Malmquist and Törnqvist Productivity Indexes: Returns to Scale and Technical Progress with Imperfect Competition

Caves, Christensen and Diewert proposed a method for estimating a theoretical productivity index for a firm using Törnqvist input and output indexes, augmented by exogenous estimates of local returns to scale. However, in order to implement their method, they assumed that the firm maximized revenue in each period, conditional on the observed input vector in each period, taking output prices as fixed. This assumption is not warranted when there are increasing returns to scale. Thus in the present paper, it is assumed that the firm solves a monopolistic profit maximization problem when there are increasing returns to scale and the results of Caves, Christensen and Diewert are modified in accordance with this assumption.Productivity, index numbers, Malmquist indexes, Törnqvist indexes, returns to scale, non-competitive behavior, flexible functional forms.

The Normalized Quadratic Expenditure Function

A concise introduction to the Normalized Quadratic expenditure or cost function is provided so that the interested reader will have the necessary information to understand and use this functional form. The Normalized Quadratic is an attractive functional form for use in empirical applications as correct curvature can be imposed in a parsimonious way without losing the desirable property of flexibility. We believe it is unique in this regard. Topics covered included the problem of cardinalizing utility, the modeling of nonhomothetic preferences, the use of spline functions to achieve greater flexibility and the use of a “semiflexible†approach to make it feasible to estimate systems of equations with a large number of commodities.Normalized Quadratic, expenditure function, flexible functional forms, elasticities.

Scanner Data, Time Aggregation and the Construction of Price Indexes

The impact of weekly, monthly and quarterly time aggregation on estimates of price change is examined for nineteen different supermarket item categories over a fifteen month period using scanner data. We find that time aggregation choices (the choice of a weekly, monthly or quarterly unit value concept for prices) have a considerable impact on estimates of price change. When chained indexes are used, the difference in price change estimates can be huge, ranging from 0.28% to 29.73% for a superlative (Fisher) index and an incredible 14.88% to 46,463.71% for a non-superlative (Laspeyres) index. The results suggest that traditional index number theory breaks down when weekly data with severe price bouncing are used, even for superlative indexes. Monthly and (in some cases even) quarterly time aggregation were found to be insufficient to eliminate downward drift in superlative indexes. In order to eliminate chain drift, multilateral index number methods are adapted to provide drift free measures of price change.Price indexes, aggregation, scanner data, chain drift, superlative indexes, unit values, multilateral index number methods, rolling window GEKS, rolli

Using a Constant Elasticity of Substitution Index to Estimate a Cost of Living Index: From Theory to Practice

Indexes often incorporate various biases due to their methods of construction. The Constant Elasticity of Substitution (CES) index can potentially eliminate substitution bias without needing current period expenditure data. The CES index requires an elasticity parameter. We derive a system of equations from which this parameter is estimated. We find that consumers are highly responsive to price changes at the elementary aggregation level. The results support the use of a geometric rather than arithmetic mean index at the elementary aggregate level. However, we find that even the use of a geometric mean index at the elementary aggregate level may not sufficiently account for the observed level of consumer substitution.Price indexes; elasticity of substitution; scanner data

Instrumentation of the variable-angle magneto-optic ellipsometer and its application to M-O media and other non-magnetic films

A new and comprehensive dielectric tensor characterization instrument is presented for characterization of magneto-optical recording media and non-magnetic thin films. Random and systematic errors of the system are studied. A series of TbFe, TbFeCo, and Co/Pt samples with different composition and thicknesses are characterized for their optical and magneto-optical properties. The optical properties of several non-magnetic films are also measured

Wavelength dependencies of the Kerr rotation and ellipticity for the magneto-optical recording media

Here we present wavelength dependence measurements of Co/Pd and Co/Pt superlattice samples with different compositions. We explore the relationship between the composition and the magneto-optical spectra. The induced magnetization in the Pt of Co/Pt or in the Pd of Co/Pd samples plays an important role in the magneto-optical activity, and is discussed for the samples measured. The experimental set-up and the samples used are described. The measurement results of one Co/Pt sample and a series of Co/Pd samples are discussed

Micro-optic lens for data storage

A new type of microlens for data storage applications that has improved off-axis performance is described. The lens consists of a micro Fresnel pattern on a curved substrate. The radius of the substrate is equal to the focal length of the lens. If the pattern and substrate are thin, the combination satisfies the Abbe sine condition. Therefore, the lens is free of coma. We analyze a 0.5 numerical aperture, 0.50 mm focal length lens in detail. A 0.16 numerical aperture lens was fabricated holographically, and results are presented

Biorefining of pigeon pea:Residue conversion by pyrolysis

Pyrolysis is an important technology to convert lignocellulosic biomass to a renewable liquid energy carrier known as pyrolysis oil or bio-oil. Herein we report the pyrolysis of pigeon pea wood, a widely available biomass in the Philippines, in a semi-continuous reactor at gram scale. The effects of process conditions such as temperature (400-600 ◦C), nitrogen flow rate (7-15 mL min−1) and particle size of the biomass feed (0.5-1.3 mm) on the product yields were determined. A Box-Behnken three-level, three-factor fractional factorial design was carried out to establish process-product yield relations. Of particular interest is the liquid product (bio-oil), of which the yield was shown to depend on all independent variables in a complex manner. The optimal conditions for highest bio-oil yield (54 wt.% on dry feed intake) were a temperature of 466 ◦C, a nitrogen flow rate of 14 mL min−1 and a particle size of 1.3 mm. Validation of the optimized conditions proved that the average (n = 3) experimental bio-oil yield (52 wt.%) is in good agreement with the predicted value from the model. The properties of product oils were determined using various analytical techniques including gas chromatography-mass spectrometry (GC-MS), gel-permeation chromatography (GPC), nuclear magnetic resonance spectroscopy (13C- and HSQC-NMR) and elemental and proximate analyses. The bio-oils were shown to have low ash content (0.2%), high heating value (29 MJ kg−1) and contain high value-added phenolics compounds (41%, GC peak area) as well as low molecular weight aldehydes and carboxylic acids. GPC analysis indicated the presence of a considerable amount of higher molecular weight compounds. NMR measurements showed that a large proportion of bio-oil contains aliphatic carbons (~60%), likely formed from the decomposition of (hemi)cellulose components, which are abundantly present in the starting pigeon pea wood. Subsequent preliminary scale-up pyrolysis experiments in a fluidized bed reactor (~100 gfeed h−1, 475 ◦C and N2 flow rate of 1.5 L min−1) gave a non-optimized bio-oil yield of 44 wt.%. Further fractionation and/or processing are required to upgrade these bio-oils to biofuels and biobased chemicals