snqProfitFixEla function

Fixed Factor Elasticities of SNQ Profit function

Fixed Factor Elasticities of SNQ Profit function

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

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

Arguments

  • delta: matrix of estimated δ\delta coefficients.
  • gamma: matrix of estimated γ\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

Eij=qiqizjzj=qizjzjqi 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. Eij=0.5E_{ij}=0.5 means that if the quantity of fixed factor j (zjz_j) increases by 1%, the quantity of netput i (qiq_i) will increase by 0.5%.

See Also

snqProfitEst and snqProfitEla.

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 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 ) }