GE (version 0.3.0)

DCES: Displaced CES Utility Function and Displaced CES Demand Function

Description

Compute the displaced CES utility function and the displaced CES demand function (Fullerton, 1989).

Usage

DCES(es, beta, xi, x)
DCES_demand(es, beta, xi, w, p)
DCES_compensated_demand(es, beta, xi, u, p)

Arguments

es

the elasticity of substitution.

beta

a n-vector consisting of the marginal expenditure share coefficients.

xi

a n-vector. Each element of xi parameterizes whether the particular good is a necessity for the household (Acemoglu, 2009, page 152). For example, xi[i] > 0 may mean that the household needs to consume at least a certain amount of good i to survive.

x

a n-vector consisting of the inputs.

w

a scalar indicating the income.

p

a n-vector indicating the prices.

u

a scalar indicating the utility level.

Functions

• DCES: Compute the displaced CES utility function (Fullerton, 1989), e.g. (beta_1 ^ (1 / es) * (x_1 - xi_1) ^ (1 - 1 / es) + beta_2 ^ (1 / es) * (x_2 - xi_2) ^ (1 - 1 / es)) ^ (es / (es - 1) wherein beta1 + beta2 == 1.

  When es==1, the DCES utility function becomes the Stone-Geary utility function.

• DCES_demand: Compute the displaced CES demand (Fullerton, 1989).

• DCES_compensated_demand: Compute the displaced CES compensated demand (Fullerton, 1989).

References

Acemoglu, D. (2009, ISBN: 9780691132921) Introduction to Modern Economic Growth. Princeton University Press.

Fullerton, D. (1989) Notes on Displaced CES Functional Forms. Available at: https://works.bepress.com/don_fullerton/39/

Examples

# \donttest{
es <- 0.99
beta <- prop.table(1:5)
xi <- 0
w <- 500
p <- 2:6

x <- DCES_demand (
  es = es,
  beta = beta,
  xi = xi,
  w = w,
  p = p
)

u <- DCES(es = es,
          beta = beta,
          xi = xi,
          x = x)

SCES(es = es,
     alpha = 1,
     beta = beta,
     x = x)

DCES_compensated_demand(
  es = es,
  beta = beta,
  xi = xi,
  u = u,
  p = p
)

DCES_compensated_demand(
  es = es,
  beta = beta,
  xi = seq(10, 50, 10),
  u = u,
  p = p
)
# }