# snqProfitWeights: SNQ Profit function: Weights of prices for normalization In micEconSNQP: Symmetric Normalized Quadratic Profit Function

## Description

Returns a vector of weights to normalize prices on a Symmetric Normalized Quadratic (SNQ) Profit function.

## Usage

 1 snqProfitWeights( priceNames, quantNames, data, method = "DW92", base = 1 ) 

## Arguments

 priceNames a vector of strings containing the names of netput prices. quantNames a vector of strings containing the names of netput quantities. data a data frame containing the data. method the method to determine the weights (see details). base the base period(s) for scaling prices (see details).

## Details

If argument method is 'DW92' the method of Diewert and Wales (1992) is applied. They predetermine the weights by

θ_{i} = \frac{ \displaystyle ≤ft | \overline{x}_{i} \right| p_{i}^{0} }{ \displaystyle ∑_{i=1}^{n} ≤ft| \overline{x}_{i} \right| p_{i}^{0}}

Defining the scaled netput quantities as \widetilde{x}_{i}^{t} = x_{i}^{t}\cdot p_{i}^{0} we get following formula:

θ_{i} = \frac{ \displaystyle ≤ft| \overline{ \widetilde{ x } }_{i} \right|}{ \displaystyle ∑_{i=1}^{n} ≤ft| \overline{ \widetilde{ x } }_{i} \right|}

The prices are scaled that they are unity in the base period or - if there is more than one base period - that the means of the prices over the base periods are unity. The argument base can be either
(a) a single number: the row number of the base prices,
(b) a vector indicating several observations: The means of these observations are used as base prices,
(c) a logical vector with the same length as the data: The means of the observations indicated as 'TRUE' are used as base prices, or (d) NULL: prices are not scaled.

## Author(s)

Arne Henningsen

snqProfitEst.
 1 2 3 4 5 6 7  data( germanFarms, package = "micEcon" ) germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput germanFarms$qVarInput <- -germanFarms$vVarInput / germanFarms$pVarInput germanFarms$qLabor <- -germanFarms$qLabor priceNames <- c( "pOutput", "pVarInput", "pLabor" ) quantNames <- c( "qOutput", "qVarInput", "qLabor" ) snqProfitWeights( priceNames, quantNames, germanFarms )