# snqProfitFixEla: Fixed Factor Elasticities of SNQ Profit function In micEconSNQP: Symmetric Normalized Quadratic Profit Function

## Description

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

## Usage

 1 2  snqProfitFixEla( delta, gamma, quant, fix, weights, scalingFactors = rep( 1, length( weights ) ) ) 

## Arguments

 delta matrix of estimated δ coefficients. gamma matrix of estimated γ coefficients. quant vector of netput quantities at which the elasticities should be calculated. fix vector of quantities of fixed factors at which the elasticities should be calculated. weights vector of weights of prices used for normalization. scalingFactors factors to scale prices (and quantities).

## Note

A fixed factor elasticity is defined as

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

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

## Author(s)

Arne Henningsen

snqProfitEst and snqProfitEla.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  # just a stupid simple example snqProfitFixEla( matrix(1:6/6,3,2 ), matrix(4:1/4,2 ), c(1,1,1), c(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$time <- c( 0:19 ) priceNames <- c( "pOutput", "pVarInput", "pLabor" ) quantNames <- c( "qOutput", "qVarInput", "qLabor" ) fixNames <- c( "land", "time" ) estResult <- snqProfitEst( priceNames, quantNames, fixNames, data=germanFarms ) estResult$fixEla # price elasticities at mean quantities of netputs # and fixed factors # fixed factor elasticities at the last observation (1994/95) snqProfitFixEla( estResult$coef$delta, estResult$coef$gamma, estResult$data[ 20, quantNames ], estResult$data[ 20, fixNames ], estResult$weights, estResult$scalingFactors )