How Do You Know if an Isoquant Is Continuously Decreasing

Isoquants

Isoquants are typically fatigued on uppercase-labor graphs, showing the trade-off between majuscule and labor in the production function and the decreasing marginal returns of both inputs.

From: Electricity Cost Modeling Calculations , 2011

The Economic science (and Econometrics) of Cost Modeling

Monica Greer Ph.D , in Electricity Marginal Cost Pricing, 2012

ASIDE: Leontief Product Technology ^six

The implied 50-shaped isoquants ⁷ of the Leontief production office are shown in Effigy 4.4. Such engineering is referred to alternatively every bit "fixed proportions," "no substitution," or "input–output" engineering (or some iteration thereof). At any particular output level (Y*) there is a necessary level of capital letter (K*) and labor (L*) that cannot be substituted. Note that these levels are determined purely technologically. Increasing only labor inputs (from L* to 50′ for instance) will not result in whatsoever higher output. Rather, the extra labor, without the extra capital letter to piece of work with, volition be entirely wasted. The implication is that fixed proportions technology is "no less than a formal rejection of the marginal productivity theory. The marginal productivity of whatsoever [factor] … is zero" (Leontief, 1941, p. 38).

Figure four.4. Leontief production technology and Isoquants.

The production function for a no-substitute case can exist written equally

(4.48) $Y=\text{min}(K/v,L/u),$

which is also referred to as a Leontief production function—every bit this class was introduced by Wassily Leontief in 1941. Note that if K is at K* and L is at 50′, then

(4.49) $\mathrm{Thou}*/v<L\prime /u.\text{Thus},Y=\mathrm{Yard}*/5.$

If so, and then the technically efficient level of labor would, by definition, be where

(iv.50) $K*/v=L/u\text{or}L=(u/\mathrm{five})\mathrm{Thou}*,$

which, as is obvious in Figure four.4, is at L*. As a result, and then information technology is the example that the post-obit holds all forth the ray from the origin:

(four.51) $Y/\mathrm{50}=(1/5)\mathrm{One\; thousand}/L.$

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The Economic science (and Econometrics) of Cost Modeling

Monica Greer PhD , in Electricity Cost Modeling Calculations (2d Edition), 2022

ASIDE: Leontief Product Engineering science ^{half dozen}

The implied L-shaped isoquants ⁷ of the Leontief Production Function are shown in Figure 4.4. Such a engineering is referred to alternatively as "Fixed Proportions", "No Exchange", or "Input-Output" technology (or some iteration thereof). At any particular output level Y*, there is a necessary level of uppercase (Thousand*) and labor (L*) which cannot be substituted. Annotation that these levels are determined purely technologically. Increasing only labor inputs (from 50* to L′ for instance) will not effect in any higher output. Rather, the extra labor, without the actress capital to work with, will exist entirely wasted. The implication is that fixed proportions applied science is "no less than a formal rejection of the marginal productivity theory. The marginal productivity of any [factor] ... is nix" (Leontief, 1941, p. 38).

Figure 4.4. Leontief Production Technology.

Leontief (no commutation) isoquants.

(Source: MLGreer.)

The production function for a no-substitutes case tin can be written as:

(4.48) $Y=min\left(\mathrm{1000}/v,\mathrm{Fifty}/u\right)$

which is also referred to as a Leontief Production Function as this form was introduced past Wassily Leontief (1941). Notice that if Thousand is at K* and Fifty is at L′, then:

(4.49) $K⁎/v<L\prime /u.\text{Thus},Y=G⁎/5.$

If so, then the technically efficient level of labor would, by definition, be where:

(4.l) $K⁎/5=L/u\text{or}L=\left(u/v\right)G⁎$

which, equally is obvious in Figure 4.four, is at L*. Equally a result, then information technology is the case that the following holds all forth the ray from the origin:

(4.51) $Y/L=\left(\mathrm{i}/5\right)K/L.$

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Innovation and Energy Prices

David Popp , in Encyclopedia of Energy, 2004

one The Concept of Technological Change

It is useful to sympathize how economists decompose the reaction of individual actors to a toll change. Consider, for instance, the reaction of a house to higher energy prices. Economists employ a production role to correspond the human relationship between inputs and outputs. Typical notation is

$Y=f\left(\mathrm{50},K,E,M,t\right),$

where Y is output, L is labor, K is capital letter, Eastward is energy, M is materials, and t is applied science. A product office can be represented by an isoquant that illustrates all possible combinations of labor and energy that can produce a given level of output. Effigy i provides an example of a production process using two inputs: labor and energy. Note that along any one isoquant, technology is held constant; that is, each isoquant represents product possibilities for a given technology. The straight line P₀P₀ in the effigy is an isocost line. The isocost line represents all combinations of labor and energy that cost the aforementioned. Costs increase for isocost lines moving abroad from the origin. The business firm chooses how to produce a given level of output by finding where these ii lines are tangent. At that point, the costs of product are everyman. Graphically, this is the lowest possible isocost line that touches the isoquant.

Effigy ane. Diagram illustrating the apply of an isoquant and isocost line to find the cost-minimizing choice of inputs. At time t, the production function is represented by isoquant₀. Along the isoquant, total output is constant. Initial prices are given by the isocost line P₀P₀. (Notation: In this diagram, P does non stand for actual prices but is just a label for the relative price lines.) Initial production is at point A, where the two lines are tangent. This is the lowest possible isocost line that touches the isoquant. The interpretation is that this is the cheapest way possible to produce the level of output represented past the isoquant.

When energy prices rise, nosotros expect the firm to use fewer free energy inputs. In Fig. 2, an increase in energy prices makes the isocost line steeper, every bit shown by the line segment P′₀P′₀. Intuitively, for the same level of expenditure, the firm now purchases fewer units of free energy. As a upshot of the price increment, the cost-minimizing combination of labor and energy now involves more labor and less free energy. An example of this would be a firm making less utilise of energy-intensive machinery and replacing the machines' capabilities with more than manual labor. Such a change in reaction to a cost change, illustrated by the shift from betoken A to point B on Fig. ii, is known every bit cistron substitution. Note that the same production technology is being used but that different amounts of inputs are used in the procedure.

Figure ii. Diagram illustrating the distinction between factor substitution and technological modify. At time t, the production function is represented by isoquant₀. Initial prices are given by the isocost line P₀P₀. Initial production is at signal A. As free energy prices ascension, the isocost curve becomes steeper, as shown past the line P′₀ P′₀. As a result of the price increment, the choice of inputs shifts to point B; that is, more than labor and less energy are used. Because applied science is constant forth the isoquant, the shift from A to B represents factor exchange. During the next period, technological advances shift the isoquant to isoquant_ane. If relative prices remain the same, the cost-minimizing combination of labor and energy is now at bespeak C. The move from B to C is an example of technological change.

Of course, factor substitution is not the only reaction that a firm may have to higher energy prices. Over time, nosotros would expect new machines that utilize energy more than efficiently to be produced. New technology is represented by a new production function:

$Y=f(L,K,E,K,t^{\prime }).$

Because engineering science is constant along an isoquant, technological change results in an inward shift of the isoquant; the same level of output tin now exist produced using fewer inputs. In Fig. 2, technology shifts the isoquant from isoquant₀ to isoquant₁. Assuming that the ratio of prices for labor and energy remains the same, the choice of inputs moves from point B to betoken C. The movement from signal B to signal C on the effigy is an example of technological alter.

This process of technological change proceeds in stages. Writing in 1942, Schumpeter referred to the procedure every bit "creative destruction." First, an idea must be born. This phase is known equally invention. New ideas are then developed into commercially viable products. This stage is referred to equally innovation. Frequently, these two stages of technological alter are studied together under the rubric of inquiry and evolution (R&D). Finally, to have an result on the economy, individuals must choose to make utilize of the new innovation. This adoption process is known as diffusion. At each stage, incentives, in the form of either prices or regulations, will affect the evolution and adoption of new technologies. This article begins with an overview of results pertaining to innovation and diffusion. A discussion of diffusion follows.

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The Uppercase Goods Sector in LDCs: Economic and Technical Development

Howard Pack , in Merchandise, Stability, Technology, and Equity in Latin America, 1982

V REQUIREMENTS OF Price EFFICIENCY AND Blueprint INNOVATION

The long-term competitiveness of LDC capital goods producers depends on activities related to ii capacities: reducing excess product costs attributable to the types of inefficiencies cited earlier and undertaking research and specially altering designs.

In the longer term, the LDC producer must compete not only in cost but in design. The engineering science sector in developed countries engages in a considerable amount of inquiry. This leads to a steady menstruum of improvements, which reduce operating costs at the input prices in developed countries. Such alterations are relevant to LDC producers, especially those producing equipment under license. The licensee generally volition not exist able to obtain complete information on new improvements that the licensor makes to raise the operation of equipment. Moreover, these improvements frequently are not labor saving in the sense of requiring fewer workers per machine. Instead, the speed of the auto or its efficiency in using materials is increased. Depending on the price of the newer machine, potential buyers may prefer the newer design because a given investment expenditure volition result in a larger present discounted value. Thus, fifty-fifty if the LDC firms initially tin match or undercut the international price, there is an inexorable attenuation of their initial cost advantage, unless their production is upgraded.

The necessity of newer designs in the longer term is not express to the requirements of the export market place. Domestically produced equipment may initially exist bachelor at lower cost than imported equipment. Simply if strange companies improve the design of their equipment more than speedily than local ones, a point will be reached at which production costs arising from the use of locally produced equipment will exceed those associated with imported machinery. Unless the domestic engineering sector is protected, purchasers volition gravitate toward imports and the sector will exhibit stagnant product and excess chapters, much as the Indian textile-machinery sector has washed. ²⁵

The demand for research is likely to be greater if the LDC industry has not adapted the factor proportions of the equipment. The reason is that inquiry in developed countries is localized in the more capital-intensive function of the isoquant. But fifty-fifty if local designs are used, the need to offset the effects of new improvements from abroad will eventually occur. Equally long every bit domestically produced equipment is used in the product of commodities whose production is also possible with imported equipment, efficiency volition somewhen require domestic producers to meet this contest. These considerations are conveniently summarized in Fig. 1.

Fig. i. Choices facing equipment users.

In Fig. 1, let A denote the initial unit of measurement isoquant in the adult land, B the somewhat more than labor-intensive isoquant achievable by LDC-produced equipment, and w´w´ the initial wage–rental ratio. Initially, minimum costs are accomplished by producing with type-B equipment. If B remains unchanged while A moves toward the origin as a result of ongoing research, the ii techniques yield equal costs when A _i is reached. ²⁶ Any farther improvement leads to blazon-A equipment's becoming cheaper, even at LDC costs. It can also be seen that if considerably more labor-intensive processes, such equally C, are available, reflecting, say indigenous designs, these volition remain competitive for a longer time, until A _two is achieved. But fifty-fifty C, an indigenous technique, will eventually be displaced, unless it tin can be improved.

Thus although LDC production capable of replicating before vintages presents an attractive potential for achieving a desirable charge per unit of technical upgrading, the world is non this benign. Unimproved versions of B or C may not be competitive for very long, though this is an empirical question about which little is known. The desired goal—obtaining some indigenous control over the rate of introduction of technology—will surely be conditioned by the continuing design progress of equipment producers in adult countries. Without significant abilities to reduce costs and achieve design improvements, the scope for controlling a nation's technical development is limited.

The reason for the earlier emphasis on possible sources of cost reduction in LDC equipment production should now exist clear. For a time, LDC companies may, in the absenteeism of a pattern ability, forbid the loss of competitiveness past reducing costs of production through process research. But the efficiency gains from such improvements may be costly to obtain and are exhaustible. Reorganizing the flow of piece of work, improving maintenance, and cleaning the sand from casting-store floors are in one case-and-for-all changes, though they may have large, cost-cutting effects. ²⁷ Eventually, more fundamental efforts will be required to increase competitiveness, specially by design changes. By maintaining short- and intermediate-term competitiveness, nonetheless, disembodied efficiency gains tin can allow the gradual buildup of the requisite enquiry capacity. ²⁸ Building upwards that capacity is, of form, a major undertaking, which ranges from training technical personnel, to establishing institutions in which they are usefully employed, to developing institutes of weights and measures. ²⁹

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External Costs of Free energy

Darwin C. Hall , in Encyclopedia of Energy, 2004

1.4 Joint Pollutants, Nonconvexities, and Nondepletable Catalytic Pollutants

Chemical reactions do non follow the assumptions of economical models. Ozone (smog) is created past the reaction of hydrocarbons and NO ₁₀ . Unburned hydrocarbons are released when we produce, process, and eat petroleum to get energy. Nitrogen, approximately 78% of the atmosphere, is stable at low temperatures, but fossil fuel consumption releases oestrus that creates NO ₁₀ . The ozone isopleths in Fig. 5A , like to isoquants, give the combinations of reactive organic gases (ROGs) and NO _ten that create a given amount of ozone. Because the isopleths include regions with positive slopes, in these regions decreases in NO _x actually increase the corporeality of ozone, belongings ROGs constant, every bit shown past the arrow in Fig. 5A. The marginal do good of NO _x abatement kickoff rises and then falls, as shown in Fig. 5B, which is an example of nonconvexity.

Effigy 5. (A) Ozone isopleths. (B) Marginal benefit curve (MB) derived from isopleths.

Optimal abatement does not occur where the curves cross in Fig. 5B. First, if area A is less than B, it is better to do nothing (ceteris paribus). Second, emission control options typically reduce both NO _x and ROGs (mutatis mutandis), shifting the marginal do good bend. Third, nitrate compounds from the nitrogen oxides are particulates with an aerodynamic diameter <10   μm, small enough to skid through the nasal barriers and social club into the lungs. The human being body'south immune system reacts in means that cause irritation and exacerbate respiratory illness. Consequently, NO _x causes impairment straight as well as indirectly through ozone. Since NO _x acts as a goad in the germination of ozone, the aforementioned molecule tin can later contribute to particulate. The analogy in economic theory is a public "bad", which is nondepletable in use. Hence, the marginal benefit of abatement is institute by adding the demand for particulate abatement vertically to the demand for NO _x abatement derived from the need for ozone abatement. These complexities render obsolete the economic theory of externalities for application to energy from fossil fuel.

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Determinants of technical efficiency in the bioenergy industry in the EU28 region

Mohd Alsaleh , ... H.O. Mohd-Shahwahid , in Renewable and Sustainable Free energy Reviews, 2017

2.two Showtime stage: data envelopment analysis

As per erstwhile study [10], the DEA approach frames observations of input and output ratios through linear programming techniques. The linear programming substitution is acceptable between observed input groups on an isoquant (the aforementioned book of output is generated with reduction in the volume of the used inputs) that was assumed by the DEA statistical method. Previous written report [10,xiv] was the starting time to utilise the DEA approach to compute the efficiency of each decision-making unit (DMU), given past the maximum ratio of weighted outputs to inputs weight. The more output produced from the given inputs, the more efficient the production of the DMU. Based on before studies [4,sixteen] the technical efficiency model is framed in Eq. (1). As a outcome, the technical, pure technical and scale efficiency scores are restricted between the values of (0) and (1). To select the ideal weights, nosotros adopted the post-obit mathematical programming trouble:

(1) $\begin{array}{ccc}{}_{\mathrm{u},\mathrm{y}}{}^{\min }(\frac{{\mathrm{u}}^{\mathrm{v}}{\mathrm{y}}_{\mathrm{i}}}{{\mathrm{v}}^{\mathrm{v}}{\mathrm{x}}_{\mathrm{i}}}),\frac{{\mathrm{u}}^{\mathrm{5}}{\mathrm{y}}_{\mathrm{i}}}{{\mathrm{5}}^{\mathrm{v}}{\mathrm{ten}}_{\mathrm{i}}}\le \mathrm{ane},& j=\mathrm{ane},2,\dots ,\mathrm{northward},& \mathrm{u},v\ge 0\end{array}$

(two) $\begin{array}{ccc}{}_{\mathrm{u},\mathrm{\phi }}{}^{\min }\mathrm{u}^{\mathrm{v}}{){\mathrm{\phi }}^{\mathrm{v}}{\mathrm{10}}_{\mathrm{i}}}_{,}=1,& {\mathrm{u}}^{\mathrm{5}}{\mathrm{y}}_{\mathrm{i}}-{\mathrm{\phi }}^{\mathrm{v}}{\mathrm{k}}_{\mathrm{i}}\le 0,\mathrm{j}=1,2,\dots ,\mathrm{N},& \mathrm{\phi },\mathrm{\mu }\ge 0\end{array}$

(3) $\begin{array}{ccc}{}_{\mathrm{\theta },\mathrm{\lambda }}{}^{\min }\mathrm{\theta },\mathrm{y}\mathrm{i}+\mathit{Y}\mathrm{\lambda }\ge 0,& \mathrm{\theta }\mathrm{x}\mathrm{i}\mathrm{–}\mathit{10}\mathrm{\lambda }\ge 0,& \mathrm{\lambda }\ge 0\end{array}$

Eq. (ane) has an upshot of infinite solutions and therefore we impose the constraint ( ${\mathrm{v}}^{\mathrm{v}}\mathrm{10}$ i=1), which drives to Eq. (ii). We adjusted the notations in Eq. (ii) to reverberate the conversion from (u) and (5) to ( $\mathrm{\mu }$ ) and (φ), respectively, employing the duality in linear programming; an equivalent envelopment method of this issue is presented in Eq. (3), where (θ) is a scalar explaining the value of the efficiency result for the (ith) country and with a score between the values of (0) and (1); (λ) is the vector of (N*1) constants. The linear programming has to exist calculated (Northward) times, once for each country in the EU28 region. To calculate the technical efficiency under the hypothesis of Variable Return to Scale (VRS), the convexity constraint specifies how nearly the production function envelops the observed input and output integrations and is not needed in the constant return to scale (CRS) situation [72]. Regarding the input and output variables in DEA, written report [17] referred to the rule required to exist achieved to identify the number of inputs and outputs. The standard dominion formula that tin provide instruction tin be framed every bit:

(iv) $n\ge \mathit{max}\{m*s,\mathrm{three}(\mathrm{1000}+\mathrm{south})\text{}}$

While (N) refers to the number of DMUs, (One thousand) indicates the number of inputs and (S) points to the number of outputs. Since the bioenergy industry in the EU28 in underdeveloped, the meaning function of efficiency in bioenergy production is crucial as an important source of renewable, sustainable and dark-green free energy. Therefore, information technology is sensible to assume that the efficiency of bioenergy production in the intermediation role is critical as an effective aqueduct to provide energy for various sectors from renewable, sustainable and greenish sources of energy. Based on earlier studies [1,8,16,70,71], amongst others, the electric current study employs the technical efficiency method, which uses technical efficiency as the primary primal in improving the bioenergy manufacture in the EU28 region.

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Ecology efficiency for 192 thermal power plants in the Yangtze River Delta considering heterogeneity: A metafrontier directional slacks-based measure arroyo

Xingle Long , ... Jing Zhang , in Renewable and Sustainable Energy Reviews, 2018

2 Materials

Farrel [6] evaluated efficiency using the ratio between outputs and inputs. Charnes, Cooper and Rhodes [vii] proposed Information Envelopment Assay (DEA). Production possibility frontiers come up from the envelopment of all optimization points, which is also called an isoquant curve. Distance functions let for the proportional alter of both desirable and undesirable outputs (Shephard [8]). To overcome this disadvantage, Chung et al. [nine] introduced the directional altitude role (DDF), which allows for the disproportional change of desirable and undesirable outputs. However, DDFs often ignore input excesses or output shortfalls. Fukuyama et al. [10] proposed directional slacks-based measure by combining DDF and SBM(Slacks-based Mensurate) (Tone [11]). A Decision Making Unit (DMU) is SBM efficient if and only if information technology is DDM (directional distance function measure of efficiency) efficient (Färe and Grosskopf [12]).

Undesirable factors has attracted the swell interests from numerous scholars due to environmental degradation (Färe and Grosskopf [13]; Zhou et al. [14]; Long et al. [15]). Hua and Bian [16] discusses six different methods for treating undesirable factors in DEA: (i) ignoring undesirable factors in DEA models; (2) because undesirable outputs (inputs) every bit inputs (outputs); (3) adopting nonlinear DEA model to bargain with undesirable factors (Färe et al. [17]); (4) using a nonlinear monotone decreasing transformation for the desirable factors; (5) adopting a linear monotone decreasing transformation to handle the desirable factors (Seiford and Zhu [eighteen]); (6) directional distance function (Färe and Grosskopf [13)]. Zhou et al. [fourteen] classified DEA into radial, non-radial, slacks-based mensurate, hyperbolic, directional distance office in free energy and environmental studies according to dissimilar types of efficiency measurement. Zhang and Choi [xix] classified Malmquist–Luenberger (ML) into four kinds: contemporaneous, global, metafrontier and sequential ML according to different environmental production engineering science.

In nearly cases, efficiency is assessed within a group that shares the same production frontier, which might ignore technology heterogeneity and have estimate biases. DEA has been widely used to evaluate the efficiency of dissimilar entities, such as international system (Kummar [twenty], Wang et al. [21], Zhou et al. [22]), national or regional (Hu et al. [23], Tu [24], Wang et al. [25], Long et al. [4]), aggregated industries (Chen and Golley [26], Chen [27])，disaggregated industries such equally fisheries (Diane et al. [28]), paper plants (Chung et al. [9]), iron and steel (Wei et al. [29]), ceramic (Andrés [30,31]), cement (Oggioni et al. [32], Riccardi et al. [33], Long et al. [5]), oil refinery (Bevilacqua and Marcello [34]), wastewater handling plants (Hemandez-Sancho et al. [35]), transportation sectors (Chang et al. [36]) and other industries. Chen and Jia [37] evaluated environmental efficiencies of People's republic of china's manufacture from 2008 to 2012 through non-radial SBM model considering undesirable outputs. It is of import to reduce energy consumption in cryogenic processes for ability plants through a multistream plate-fin heat exchanger, which includes oestrus transfer calculation, surface analysis, menstruum resistance and design optimization(Wang and Li [38]).

Electricity and heat generation take the largest emission profiles, accounting for 42% of emissions worldwide in 2012 (International Energy Agency [39]). There is likewise a neat deal of literature on the efficiency of ability plants (Kumar et al. [40]; Zhou et al. [41]; Yang and Pollitt [42]; Bi et al. [43]; Heshmati et al. [44]; Zhou et al. [45]; Sueyoshi et al. [46]; Zhao et al. [47]; Wu et al. [48]). Arabi [49] evaluated Malmquist–Luenberger of thermal power plants in Iran by combining DEA with an algorithm. Munisamy and Arabi [fifty] employed a slack-based measure DEA to evaluate the eco-efficiency change of thermal power plants in Iran. Arabi et al. [51] also assessed the eco-efficiency of ability plants in Iran because heterogeneity. Yan et al. [52] adopted SBM (slacks-based measure) model to evaluate the carbon emission efficiency of thermal power industry in Cathay. Liu et al. [53] introduced a DEA cross-efficiency evaluation to estimate the eco-efficiency of coal-fired power plants. Wang et al. [54] proposed a model combined with DEA (Data envelopment analysis) and materials balance principle to measure the environmental efficiency of Red china'southward thermal power industry. Wang et al. [55] adopted DEA method to evaluate the ecology efficiency and effectiveness of China'southward thermal power industry. Monastyrenko [56] proposed a DEA model and Malmquist-Luenberger productivity alphabetize to compute the eco-efficiency of European electricity industry.

Fundamental literature on the subject has some weaknesses. First, about previous literature focuses on the ecology or ecology efficiency of nations or provinces, but few studies have examined the time and regional heterogeneity of ability plants at the house level in the Yangtze River Delta. Furthermore, many scholars have implemented directional distance functions or directional slacks-based measurement to explore environmental efficiency, which might have the disadvantage of ignoring the technology heterogeneity of different production frontiers. Many papers too analyze ecology or environmental efficiency from but a static or dynamic perspective, without a combination of these perspectives. Additionally, in order to explore the determinants of environmental or ecology efficiency, many scholars tend to carry traditional ordinary to the lowest degree squares, fixed-outcome, or random-effect analysis, all of which accept estimation biases due to the truncated distribution of ecology efficiency.

The potential bookish contributions of this newspaper are as follows. First, this paper mainly investigates environmental efficiency of 192 thermal ability plants of Yangtze River Delta through metafrontier directional slacks-based measure out, which considered engineering heterogeneity among unlike regions. Furthermore, we explore the time and regional heterogeneity of environmental efficiency. Tertiary, we besides compare ecology efficiency through both the static and dynamic viewpoints, and compare metatechnology gap ratios in order to testify whether technology heterogeneity has widened or narrowed. Last but not least, we also explore the determinants of ecology efficiency through bootstrapped truncated regression to test regional, time and coal intensity effects hypothesis.

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Free energy efficiency and economic system-broad rebound furnishings: A review of the bear witness and its implications

Paul E. Brockway , ... Victor Court , in Renewable and Sustainable Free energy Reviews, 2021

three Improved energy efficiency and economy-broad rebound furnishings

The decoupling in the in a higher place scenarios is largely the projected result of improved free energy efficiency throughout all sectors of the global economy. The scenarios include dissimilar types, sources, sizes, and costs of energy efficiency improvement, merely these improvements may lead to variety of rebound effects, which may not always be captured by the relevant models. Hence, it is first necessary to define what 'improved energy efficiency' means and how it is commonly modelled, and so to analyze how rebound furnishings can erode the associated energy savings.

three.1 Defining and modelling improved energy efficiency

Free energy efficiency is merely the ratio of useful outputs to energy inputs for a specified system – such as a motor, a motorcar tool, an industrial process, a firm, a sector, or an entire economy. Depending upon the system and the purpose at hand, inputs and outputs may be measured in energy terms, such as heat content or physical work; physical terms, such equally vehicle kilometres or tonnes of steel; or economical terms such as value-added or GDP [51]. Energy intensity is the inverse of energy efficiency and is most commonly measured in economic terms. Dissimilar free energy efficiency measures may be more or less appropriate for dissimilar systems and purposes.

Empirical and modelling studies relating to energy efficiency improvements vary in terms of:

1.

how they define the numerator and denominator of relevant energy efficiency measures (due east.g. starting time law thermodynamic, second law thermodynamic, physical, economical);

2.

the organisation boundaries to which these definitions apply (e.g. devices, households, firms, sectors, national economies);

3.

the methods used to aggregate dissimilar free energy types (i.e. whether and how differences in energy quality are accounted for [52];

4.

the source of improvements in energy efficiency (east.g. exogenous technical change, price-induced commutation, mandatory standards);

5.

the cost of achieving those improvements (eastward.grand. nothing-cost technical change, high-cost regulatory standards [53]; and

vi.

whether those improvements control for (or are assumed to be independent of) improvements in the productivity of other inputs, or increases in the utility obtained from other bolt.

Many aggregate economic models simulate the behaviour of an economy by a production role of the form: $Y=\lambda f(\pi K,\rho \mathrm{50},\tau E,\upsilon \mathrm{Grand})$ ; where Y is gross output, K is majuscule inputs, L is labour inputs, E is energy inputs, Thou is material inputs, and $\lambda ,\pi ,\rho ,\tau$ and $\upsilon$ are exogenous, time-dependent multipliers representing 'factor neutral', 'capital-augmenting', 'labour–augmenting', 'energy-augmenting' and 'materials-augmenting' technical change respectively. Technical change is causeless to meliorate the productivity ⁶ of individual inputs over fourth dimension (due east.m., ${\tau }_{t_1}>{\tau }_{t_0}$ for $t_1>t_0$ ) independently of changes in relative prices. Hence, energy-augmenting technical change should improve aggregate economical-based energy efficiency ( ${\theta }_{\mathrm{Due\; east}}=Y/\mathrm{Eastward}$ ), considering less energy is required to produce the aforementioned level of economic output. Increases in the relative price of energy should besides improve aggregate energy efficiency, because this encourages producers to substitute other inputs for free energy – just since costs have increased, output may fall. In contrast, technical change improves free energy productivity independently of changes in relative prices and without reducing output. ⁷

Energy-augmenting technical change ( $\tau )$ is one style of simulating improved energy efficiency, only this is not directly observed and hence is difficult to mensurate empirically [54]. In contrast, it is straightforward to measure the aggregate economic-based energy efficiency of a sector ( ${\theta }_E=Y/E$ ), merely this depends upon the level and cost of each input, the current state of engineering, and the level of output, as well as upon how individual inputs are measured and aggregated. In improver, a one-off or ongoing improvement in the productivity of energy inputs ( $\tau )$ will lower the toll of 'effective energy' ( $\tau E)$ and hence encourage producers to substitute (effective) energy for other inputs – which is ane of the mechanisms contributing to the rebound effect [55]. As a result, a 1% improvement in the productivity of energy inputs ( $\tau )$ within a house, sector or economy may not interpret to a 1% comeback in the aggregate free energy efficiency ( ${\theta }_E$ ) of that firm, sector, or economic system [56]. As well, changes in aggregate energy efficiency may consequence from changes in the level, price, and productivity of non-energy inputs, even in the absence of energy-augmenting technical change [56]. Similarly, improvements in energy efficiency at one level of aggregation (e.1000., an industrial sector) may not translate to improvements in energy efficiency at a higher level of aggregation (e.g., a national economy) owing to a diverseness of macroeconomic adjustments – for example, a shift towards more energy intensive appurtenances and services equally a event of a autumn in their relative price. More generally there is no necessary link betwixt improvements in ane measure out of free energy efficiency (e.g., $\tau$ ) and improvements in another measure (e.g., ${\theta }_E$ ) at either the same or different levels of aggregation. Since different studies define and measure energy efficiency improvements in different ways and for different levels of aggregation, neat care must be taken when comparing and interpreting their results.

three.2 Economy-wide rebound furnishings

Price-constructive energy efficiency improvements reduce the effective price of energy services, such every bit heating and lighting, and hence encourage increased consumption of those services, which in turn will partly showtime the free energy savings per unit of the energy service. This straight rebound effect is well established and is at present the subject area of a large and growing empirical literature [21,57–59], especially for efficiency improvements by consumers. However, energy efficiency improvements tin likewise trigger indirect and macroeconomic responses and associated rebound furnishings [59], with consequent impacts on energy consumption throughout the economy (see Appendix B for a summary of the different components of the straight, indirect and macroeconomic rebound effects).

For example, the savings in gasoline consumption from using fuel-efficient cars may be spent on other goods and services that as well crave energy to industry and use (indirect rebound). Similarly, the widespread adoption of energy efficient cars may reduce gasoline demand and hence gasoline prices, that volition in turn encourage increased consumption of gasoline and other energy (macroeconomic rebound) and have secondary impacts in other markets. Both direct and indirect rebound effects are partial equilibrium, since the methodologies employed to judge them (e.g., input-output models) hold input and commodity prices fixed throughout the economic system, and only consider variations in the effective price of the energy service itself. In contrast, the macroeconomic rebound effects are general equilibrium, since the methodologies employed to estimate them (east.k., computable general equilibrium models) allow input and article prices to vary throughout the economy. In practise, these different effects occur simultaneously and their net result - the economy-broad rebound effect – is normally expressed as a percentage of the expected economy-broad energy savings, as estimated from a counterfactual scenario where none of these adjustments occur [60,61].

Economy-wide rebound effects are challenging to judge, but in that location is growing evidence to suggest they may be large. For example, Saunders [26] uses data over the catamenia 1850–2000 to judge economy-broad rebound effects in backlog of 60% for Sweden, whilst Bruns et al. [62] uses information over the menstruation 1973–2016 to gauge rebound furnishings of ~100% for the US (both of these studies are reviewed beneath). Suggestive evidence is also provided by van Benthem [22] who finds that economic growth in developing countries is as energy-intensive every bit past growth in industrialized countries, despite dramatic improvements in the energy efficiency of private technologies. The equality in energy intensity suggests that the energy savings from improvements in individual technologies have been offset past other trends, such equally a shift toward more than energy-intensive patterns of consumption [x,22]. Similarly, Csereklyei et al. [10] show that the long-term decline in regional and global free energy intensity is due to countries getting richer, rather from them producing detail levels of wealth with less energy.

The post-obit two sections review some recent estimates of the magnitude of economy-wide rebound effects, including both ex-ante estimates from macroeconomic models and ex-post estimates from historical information. The selected studies were identified from keyword searches in Google Scholar, using the criteria that: a) the studies estimate rebound effects at the economic system-wide level; and b) they explicitly or implicitly include i or more of the macroeconomic furnishings listed in Appendix B. Thus, for example, nosotros exclude studies that focus upon individual energy services [63], or upon private economic sectors [64], besides as those that rely solely upon input-output models (e.g., [65–69]), considering the latter neglect macroeconomic rebound effects. While the resulting sample is not fully comprehensive, it provides a representative coverage of the available testify and includes the most highly cited studies in this area.

We split up the show into two groups: estimates from computable full general equilibrium (CGE) models (Section 4) and estimates from other methodologies (Department 5).

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