Electric Utility Cost Data for Electricity Generation by Nerlove and Christensen-Greene Data is similar to Electric Utility data described in McGuigan and Moyer, pp

Electric Generation Database The data have been provided by William Greene. Laurits R. Christensen and William Greene, “Economies of Scale in U.S. Electric Power Generation,” Journal of Political Economy 84, no. 4 (August 1976). The number of firms has fallen from 145 to 99 to account for holding companies.

Variable Definitions: The variables in this file are: COST Total cost in millions of current dollars KWH Millions of kilowatt hours of output P L The price of labor P K The rental price index of capital P F The price index for fuels S L The cost share of labor S K The cost share of capital S F The cost share of fuel Number of Observations: 99

Data Set OBSNO COST KWH PL PK PF SL SK SF

OBSNO COST KWH PL PK PF SL SK SF

OBSNO COST KWH PL PK PF SL SK SF

OBSNO COST KWH PL PK PF SL SK SF

OBSNO COST KWH PL PK PF SL SK SF

OBSNO COST KWH PL PK PF SL SK SF

COST KWH Notice the scatter. Costs appear to increase proportionally with output.

Simple Log-Log Regression LS // Dependent Variable is LOG(COST) Sample: 1 99Included observations: 99 VariableCoefficientStd. Errort-StatisticProb. C LOG(KWH) R-squared Mean dependent var 3.06 Adjusted R-squared S.D. dependent var 1.46 S.E. of regression Akaike info criterion-2.42 Sum squared resid Schwarz criterion-2.37 Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) 0.00 Substituted Coefficients: LOG(COST) = *LOG(KWH) Cost Elasticity is 0.84 (A 1% increase in output increases cost by 0.84%) Suggests Increasing Returns to Scale

Cost Functions: Linear Homogeneous in Prices If all prices double, costs double Cost Functions are linear homogeneous in prices. Cost =  0 Q  1 P f  2 P k  3 P L  4 or Log(Cost) = Log(  0 ) +  1 Log(Q) +  2 Log(P f ) +  3 Log(P k ) +  4 Log(P L ) and  2  3  4 = 1

 2  3  4  or  4  2  3 Cost =  0 Q  1 P f  2 P k  3 P L  2  3 Rearranging: (Cost/P L ) =  0 Q  1 (P f /P L )  2 (P k /P L )  3 Taking Logs ln(Cost/P L ) = ln  0 +  1 ln Q +  2 ln(P f /P L ) +  3 ln (P k /P L ) Generalizing, ln(Cost/P L ) = ln  0 +  1 ln Q +  1 (ln Q) 2 /2 +  2 (ln(P f /P L )) +  3 (ln (P k /P L )) +  4 (ln(P f /P L )) 2 /2 +  5 (ln (P k /P L )) 2 /2 +  6 (ln(P f /P L )) (ln (P k /P L ))  8 ln Q (ln(P f /P L )) +  9 ln Q (ln (P k /P L )).88.05

Equation: LOG(COST/PL) = C(1) C(7)*(LOG(PK /PL)))/2 + C(8)*(LOG(PF/PL)-MEAN(LOG(PF/PL)))*(LOG(PK + + Equation: LOG(COST/PL) = C(1) C(5)*(LOG(PK/PL)

Mean Output Long Run Average Cost LAC LMC ln C = c(1) + c(2)*ln(kwh) + ½ c(3)*ln(kwh) 2 + … Cost elasticity = c(2) + c(3)* ln(kwh) ,356

Using Cost Elasticity to find Minimum Efficient Size Cost Elasticity = MC/AC =  ln(Cost)/  ln(Output) Minimum Efficient Size is where cost elasticity equals one or Ave. Cost is a minimum From Regression: 1 = cost elasticity =  ln(Cost)/  ln(Output) = * [ln(kwh) – mean(kwh)] Solving for kwh where ther are constant returns to scale [ln(kwh) – mean(ln(kwh))] = (1 – 0.88) /.05 = 2.4 ln(kwh) = mean(ln(kwh)) = = 10.7 KWH = exp(10.7) = Therefore, at kwh = 4,000, ce =.88 at kwh = 44356, ce = 1 Subsequent analysis shows scale economies occur at a relatively smaller output. That is, at an output level that represents a smaller percentage of total market demand. 1. due to productivity improvements 2. market demands are growing Opens up the door to more competition

Many network industries exhibit economies of scope, density or scale From Shapiro and Varian, Information Rules One of the most fundamental features of information goods is that their cost of production is dominated by “first copy costs.” In the language of economics, the fixed costs of production are large, but the variable cost of reproduction are small. This cost structure leads to substantial economies of scale: the more you produce, the lower your average cost of production. But there is more to it than just economies of scale, the fixed costs and the variable costs of producing information have a special structure. The dominant component of the fixed costs of producing information are sunk cost, cost that are not recoverable if production is halted. … Sunk costs generally have to be paid up front, before commencing production. The variable cost of information production also have an unusual structure: the cost of producing an additional copy typically does not increase, even if a great many copies are made. These cost structures characterize the airline industry and others but the information goods is an extreme example. Lessons in Pricing: Don’t get greedy. Play tough

Airline Industry Hubs with Density Economies Old Route Structures Hub and Spoke LTL truckers tried it but found it provided too slow service in regional markets