we will look at how the authors empirically showed that distortion arising from resource misallocation exists in China and India as well as how reallocation could lead to TFP gains in these countries.
In the model, the authors assumed that there are several industries. Each industry consists of several heterogeneous monopolistic competitive firms, which produce differentiated products. A representative assembly plant  assembles these differentiated goods to create a final good for the economy. The final goods market is characterized by a perfect competitive setting. The diagram below illustrates the model of this economy.
Firms at the industry level differ in their productivities, whereby a more productive firm would have a higher TFP and marginal revenue product of labor and capital (MRPL and MRPK respectively).
Optimal Resource Allocation
To discuss the case of optimal resource allocation, we shall use labor as a single factor in production. By extension, the allocation of capital follows the exact same reasoning. An optimizing monopolistic competitive firm employs labor until the marginal cost of employing an additional unit of labor equalizes the MRPL. In order to maximize total output of the industry, firms should be allocated resources according to their productivity level, up to the point that MRPL equalizes across firms. This is because when the MRPL doesnââ‚¬â„¢t equalize across firms, a reallocation of labor to a firm with higher MRPL can increase the aggregate output, as this firm is able to produce a higher level of output with a given unit of labor. As labor is increasingly allocated to firms with higher productivity, the property of diminishing marginal product of labor will cause differing initial levels of MRPL to equalize across the firms. As a result, in an economy without any resource misallocation, more productive firms would receive more labor and thus, can supply more output and charge a lower price.
To illustrate why output is maximized when resources are optimally allocated, we assume that a simplified economy that has just two firms in an industry and employs a single input, labor. As shown in graph 1 below, with Firm 2 being the more productive firm as demonstrated by its higher MRPL, when MRPL equalizes between the two firms, the result is an optimal outcome where the output produced by this industry is maximized and is represented by the maximum total area under the curves.
Graph 1: Optimal Allocation Graph 2: Misallocation
Resource Misallocation and TFP
Resource misallocation favors some firms while putting other firms at a disadvantage when acquiring resources for production. When there is a misallocation, the quantities of inputs allocated are not optimal. This is depicted in graph 2 above, where a wedge is driven between the MRPL across the firms. This results in a less than optimal level of output, where the shaded grey portion represents the loss of output due to misallocation.
Given a fixed amount of input, an industry where resources are misallocated produces less output than one without misallocation. Hence, when misallocation of resources occurs, the industryââ‚¬â„¢s overall productivity level is lowered. When resource misallocation occurs in many industries across the economy, the overall manufacturing TFP in the country falls.
Gains from Reallocation
To test their model empirically, the authors introduced the concept of revenue productivity (TFPR), which represents a geometric average of MRPK and MRPL. With misallocation, MRPK and MRPL do not equalize and this creates a dispersion of TFPR across firms. Here, a larger dispersion of TFPR indicates greater distortion. The authors calculated the TFPR of the manufacturing industries in China, India and the United States (US). They found that there is greater dispersion of TFPR in China and India than in US.
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Figure 1: Distribution of TFPR in China, India and the United States
The larger TFPR dispersion in China and India suggests that resources are misallocated to a greater extent in these countries than in the US. Hence, the US is used as the benchmark of efficient resource allocation.
The authors then hypothetically reallocated resources across the firms in China and India, such that the marginal product in China and India are equalized to extent observed in the US. Such reallocation of resources to efficient levels as observed in the US results in a 30%-50% and 40%-60% gain in the TFP of China and India respectively. This affirms that there are potential gains when resources are optimally re-allocated.
The authors found empirical evidence that misallocation of resources is one of the causes of differing TFP across countries. Through estimating the differences in marginal products of labor and capital across plants, the authors found larger gaps in China and India as compared to the US. By hypothetically moving to allocation patterns observed in the US, the authors found that this would be able to boost TFP by significant proportions.