# snqProfitEla: Price Elasticities of SNQ Profit function In micEconSNQP: Symmetric Normalized Quadratic Profit Function

## Description

Calculates the Price Elasticities of a Symmetric Normalized Quadratic (SNQ) profit function.

## Usage

 1 2 3  snqProfitEla( beta, prices, quant, weights, scalingFactors = rep( 1, length( weights ) ), coefVcov = NULL, df = NULL ) 

## Arguments

 beta matrix of estimated β coefficients. prices vector of netput prices at which the elasticities should be calculated. quant vector of netput quantities at which the elasticities should be calculated. weights vector of weights of prices used for normalization. scalingFactors factors to scale prices (and quantities). coefVcov variance covariance matrix of the coefficients (optional). df degrees of freedom to calculate P-values of the elasticities (optional).

## Value

a list of class snqProfitEla containing following elements:

 ela matrix of the price elasticities. vcov variance covariance matrix of the price elasticities. stEr standard errors of the price elasticities. tval t-values of the price elasticities. pval P-values of the price elasticities.

## Note

A price elasticity is defined as

E_{ij} = \frac{ \displaystyle \frac{ \partial q_i }{ q_i } } { \displaystyle \frac{ \partial p_j }{ p_j } } = \frac{ \partial q_i }{ \partial p_j } \cdot \frac{ p_j }{ q_i }

Thus, e.g. E_{ij}=0.5 means that if the price of netput j (p_j) increases by 1%, the quantity of netput i (q_i) will increase by 0.5%.

## Author(s)

Arne Henningsen

snqProfitEst.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  # just a stupid simple example snqProfitEla( matrix(101:109,3,3), c(1,1,1), c(1,-1,-1), c(0.4,0.3,0.3) ) # now with real data data( germanFarms, package = "micEcon" ) germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput germanFarms$qVarInput <- -germanFarms$vVarInput / germanFarms$pVarInput germanFarms$qLabor <- -germanFarms$qLabor germanFarms$time <- c( 0:19 ) priceNames <- c( "pOutput", "pVarInput", "pLabor" ) quantNames <- c( "qOutput", "qVarInput", "qLabor" ) estResult <- snqProfitEst( priceNames, quantNames, c("land","time"), data=germanFarms ) estResult$ela # price elasticities at mean prices and mean quantities # price elasticities at the last observation (1994/95) snqProfitEla( estResult$coef$beta, estResult$data[ 20, priceNames ], estResult$data[ 20, quantNames ], estResult$weights, estResult$scalingFactors )