snqProfitEla             package:micEcon             R Documentation

_E_l_a_s_t_i_c_i_t_i_e_s _o_f _S_N_Q _P_r_o_f_i_t _f_u_n_c_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

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

_U_s_a_g_e:

      snqProfitEla(  beta, prices, quant, weights )

_A_r_g_u_m_e_n_t_s:

    beta: matrix of estimated beta 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.

_N_o_t_e:

     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%.

_A_u_t_h_o_r(_s):

     Arne Henningsen ahenningsen@agric-econ.uni-kiel.de

_S_e_e _A_l_s_o:

     'snqProfitEst'.

_E_x_a_m_p_l_e_s:

        # 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 )
        germanFarms$qOutput   <- germanFarms$vOutput   / germanFarms$pOutput
        germanFarms$qVarInput <- -germanFarms$vVarInput / germanFarms$pVarInput
        germanFarms$qLabor    <- -germanFarms$qLabor
        germanFarms$time      <- c( 0:19 )
        pNames <- c( "pOutput", "pVarInput", "pLabor" )
        qNames <- c( "qOutput", "qVarInput", "qLabor" )

        estResult <- snqProfitEst( pNames, qNames, 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$estData[ 20, pNames ],
           estResult$estData[ 20, qNames ], estResult$weights )

