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The Classical Marxian Growth Model

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University of Massachusetts - Dartmouth

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Running head: THE CLASSICAL-MARXIAN GROWTH MODEL

The Classical-Marxian Growth Model

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THE CLASSICAL-MARXIAN GROWTH MODEL 2

Write down the five equations that represent the Classical-Marxian model with the

conventional (fixed) wage theory.

The five equations representing the Classical-Marxian model with the conventional (fixed) wage

theory are as follows.

The first equation is the rice system equation,

Ap(1+r) + wl = p with yp =1.

Then we derive the wage-profit curve

w = 1/ {y [I – (1+r) A]

-1

l}, where y = x(I-A) represents the vector for the net products

with x being gross products, I the identity matrix, A commodity inputs matrix, r the normal

profits rate, and w is the wage rate.

The third equation is the total employment, L.

L = xl = y(I-A)

-1

l

Here, maximum wage, W*, is obtained if profit is zero. If the wage is zero, the profit reaches a

maximum rate of R*.

The fourth equation would be derived in terms of rate of exploitation as ratio of profit to wage

wL. Thus,

s = P/W = (P/L)/w1 = (W*-w

1

)/w

1

= W*/w

1

– 1 = (1/tgα) – 1,

Where, tgα = w1/W* = w1/(1/L) = w1L/Y

tgß = (W*-w

1

)/Or

1

= (P/L)/(P/K) = K/L

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Running head: THE CLASSICAL-MARXIAN GROWTH MODEL The Classical-Marxian Growth Model Name Institution Affiliation THE CLASSICAL-MARXIAN GROWTH MODEL 2 Write down the five equations that represent the Classical-Marxian model with the conventional (fixed) wage theory. The five equations representing the Classical-Marxian model with the conventional (fixed) wage theory are as follows. The first equation is the rice system equation, Ap(1+r) + wl = p with yp =1. Then we derive the wage-profit curve w = 1/ {y [I – (1+r) A]-1l}, where y = x(I-A) represents the vector for the net products with x being gross products, I the identity matrix, A commodity inputs matrix, r the normal profits rate, and w is the wage rate. The third equation is the total employment, L. L = xl = y(I-A)-1l Here, maximum wage, W*, is obtained if profit is zero. If the wage is zero, the profit reaches a maximum rate of R*. The fourth equation would be derived in terms of rate of exploitation as ratio of profit to wage wL. Thus, s = P/W = (P/L)/w1 = (W*-w1)/w1 = W*/w1 – 1 = (1/tgα) – 1, Where, tgα = w1/W* = w1/(1/L) = w1L/Y tgß = (W*-w1)/Or1 = (P/L)/(P/K) = K/L THE CLASSICAL-MARXIAN GROWTH MODEL For the fifth equation, the wage share remains unchanged as well as exploitation rate. Thus we have, w = K/w1L What are the five endogenous variables? The five endogenous variables are market price p, profit rates r, interest I, gross product x, and wage w. What are the exogenous parameters? The exogenous ...
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