snqProfitFixEla {micEconSNQP}

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 \delta coefficients.

gamma

matrix of estimated \gamma 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

See Also

snqProfitEst and snqProfitEla.

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
if( requireNamespace( 'micEcon', quietly = TRUE ) ) {
   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 )
}