# List of equations by chapter

Open Access

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 8

Equation

Key equation

Description

Type

Equation number

Section

Chapter 1

ωt = Πt / Kt′

K

rate of integral profit

accounting convention

1.1

1§13

Xt 🢔 = [(δ+μ)K + wL + Π]t

K

output of production realised

accounting convention

1.2

1§14

Lα = Lα ϊ

K

actual labour (labour-capacity exerted at a power α)

definition

1.3

1§14

Xt 🢔 = [(δ +μ)K + mLα]t

K

output of production realised

exposition

1.4

1§14

Πt = mLαt – wLt

K

surplus-value (= integral profit)

exposition

1.5

1§14

ωt = Πt / Kt′ = [(mLα)t – (wL)t] / Kt′

K

rate of integral profit

implication

1.6

1§14

YGt 🢔 = [δK + mLα]t

K

implication (given concept of YG)

1.7

1§14

Yt 🢔 = [mLα]t

K

implication (given concept of Y)

1.8

1§14

Chapter 2

ΔK = åΠ

growth of capital [0 < å < 1]

definition

2.1

2§3

K/L = τ

capital to labour ratio

definition

2§4

L = (1/τ) K

growth of labour employed

definition [requirement]

2.2

2§4

u = f1L) + f2(pop)

unemployment [f1′< 0; f2′> 0]

definition

2.3

2§4

Δw = f1(Δu) + f2L)

change of wage rate [f1′< 0; f2′> 0]

exposition

2.4

2§4

et = Πt / wLt

rate of surplus-value

definition

2.5

2§5

ωt = (et) / (Kt′/wLt)

rate of integral profit

implication

2.6

2§5

et = f1(w)t + f2(α)t

rate of surplus-value [f1′<0; f2′>0]

implication

2.7

2§5

(ϊ)t = (|ϊ|)t

intensity of labour

physical and compliance limit | |

2.8

2§5

(α)t = (|α|)t

production power of labour

implication

2.9

2§5

ΔK = åewL

growth of capital

implication

2.10

2§6

Chapter 3 (time indices omitted)

W = wL

wages sum

definition

3.1

3§10

XP 🢔 = (δ +μ)K + mPLα

output, planned production of

exposition (cf. 1.4)

3.2

3§10

YP 🢔 = mPLα

exposition (cf. 1.8)

3.3

3§10

ΠP 🢔 = mPLα – W

surplus-value, planned production of

exposition (cf. 1.5)

3.4

3§10

Y = Π + W

definition of macro domain

3.5

3§10

E = I + C

expenditure (enterprises sector)

definition of macro domain

3.6

3§10

Y 🢔 = E

macro determination

3.7

3§10

Y 🢔 = I + C

idem

implication

3.7’

3§10

It 🢔 = f(ωt-1; Xdt; Pvft)

investment

determination

3.8

3§10

C = Ck + Cw

consumption, macro

definition

3.9

3§10

Π 🢔 = I + Ck + (Cw–W)

validation surplus-value, macro

implication (expositional)

3.10

3§10

Sw = W – Cw

saving out of wages

definition

3.11

3§10

Π 🢔 = I + Ck – Sw

K

validation surplus-value (by macro expenditure)

implication

3.12

3§10

Chapter 4

Explication

ωi = Πi / K′i = [miLα ϊi – (wL)i] / Ki

rate of integral profit

implication (cf. 1.3 and 1.6)

4.1

4§4-a

Xi = δKi + μKi + wLi + Πi

output of production realised

accounting convention (cf. 1.2)

4.2

4§4-a

pqi ≤ μKi + wLi

prime costs (output in terms of price and quantity vectors)

accounting convention

4.3

4§4-a

Πn /(Kn – LVi) > [pqi – (μKi +wLi)]/LVi

decision criterion for scrapping

accounting convention

4.4

4§4-a

Chapter 5

R = Π – iεK

K

internal profit

definition

5.1

5§1

ρ = R / (K – εK) = (mLα – wL – iεK) / (K – εK)

K

rate of internal profit on the internal capital

accounting convention (given 5.1)

5.2

5§1

ρ = (ω – iε) / (1 – ε)

rate of internal profit on the internal capital

implication (5.2 divided by K)

5.3

5§1

R = I + Ck – Sw – iεK

validation of internal profit

implication (3.10 into 5.1)

5.4

5§2

ρ = (I + Ck – Sw – iεK) / (K – εK)

K

rate of internal profit on the internal capital

implication (5.4 into 5.2)

5.5

5§2

Sw ≡ sw(wL)

saving out of wages

definition

5§3

ΔKt = It

growth of capital

definition

5.6

5§5

ΔK*t = It – scrapt

growth of capital, net

definition

5.6a

5§5

It = f(ρt-1; øt-1)

investment (positively related with ρ and negatively with ø)

determination (see text for distinction from 3.8)

5.7

5§5

Main sections

GCOL = Fg + Wg

state expenditure on collective goods and services

convention of state

8.1

8§1

Yg = Wg

net value-added (net product) of the state

convention of state

8.2

8§1

G* = (Wg + Fg) + Ig + (Qg + Zg) + Ag

state expenditure

accounting definition

8.3Ag

8§2

G = (Wg + Fg) + Ig + (Qg + Zg)

state expenditure (minus subsidies Ag)

definition

8.3

8§2

CFg = T + SSC + OR + B

current finance of state expenditure

accounting definition

8.4

8§4

CFg = G

idem

accounting definition

8.5

8§4

Cwg = Wg – Swg

consumption by the state’s wage earners

definition

8.6

8§6

Cqg = Qg – Sqg

consumption out of interest paid by the state

definition

8.7

8§6

Czg = Zg – Szg

consumption out of social security transfers

definition

8.8

8§6

Smg = Swg + Sqg + Szg

state-mediated savings

definition

8.9

8§6

Π 🢔 = [(Ie + Ck) – Swc] + G – [Swg + Sqg + Szg]

[italics] validation surplus-value

exposition

8.10

8§6

Π 🢔 = [(Ie + Ck) – Swc] + G – Smg

K

[italics] validation surplus-value

exposition (= 8.10)

8.11

8§6

Amplifications

Π 🢔 = Ie + Ck + (Cwe–We)

validation surplus-value, macro

amended notation

3.10*

8§6-b

Π 🢔 = Ie + Ck – Swe

validation surplus-value, macro

amended notation

3.12*

8§6-b

Y = Ye + Yg

definition of macro domain

8.6b.1

8§6-b

Ye 🢔 = [mLα]

[italics] net value-added by enterprises sector

implication of domain extension

1.8*

8§6-b

Ye = We + Π

[italics] net value-added by enterprises sector

implication of domain extension

3.5*

8§6-b

Π = Ye – We

[italics] surplus-value

implication of domain extension

3.5*’

8§6-b

Ee = Ie + Ck + Cwe

final non-state expenditure with enterprises

implication of domain extension

3.6’* and 3.8*

8§6-b

Eg = [Ig + Fg]+[(Cwg + Cqg + Czg)]

direct & indirect state exp. with enterprises

exposition

8.6b.2

8§6-b

Ye 🢔 = Ee + Eg

[italics] total expenditure with enterprises

definition of macro domain

8.6b.3

8§6-b

Π 🢔 = (Ee + Eg) – We

[italics] validation surplus-value, macro

implication of domain extension

8.6b.4

8§6-b

Π 🢔 = [(Ie + Ck) + (Cwe–We)] + [Ig + Fg]+[(Cwg + Cqg + Czg)]

implication (expositional)

8.6b.5

8§6-b

Π 🢔 = [(Ie + Ck) + (CweWe)] + [Ig + Fg + Wg + Qg +Zg] – [Swg + Sqg + Szg]

implication (expositional)

8.6b.6

8§6-b

R = Π – Qe

[italics] internal profit

definition

8.6c.1

8§6-c

R = [(Ie + Ck) – Swe] – [Qe] + [G – Smg]

validation of internal profit

implication

8.6c.2

8§6-c

Main section

T = Tsv + To

total taxes (case of taxation surplus-value)

definition

8.12

8§7

Πat = Π – Tsv

after tax surplus-value

definition

8.13

8§7

Πat = [(Ie + Ck) – Swe] + [G – Smg – Tsv]

K

idem, decomposed: validation perspective

implication

8.14

8§7

Amplification

T = Tr + To*

total taxes (case of taxation internal profit)

definition

8.7a.1

8§7-a

Rat = R – Tr

after tax internal profit

definition

8.7a.2

8§7-a

Rat = [(Ie + Ck) – Swe] – [Qe] + [(G – Smg) – Tr]

idem, decomposed: validation perspective

implication

8.7a.3

8§7-a

Main section

CFg = Tsv + To + SSC + OR + B

current finance of state expenditure (net)

implication

8.4

8§8

(8.12 substituted into 8.4)

TH = Tsv + To + SSC + OR

hybrid taxes

definition

8.15

8§8

THo = TH – Tsv

other hybrid taxes

definition

8.16

8§8

CFg = TH + B

current finance of state expenditure

implication

8.17

8§8

Sg = TH – G

current savings of the state

definition

8.18

8§8

Πat = [(Ie + Ck) – Swe] + [(G–TH) – Smg + THo]

after tax surplus-value: validation perspective

implication

8.19

8§8

Πat = [(Ie + Ck) – Swe] + [– Sg – Smg + THo]

K

idem

implication

8.20

8§8

# The unity of the capitalist economy and state

## Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 7 7 1