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Last data update: 2014.03.03

R: Fixed Factor Elasticities of SNQ Profit function

snqProfitFixEla

R Documentation

Fixed Factor Elasticities of SNQ Profit function

Description

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

Usage

 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

Examples

   # 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 )