An indifference curve — indifference

This function gives points along an indifference curve in (q_dot_s/q_dot_s_orig, C_dot_o/C_dot_o_orig) space. The indifference curve assumes CES utility. The equation of the indifference curve is u_dot/u_dot_orig = [f_Cs*(q_dot_s/q_dot_s_orig)^rho + (1-f_Cs)*(C_dot_o/C_dot_o_orig)^rho]^(1/rho).

Usage

indifference_func(
  qs_qs0,
  qs1_qs0,
  Co1_Co0,
  f_Cs_orig,
  sigma,
  rho = (sigma - 1)/sigma
)

Arguments

qs_qs0: The ratio q_dot_s/q_dot_s_orig. Sweeping this variable (x) gives the indifference curve parameterized by the other arguments.
qs1_qs0: The x coordinate of a point on this indifference curve.
Co1_Co0: The y coordinate of a point on this indifference curve.
f_Cs_orig: The fraction of original spending on the energy service relative to the sum of energy service and other goods spending, calculated by C_dot_s_orig / (C_dot_s_orig + C_dot_o_orig).
sigma: The elasticity of substitution between the energy service and other goods.
rho: The exponent in the CES utility function. Default is (sigma-1)/sigma.

Value

The value of C_dot_o/C_dot_o_orig, given values of remaining arguments.

Details

This function is vectorized.

Examples

qs1_qs0 <- 1
Co1_Co0 <- 1
sigma <- 0.3
f_Cs_orig <- 0.01
DF <- data.frame(x = seq(0.5, 1.5, by = 0.1)) %>% 
  dplyr::mutate(
    y = indifference_func(x, qs1_qs0 = qs1_qs0, Co1_Co0 = Co1_Co0, 
                          f_Cs_orig = f_Cs_orig, sigma = sigma)
  )
DF
#>      x         y
#> 1  0.5 1.0180150
#> 2  0.6 1.0100956
#> 3  0.7 1.0056743
#> 4  0.8 1.0029720
#> 5  0.9 1.0012089
#> 6  1.0 1.0000000
#> 7  1.1 0.9991380
#> 8  1.2 0.9985037
#> 9  1.3 0.9980246
#> 10 1.4 0.9976545
#> 11 1.5 0.9973634