ppnewint8 {clptheory}

Capital stock model 4 using the New Interpretation.

Description

This function computes the uniform rate of profit, prices of production and labor values for a capital stock model using the New Interpretation. The model allows differential wage rates across industries and takes account of unproductive labor for labor value calculations.

Usage

ppnewint8(A, Ap, l, lp, w, wp, v, Q, Qp, D, Dp, K, t, lp_simple)

Arguments

A

input-output matrix (n x n).

Ap

input-output matrix for the subset of productive industries (m x m).

l

vector of complex labor input (1 x n).

lp

vector of complex labor input for the subset of productive industries (1 x m).

w

vector of nominal wage rates (1 x n).

wp

vector of nominal wage rates for the subset of productive industries (1 x m).

v

value of labor power (scalar).

Q

gross output vector (n x 1).

Qp

gross output vector for the subset of productive industries (m x 1).

D

depreciation matrix (n x n).

Dp

depreciation matrix for the subset of productive industries (m x m).

K

capital stock coefficient matrix (n x n).

t

turnover times matrix (n x n diagonal).

lp_simple

vector of simple labor input for the subset of productive industries (1 x m).

Value

A list with the following elements:

meig

Maximum eigen value of A

urop

Uniform rate of profit (as a fraction)

mrop

Maximum rate of profit (as a fraction)

ppabs

Price of production vector (absolute)

pprel

Price of production vector (relative)

lvalues

Labor values vector

mevn

Monetary expression of value using net output

mevg

Monetary expression of value using gross output

Nnonneg

Is N Nonnegative? (1=Y,0=N)

Nirred

Is N Irreducible? (1=Y,0=N)

References

Basu, Deepankar and Moraitis, Athanasios, "Alternative Approaches to Labor Values andPrices of Production: Theory and Evidence" (2023). Economics Department Working Paper Series. 347. URL: https://scholarworks.umass.edu/econ_workingpaper/347/

Examples

# ------ Data
# Input-output matrix
A <- matrix(
data = c(0.265,0.968,0.00681,0.0121,0.391,0.0169,0.0408,0.808,0.165),
nrow=3, ncol=3, byrow = TRUE
)
# Direct labor input vector (complex)
l <- matrix(
data = c(0.193, 3.562, 0.616),
nrow=1
)
# Real wage bundle
b <- matrix(
data = c(0.0109, 0.0275, 0.296),
ncol=1
)
# Gross output vector
Q <- matrix(
data = c(26530, 18168, 73840),
ncol=1
)
# Direct labor input vector (simple)
l_simple <- l
# Market price vector
m <- matrix(data = c(4, 60, 7),nrow=1)
# Uniform nominal wage rate
wavg <- m%*%b
# Vector of nominal wage rates
w <- matrix(data=c(wavg-0.5,wavg,wavg+0.5),nrow=1)
# Value of labor power
v <- 3/5
# Depreciation matrix
D <- matrix(data = c(0,0,0,0.00568,0.0267,0.0028,0.00265,0.0147,0.00246),
nrow=3, ncol=3, byrow = TRUE
)
# Capital stock coefficient matrix
K <- matrix(
data = c(0,0,0,0.120,0.791,0.096,0.037,0.251,0.043),
nrow=3, ncol=3, byrow = TRUE
)
# Diagonal turnover matrix
t <- diag(c(0.317, 0.099, 0.187))
# Compute prices of production
ppnewint8(A=A,Ap=A[1:2,1:2],l=l,lp=l[1,1:2],w=w[1,],wp=w[1,1:2],v=v,
Q=Q,Qp=Q[1:2,1],lp_simple=l[1,1:2],D=D,Dp=D[1:2,1:2],K=K,t=t)