Economies of scale in u s electric power generation 1976
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Economies of Scale in U.S. Electric Power Generation (1976). Authors: Laurits R. Christensen and William H. Greene Presented by: Jared Hayden Econ 435. Overview. Study aims to e stimate economies of scale for U.S. firms producing electric power

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Economies of Scale in U.S. Electric Power Generation (1976)

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Economies of Scale in U.S. Electric Power Generation(1976)

Authors: Laurits R. Christensen and William H. Greene

Presented by: Jared Hayden

Econ 435


Study aims to estimate economies of scale for U.S. firms producing electric power

Comparison between 1955 and 1970 using cross sectional data

Data analyzed using a translog cost function

The paper adds and compares results to the pioneering work on the subject done by Marc Nerlove(1963)

1976 Context

  • Electricity rates rising at “historically unprecedented rates”

  • Weiss proposes idea to vertically disintegrate the industry by separating generation from transmission and distribution (1975)

    • Weiss believed competition in generation would put downward pressure on electricity rates

  • Leads to critical question: Would significant scale economies be sacrificed by allowing many potential suppliers to compete in generation market?

    • If so, could offset the benefits of increased competition

Need for Study

  • The regulation of the U.S. electric power industry is on the firm level

  • Information on the economies of scale for firms is required to assess the affect of such a reorganization of the industy

  • This study aims to attain this information by using the neoclassical cost function approach, as Nerlove (1963) pioneered

  • Advancements in duality theory and functional form specification between 1963 and 1976 allow a more general model than that of Nerlove

  • The study places emphasis on distinguishing economies of scale and decreases in cost due to technical change.

    • Accomplish this by using cross-sectional data on firms with same access to plant design

    • Show change over time by analyzing Nerlove’s data from 1955 and new data from 1970

Electric Power Industry

  • Dominant form of electricity generation in time period was steam-driven turbines (i.e. coal plants)

    • Nuclear had yet to make and impact and hydro was running out of attractive dam sites.

    • Internal combustion engines primarily employed in only peak demand periods.

  • Study limits attention to conventional steam driven plants

    • Conventional plants account for 90% of sample firms’ total generation

  • Study also limits sample to investor owned utilities with upwards of $1 million in annual revenue

    • Accounts for 77% of total power produced in the U.S. in 1970

Economies of Scale in ElectricityGeneration

  • It is unanimously agreed upon that economies of scale exists in electricity generation

  • Debate lies over what range the economies of scale exists

    • Hulbert (1969) estimated that economies of scale exist all the way up to 25,000 MW

    • Johnson (1960) and Nerlove (1963) concluded that economies of scale were exhausted at a “relatively modest firm size”

Electricity Growth1955-1970

1955 sales to ultimate consumers: 369 billion kWh

1970 sales to ultimate consumers: 1,085 billion kWh

Number of firms declined slightly, so output per firm increased threefold!

Technology allowed firms to expand to exploit scale economies or rapid expansion has exhausted economies of scale??

Need for current econometric analysis.

Modeling Neoclassical Cost Function

  • Duality theory: cost and production functions which are dual to each other.

  • Chose to estimate cost function

    • Input levels endogenous

    • Output level and input prices exogenous

  • Allows implied demand equations that are linear in parameters and represent general production structures

  • Chose translog cost function

    • No restrictions on substitution possibilities

    • Allows scale economies to vary with output

    • Special cases of translog function can be directly compared to Nerlove’s findings

Translog Cost Function

  • Y = output Implications

  • Pi’s = prices of factor inputs (K,L,F)

  • Yij = Yji

  • Homogenous of degree 1 in prices

    • i.e. total cost increases proportionally

      to all prices increasing by factor, holding


Derived Functions

Demand function for production factors (Shephard’s Lemma!)

Cost Share of ith-factor input

Allen partial elasticities of substitution

Own-price elasticity of demand for ith factor of production

Scale Economies (1-elasticity of total cost with respect to output)

*positive = scale economies , negative = scale diseconomies

*natural interpretation in percentage terms

Translog Function Restrictions

  • Translog function does not impose homothetic or homogeneity restrictions

    • Homothetic: monotonic transformation of homogenous function

    • Homogenous: f(tx1 + tx2) = tk(x1 + x2)

    • Can be restricted and tested statistically

  • Can also restrict to being unitarily elastic by eliminating the second order term in prices

  • Homotheticity restriction:

  • Homogeneity restictions:

  • Unitary elasticity restriction:

6 Models

Model A: Translog Function

Model B: Translog with homotheticity restriction

Model C: Translog with homogeneity restriction

Model D: Translog with unitary elasticity restriction

Model E: Translog with homotheticityand unitary elasticity restrictions

Model F: Translogwith homogeneity and unitary elasticity restrictions

Estimation Procedure

  • OLS is attractive in simplicity, but neglects information in cost shares and multicollinearity may be a problem

  • Cost shares as a multivariate regression system inadequate as crucial cost function information is neglected

  • Chose procedure of jointly estimating cost function and cost shares a multivariate regression system

    • Specify additive disturbances for each of the share equations (assume joint normal distribution)

    • Allow nonzero correlations for single firm but zero correlations across firms(Zellner procedure)

    • Delete one of the share equations from system for system to work


  • Capital, Labor, and Fuel as inputs (K, L, F)

  • Require prices and cost shares for 3 inputs

  • Nerlove’s did not construct cost share data and mis-specified holding companies (possibly underestimating scale economies)

    • Christensen and Greene revised his work to compare results (reduced 1955 observations from 145 to 124)

  • 1970 data includes 114 firms and holding companies

  • Used same data procedures as Nerlove with two exceptions:

    • Used plant by plant fuel prices instead of state averages

    • Used plant by plant labor prices instead of state averages

  • Three data sets were used for each model (A-F)

    • 1955I, 1955II (revised), 1970

Empirical Results

Model A-1955II and 1970

  • T-ratios suggest nonhomotheticity parameters (Yyi) and substitution parameters (Yij) that neither homotheticity hypothesis nor unitary elasticity hypothesis is consistent with any of the data sets

  • Confirmed by table 5 by likelihood ratio statistics (all restricted models rejected handily)

Estimated Elasticities

  • Shows that there may be significant substitution possibilities at the firm level

Estimated Economies of Scale

  • Homogenous models incorrectly show inexhaustible scale economies

  • Non-homogenous models show the scale economies are being exhausted with in the output range of the sample

  • Unitary elasticity yields a worse fit to data, but little effect on estimation of scale economies

  • “erroneous” Nerlove model used incorrect formula

  • Shows U shape of Average Cost Curve

1955 Average Cost Curves (Nerlove)

  • Implies Nerlove underestimated scale economies

  • Shown by homogenous models C and F

Estimated Economies of Scale at Firm Level

  • Can observe trend of flattening average cost curve

  • Economies of scale decrease as the firm grows large

Model A Average Cost Curves (1955I, 1955II, and 1970)

Ranges of Significant Scale Economies

Model A-No significant economies range (1970)

*5% significance


  • There is large range of firm size yielding constant returns to scale

  • Aggregate cost related to number of firms operating in flat area of average cost curve

  • Drop in cost attributed mostly to technical change, not exploitations of economies of scale (still some relatively small gains from scale economies)

    • 1970 average cost curve downward displacement of 1955II average cost curve

    • Little correlation between cost reduction and firm growth rate

  • Reducing number of generation firms may yield cost savings

    • If all firms operated at minimum average cost, could save $175.1 million (47.9% labor, 28.3% capital, 23.8% fuel)

    • 33 firms could produce total output that was generated by 114 firms in 1970

Grand Conclusions

1955: scale economies available to most firms

1970: majority of electricity generation operating on flat portion of average cost curve

Great scale economies at low levels of output, but average cost curves flatten out at relatively moderate firm size

A small number of very large firms not required for optimal exploitation of scale economies

Policies designed to promote competition in generation cannot be faulted in terms of sacrificing scale economies


  • Potential question:

    • How would inclusion of modern generation mix change the paper? (Coal, Nuclear, Natural Gas)

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