Marginal Rate Of Transformation Research Articles

FISCAL ASPECTS OF THE EQUITY-EFFICIENCY TRADE-OFF

This study makes an attempt to trace out the extent to which (in)direct taxation distorts consumers’ behavior, thus being a hindrance towards achieving an optimal allocation of resources between equity and efficiency targets. To substantiate our argument, a utility maximization model is built to examine whether fiscal policy restores public confidence in attaining equilibrium between the marginal rate of substitution (MRS) and the marginal rate of transformation (MRT). The validity of our model is then tested by using a sample of eleven countries. Comparing actual with optimal (in)direct tax rates, we find that the tax system of eight countries tends to favor equity over efficiency (actual direct (indirect) tax rates higher (lower) than optimal direct (indirect) tax rates) and the tax system of three countries tends to apply the efficiency principle.

Marginal rates of technical changes and impact in stochastic data envelopment analysis: An application in power industry

Marginal rates of technical changes and marginal impact are useful tools to calculate the trade-offs between production factors in a production process. In the data envelopment analysis (DEA) framework, the calculation of these trade-offs (marginal rates of technical substitution, marginal rates of transformation, marginal productivity and marginal costs) using the existing deterministic approaches may be sensitive to uncertainty and variability of the input and output data. Therefore, in this contribution, we introduce a stochastic DEA model based on chance-constrained programming to develop a measure of the marginal rates of firms facing data uncertainty. In this contribution, chance-constrained programming is used to develop a procedure to calculate these trade-offs. Our proposed stochastic procedure is applied to sample data on 31 power plants. The empirical results on marginal rates obtained from our proposed stochastic programs revealed that the results are different at various tolerance levels of chance constraints.

Monetary Policy, Neutrality, and the Environment

AbstractWe study the interaction between monetary/fiscal policies in a Ramsey–Sidrauski model augmented with the “Green Golden Rule.” We demonstrate conditions whereby monetary and fiscal policy under different utility and preference assumptions are or are not environmentally neutral. Despite its nonseparability in utility, we demonstrate that money is environmentally neutral. Policy impacts the environment via the marginal rate of transformation rather than the marginal rate of substitution between consumption and environment. Fiscal policies under a balanced budget are environmentally nonneutral. Only under a nonbalanced budget, when deficits are monetized, is money environmentally nonneutral. Under cash‐in‐advance and transactions costs, money is environmentally nonneutral.

Technology inequality, Marginal Rate of Transformation and Rate of Substitution measurement by DEA: The sustainability improvement of passenger cars

To the best of our knowledge, the previous Data Envelopment Analysis studies on passenger-car sustainability have neglected to measure technology-based measures, technology inequality, and technology diffusion barriers. To fill this research gap, this study proposes a new framework consisting of Data Envelopment Analysis, K-means clustering method, Gini coefficient, and the group-based decomposition method. Adopting these methods, this study examines the Marginal Rate of Transformation and the Rate of Substitution, identifies both desirable congestion (or eco-innovation) and undesirable congestion, evaluates technology inequality, and explores the main barriers to technology diffusion. Empirically, we assess new passenger cars released in the United States in 2020. The main conclusions are summarized as follows: First, under managerial disposability, the generally negative Marginal Rate of Transformation and Rate of Substitution across passenger cars suggest that the majority of car manufacturers are environmentally conscious. This outcome is partly the result of the minimum environmental standards set for car manufacturers. Second, the majority of passenger cars displayed the possibility of strong desirable congestion (clean-technology innovation) and no undesirable congestion simultaneously. The majority of passenger cars need to decrease carbon dioxide emissions along with an increase in fuel consumption efficiency (miles per gallon). This finding indicates that regulatory strategies have been mostly effective at directing eco-technological innovation toward mitigating a significant source of climate change. Finally, technology inequality was driven by both cross-group and within-group inequalities. Moreover, considerable heterogeneity existed in the within-group decomposition of the overall efficiency Gini coefficient result.

Divine Proportion of The Invisible Hand: a New Look at Adam Smith’s Natural Theology

Recent research on labor-search-leisure model has described local multiple equilibria of Invisible hand under wage and price dispersion. This paper analyzes the general competitive equilibrium, where the Invisible hand creates harmonic proportions of mutually beneficial exchange. The analysis results in the rigorous mathematical proof that at the general competitive equilibrium both the marginal rate of substitution of leisure for consumption and marginal rate of transformation of production into services are equal to the golden ratio conjugate, whereas both the intensity of consumption and the sales-costs of production ratio are equal to the golden ratio itself, also called the divine proportion. On commodity market the golden ratio conjugate equalizes the gravitation or attractiveness of both seller and buyer. Local monopoly and monopsony disappear, and the competitive equilibrium really becomes perfect. In marriage markets the golden ratio conjugate equalizes the attractiveness of both man and woman and creates the ideal family. These results bring us back to the theological grounds of Adam Smith’s works; it gives a new view on his idea of natural rates of both wages and profit. It really can be argued that there was a good reason to apply the natural theology approach to the analysis of exchange at times of the ‘Wealth of Nations’.

Exploring the Spatial Heterogeneity of Residents' Marginal Willingness to Pay for Clean Air in Shanghai.

Previous studies have paid little attention to the spatial heterogeneity of residents' marginal willingness to pay (MWTP) for clean air at a city level. To fill this gap, this study adopts a geographically weighted regression (GWR) model to quantify the spatial heterogeneity of residents' MWTP for clean air in Shanghai. First, Shanghai was divided into 218 census tracts and each tract was the smallest research unit. Then, the impacts of air pollutants and other built environment variables on housing prices were chosen to reflect residents' MWTP and a GWR model was used to analyze the spatial heterogeneity of the MWTP. Finally, the total losses caused by air pollutants in Shanghai were estimated from the perspective of housing market value. Empirical results show that air pollutants have a negative impact on housing prices. Using the marginal rate of transformation between housing prices and air pollutants, the results show Shanghai residents, on average, are willing to pay 50 and 99 Yuan/m2 to reduce the mean concentration of PM2.5 and NO2 by 1 μg/m3, respectively. Moreover, residents' MWTP for clean air is higher in the suburbs and lower in the city center. This study can help city policymakers formulate regional air management policies and provide support for the green and sustainable development of the real estate market in China.

Monetary Policy, Neutrality and the Environment

We study the interaction between monetary and fiscal policies in a Ramsey-Sidrauski model augmented with environmental capital. Equilibrium solutions are studied through the “Green Golden Rule”. Despite the non-separability of money in utility and intertemporally non-separable preferences, money is environmentally neutral. Policy impacts the environment via the marginal rate of transformation rather than the marginal rate of substitution between consumption and environment. Fiscal policies, lump sum and distortionary, under a balanced budget, are also environmentally non-neutral. Only under a non-balanced budget, when deficits are monetized, is money environmentally non-neutral. In alternative approaches (Cash-in-Advance, Transactions Costs), money is environmentally non-neutral. JEL Classification: E52, E62, H23

PM2.5 pollution-related health effects and willingness to pay for improved air quality: Evidence from China’s prefecture-level cities

The public health risks attributed to PM2.5 pollution exposure are far greater in China than in many other countries. Few studies have focused on the potential impact of PM2.5 pollution on respondents’ self-rated health, physical health, and mental health. Using an instrumental variable model and constructing instrumental variables of ventilation coefficients, this study analyzes 2011, 2013, and 2015 data from the China Health and Retirement Longitudinal Study (CHARLS), a nationally representative sample of adults over 45 years of age. By matching the health data with the PM2.5 data in 272 prefecture-level cities, this study examines the impact of PM2.5 pollution on public health and measures the marginal cost (MC) of PM2.5 reduction. Empirical results show that PM2.5 can significantly lower self-rated health and increase the probability of chronic diseases and mental depression. Using the marginal rate of transformation between income and PM2.5, the results show residents, on average, are willing to pay 869 Yuan for reduced PM2.5. Moreover, respondents’ gender, age, education level, and locality significantly affect PM2.5 pollution-related health and the MC for clean air. Specifically, MC levels in males are higher than those in females; people aged over 60 show the highest MC levels; the respondents who are less educated are willing to pay more for pollution mitigation; and residents living in Eastern China have a greater MC for PM2.5 pollution control. We further propose several important recommendations for policy-makers based on our results, which offer new evidence to mitigate PM2.5 pollution in China.

Marginal Rate of Transformation and Rate of Substitution measured by DEA environmental assessment: Comparison among European and North American nations

This study discusses the new use of DEA (Data Envelopment Analysis) environmental assessment to measure MRT (Marginal Rate of Transformation) and RS (Rate of Substitution) among production factors (e.g., inputs, desirable and undesirable outputs). To measure the degree on MRT and RS, this study first examines a concept of disposability from the perspective of economic strategies to combat various environmental issues. The strategies are extendable to a policy change for pollution prevention. The underlying concept is separated into natural and managerial disposability. Under managerial disposability, it is possible for us to measure an occurrence of desirable congestion, or eco-technology innovation. Considering the disposability concept, this study discusses how to measure the type and magnitude of MRT and RS. A problem of the MRT & RS measurement is that these measures usually become unstable (e.g., very large or small in these magnitudes) because DEA does not assume any functional form for economic activities. To overcome such a difficulty, this study equips DEA environmental assessment with multiplier restriction by utilizing a unique feature on a proposed data treatment. The multiplier restriction in DEA has been never explored in previous works on environmental assessment. In an application, this study finds three important economic concerns on Europe and North America. First, Western Europe outperforms Eastern Europe and North America in their unified efficiency measures under managerial disposability. This study statistically confirms a difference between Western and Eastern Europe, but not between Western Europe and North America. This result exhibits that Eastern Europe is not yet well developed at the level of the other two regions. Second, Eastern Europe has exhibited MRT estimates that are different from Western Europe and North America. The nations in Eastern Europe have an economic potential for industrial developments because the level of their industrial pollutions is less than that of the other two regions. The potential is also found in their MRT estimates. Finally, an interesting difference can be found in the RS estimate between Eastern Europe and Western Europe from 2008 to 2012. They have statistically exhibited a difference between the two regimes, but not with North America. This is because most nations in both Western Europe and North America have already attained a high level of economic successes so that they have a limited industrial potential under current production technology and eco-technology. The situation of the two regions will be changed along with new technology development. In contrast, Eastern Europe is different from the other two regions in terms of attaining such a level of social sustainability because of limited capital accumulation and limited opportunity for technology innovation.

Importance of Statistical Evidence in Estimating Valid DEA Scores.

Data Envelopment Analysis (DEA) allows healthcare scholars to measure productivity in a holistic manner. It combines a production unit's multiple outputs and multiple inputs into a single measure of its overall performance relative to other units in the sample being analyzed. It accomplishes this task by aggregating a unit's weighted outputs and dividing the output sum by the unit's aggregated weighted inputs, choosing output and input weights that maximize its output/input ratio when the same weights are applied to other units in the sample. Conventional DEA assumes that inputs and outputs are used in different proportions by the units in the sample. So, for the sample as a whole, inputs have been substituted for each other and outputs have been transformed into each other. Variables are assigned different weights based on their marginal rates of substitution and marginal rates of transformation. If in truth inputs have not been substituted nor outputs transformed, then there will be no marginal rates and therefore no valid basis for differential weights. This paper explains how to statistically test for the presence of substitutions among inputs and transformations among outputs. Then, it applies these tests to the input and output data from three healthcare DEA articles, in order to identify the effects on DEA scores when input substitutions and output transformations are absent in the sample data. It finds that DEA scores are badly biased when substitution and transformation are absent and conventional DEA models are used.

A two-stage translog marginal cost pricing approach for Floridian hospital outputs

Since the passage of the Affordable Care Act (ACA) of 2010, issues still remain regarding the mandated purchase of insurance to ensure more universal coverage. One such issue is the pricing of these insurance packages and whether or not the reimbursements will cover necessary services. Therefore, policy concerns exist that increasing the number of insured individuals may not curtail costs. Conversely, providers may not wish to treat patients covered by excessively frugal plans such as Medicaid; hence the trade-offs between access and cost control. In this article, we present findings from a cost function and a productivity approach to determine the marginal cost of providing inpatient hospital care for hospitals operating in Florida during 2005. Using these methodological approaches, we are able to use the marginal rate of transformation to determine the relative marginal costs while controlling for hospital technical and allocative inefficiency. Our work differs from earlier articles as we avoid the Greene problem for cross-sectional models through a two-step approach. By including both reimbursement rates under conditions of hospital efficiency, we can ascertain payment schemes that should, at least in theory, cover necessary costs for patient care without leading to excessive input usage.

Pricing Nonmarketed Outputs with an Application to Community Colleges

We use the directional output distance function in cost space to recover absolute prices of nonmarket goods such that the ratio of prices equals the marginal rate of transformation of outputs in production. As such, the method is quite useful for valuing nonmarketed goods such as those produced by government entities such as the National Park Service, public schools and universities, and municipalities. We provide an empirical illustration of our method using fourteen Missouri community colleges that produced full-time equivalent students, certificates, associate’s degrees, and real spending on public service and auxiliary enterprises during the period 2005–2006 to 2011–2012.

Option smiling when investors’ estimates of asset volatility disagree

This study sheds light on why heterogeneous beliefs in volatility manifest the smile effect of options and how the degree of belief disagreement influences option-implied volatility. It is found that when investors’ level of heterogeneous beliefs increases, agents who over estimate volatility raise their subjective probability about those outer dividend states and hence increase more consumption to those states. As a result, an increase of consumption causes a decrease of their marginal rate of transformation in outer states. The raising subjective probability increases the prices of outer states, while the lower marginal rate of transformation decreases the prices of that. However, the influence of the former dominates the latter, causing a fatter tail of the state-price density. As a consequence, the values increase for those call options with high strike prices and put options with low strike prices, leading to a U-shaped implied volatility and hence causes a smell effect.

Returns to Scale, Damages to Scale, Marginal Rate of Transformation and Rate of Substitution in DEA Environmental Assessment

This study discusses a new use of DEA (Data Envelopment Analysis) environmental assessment to measure MRT (Marginal Rate of Transformation) and RS (Rate of Substitution) between desirable and undesirable outputs. To discuss MRT and RS, this study first examines a concept of disposability from the perspective of corporate strategies to adapt a regulation change on undesirable outputs. The concept of disposability is separated into natural and managerial disposability. Then, this study explores the computational framework of RTS (Returns to Scale) and DTS (Damages to Scale). The type of RTS is measured within the natural disposability, while the type of DTS is measured within the managerial disposability. Considering the two types of disposability, this study discusses MRT and RS between desirable and undesirable outputs. As an illustrative example, this study applies the proposed approach to evaluate the performance of US coal-fired power plants. This study finds that the regulation policy on NOx and SO2 has been effective on their emission controls under US Clean Air Act (CAA). The regulation on CO2, or a major source of the global warming and climate change, is still insufficient in the United States. Therefore, this study recommends that US federal and local governments should regulate the amount of CO2 emission under the CAA.

The Rigidity of Labor: Processing Savings and Work Decisions through Shannon's Channels

This paper argues that constraining people to choose consumption and labor under finite Shannon capacity produces results in line with U.S. business cycle data. My model has a simple partial equilibrium setting in which risk averse consumers keep high labor supply and low consumption profile at early stage of life to hedge against wealth fluctuations. They rationally choose to keep consumption and labor unchanged until they collect enough information. I find that at high frequency consumption appears to be more sluggish than labor supply. However, when people decide to change consumption they do so by a large amount. This combination leads to higher variance of consumption with respect to labor supply. My model also finds high persistence and strong comovement of consumption and employment and delayed response of consumption and labor with respect to wealth. Furthermore, my framework generates endogenously a wedge between marginal rate of substitution and marginal rate of transformation or wages. Such wedge is bigger and more volatile the lower information flow. These findings suggest that rational inattention offers a promising avenue to bridge the gap between theory and U.S. business cycle data.

The Rigidity of Labor: Processing Savings and Work Decisions Through Shannon's Channels

This paper argues that constraining people to choose consumption and labor under finite Shannon capacity produces results in line with U.S. business cycle data. My model has a simple partial equilibrium setting in which risk averse consumers keep high labor supply and low consumption profile at early stage of life to hedge against wealth fluctuations. They rationally choose to keep consumption and labor unchanged until they collect enough information. I find that at high frequency consumption appears to be more sluggish than labor supply. However, when people decide to change consumption they do so by a large amount. This combination leads to higher variance of consumption with respect to labor supply. My model also finds high persistence and strong comovement of consumption and employment and delayed response of consumption and labor with respect to wealth. Furthermore, my framework generates endogenously a wedge between marginal rate of substitution and marginal rate of transformation or wages. Such wedge is bigger and more volatile the lower information flow. These findings suggest that rational inattention offers a promising avenue to bridge the gap between theory and U.S. business cycle data.

Dynamic contracting with persistent shocks

In this paper, we develop continuous-time methods for solving dynamic principal–agent problems in which the agent's privately observed productivity shocks are persistent over time. We characterize the optimal contract as the solution to a system of ordinary differential equations and show that, under this contract, the agent's utility converges to its lower bound—immiserization occurs. Unlike under risk-neutrality, the wedge between the marginal rate of transformation and a low-productivity agent's marginal rate of substitution between consumption and leisure will not vanish permanently at her first high-productivity report; also, the wedge increases with the duration of a low-productivity report. We apply the methods to numerically solve the Mirrleesian dynamic taxation model, and find that the wedge is significantly larger than that in the independently and identically distributed (i.i.d.) shock case.

On a Uniform Turnpike of the Third Kind in the Robinson-Solow-Srinivasan Model

On using McKenzie's taxonomy of optimal accumulation in the long-run, we report a ``uniform turnpike'' theorem of the third kind in a model original to Robinson, Solow and Srinivasan (RSS), and further studied by Stiglitz. Our results are presented in the undiscounted, discrete-time setting emphasized in the recent work of Khan-Mitra, and they rely on the importance of either a strictly concave felicity function, or on the value of a ``marginal rate of transformation'', ξσ, from one period to the next not being unity. We argue that our results, when viewed through the lens of turnpike theory, have a broader relevance to intertemporal optimization theory, as developed in economics by Ramsey, von Neumann and their followers.

Diagram for a small planet: The Production and Ecosystem Possibilities Curve

With the development of the GPI there is now an ecological alternative to GDP for measuring a country's economic performance, but we still lack an ecological alternative to the PPC for illustrating a country's economic problem. The diagram suggested here illustrates a country's production and ecosystem possibilities — including climate stability, flood control, carbon sequestration, aquifer recharge, scenery, recreation, biological diversity, and so on. Burning a rainforest to clear the land shifts a country's PPC outward, giving the visual impression of an unmitigated improvement; but such development causes a movement along the country's PEPC, as ecosystem services are transformed into GDP. The slope of the PEPC is the marginal rate of transformation, which equals the ratio of the land's marginal marketable product to its marginal ecosystem product. Changes in technology create substitution and income effects that help explain the enclosure movement and the environmental Kuznets curve. Much as employment of the human resource can be restrained to allow more leisure, development of the natural resource can be restrained to preserve more ecosystem services. Commercial lobbying interests and rivalries for positional goods create distortions that move a country along its PEPC to a materialistic misallocation, with too little conservation. An idealistic misallocation is also possible, with too much preservation of the natural environment. Small is beautiful, up to a point, and that is evident in this diagram. Jacob Viner's [Viner, J., 1937. Studies in the Theory of International Trade. Harper and Brothers, New York] analytical objections to the PPC are revived.

A Theory of Liquidity and Regulation of Financial Intermediation

This paper studies a Diamond-Dybvig model of providing insurance against unobservable liquidity shocks in the presence of unobservable trades. We show that competitive equilibria are inefficient. A social planner finds it beneficial to introduce a wedge between the interest rate implicit in optimal allocations and the economy's marginal rate of transformation. This improves risk sharing by reducing the attractiveness of joint deviations where agents simultaneously misrepresent their type and engage in trades on private markets. We propose a simple implementation of the optimum that imposes a constraint on the portfolio share that financial intermediaries invest in short-term assets. Copyright , Wiley-Blackwell.