Growth in Output: Demand-Side and Supply-Side Conditions

6.3 A Model of the Rural Industrial Sector

6.3.4 Growth in Output: Demand-Side and Supply-Side Conditions

output. The empirical observations can be expressed as ∆𝑌 > 0 when ∆𝑤 > 0 and

∆ (¹

𝑎) > 0. To reconcile the empirical observations with the theoretical results we take a relook at [6 − 14𝑎]. The second empirical finding that the labour productivity is rising implies that the second term in the equation [6 − 14𝑎] has a negative bearing. We observe rising rural industrial output (𝑌^∗) with rising rural industrial wage rate (𝑤_𝑛) and falling labour per unit of output (𝑎), as the positive bearing of 𝑤_𝑛 (first term on R.H.S. of [6 − 14𝑎] ) surpasses the impact of 𝑎 (second term on R.H.S. of [6 − 14𝑎] )

of savings that is invested is determined by 𝑅, and this was the essence of the investment function conceived by Robinson (1962, cited in Basu and Das, 2016). We consider an independent investment function on the lines of the Foley-Michl investment function discussed in Basu and Das (2016), but from a medium-run perspective (given below in [6 − 17𝑎]). The Foley-Michl investment function is a generalised function that captures influences of the three decomposed components of profit rate on investment. In the case of medium run, that is in our case the decomposed components of the profit rate , are profit share(Ɵ) and capital per unit of output(𝑣). Thus, the investment function is a function of profit share and capital-output ratio. We further recall that profit share itself is a function of wage rate and labour productivity, as given in [6-7a].We are suppressing the third component of the profit rate, which is the effective demand component as we are not referring to the short-run. Each of the decomposed components has a distinct influence on investment. Investment increases with an increase in profit share and falls when capital is less productive, that is capital-output ratio is high. We have taken a simplified linear representation of [6 − 17𝑎] in [6 − 17𝑏], where the parameters have the property 𝛾₂ > 0 and 𝛾₃ > 0.

[6-17a] ^𝐼

𝐾 = 𝑙(𝑅) = 𝑙(Ɵ (𝑤_𝑛, 𝑎), 𝑣), [it follows from [6 − 7𝑎], that Ɵ = share of profit in value added = Ɵ (𝑤_𝑛, 𝑎)]; ^𝜕𝑙

𝜕𝜃> 0, ^𝜕𝑙

𝜕𝑣< 0 [6-17a] is a general form. We use a simplified linear form as below.

[6-17b] ^𝐼

𝐾 = 𝛾₁ + 𝛾₂ . Ɵ(𝑤_𝑛 , 𝑎) − 𝛾₃ . 𝑣 Rewriting [6-16] in terms of [6-17b] we get

It is evident from [6 − 18𝑏], that 𝑣 and the variables 𝑤_𝑛 and 𝑎 through their impact on 𝜃 determine the medium-run growth in output. These relationships and ramifications of changes in these variables are further explored below.

To understand the mechanism underlying growth in output in the medium-run, we take the total differentiation of [6 − 18𝑎].

[6 − 18𝑏]∆𝑔 = 𝛾₂ . ∆𝜃(𝑤_𝑛 , 𝑎) − 𝛾₃ . ∆𝑣

A. Change in 𝜃 with change in 𝑤_𝑛

𝐶𝑎𝑠𝑒 1: Change in 𝜃 with 𝑤_𝑛, for 𝜆 = constant,

^𝜕𝜃89

𝜕𝑤𝑛 = -{

𝜆.𝑎𝑏𝑐 (𝑎𝑤𝑛+𝑏𝑐)2 (𝜆+ ^{𝑎.𝑤𝑛}

𝑎.𝑤𝑛+𝑏𝑐 )²} , Thus, ^𝜕𝜃

𝜕𝑤𝑛 < 0, as the wage rate rises, profit share falls. This is obvious as, 𝑌 = 𝑊 + 𝜋, where 𝑊 is wage bill and 𝜋 profits.

Dividing both sides by 𝑌, we get, 1 = ^𝑊

𝑌 +^𝜋

𝑌, where ^𝑊

𝑌 is the wage share and ^𝜋

𝑌 is the profit share

Rise in 𝑤_𝑛 inflates the wage share and deflates the profit share, hence ^𝜕𝜃

𝜕𝑤𝑛 < 0.

𝐶𝑎𝑠𝑒 2: Change in 𝜃 with 𝑤_𝑛, for 𝜆= 𝜆(𝑤_𝑛),

𝜕𝜃⁹⁰

𝜕𝑤_𝑛 = 𝜆. ^𝑎

𝑎𝑤_𝑛+𝑏𝑐[𝑒 − ^𝑏𝑐

(𝑎𝑤𝑛+𝑏𝑐)], where 𝑒 =

𝜕𝜆 𝜆

𝜕𝑤𝑛 𝑤𝑛

is the elasticity of 𝜆 with respect to 𝑤_𝑛.

89 Refer Appendix 4, A4-5.

As 𝑒 < 0, it follows that ^𝜕𝜃

𝜕𝑤𝑛 < 0, for 𝜆= 𝜆(𝑤_𝑛).

Hence, for both 𝜆= constant and 𝜆= 𝜆(𝑤_𝑛) ^𝜕𝜃

𝜕𝑤𝑛 < 0. This implies that 𝑤_𝑛 and 𝜃 move counter to each other. A change in the profit share affects investment and growth. Thus, both investment and rate of growth of output increase with decline in 𝑤_𝑛 and vice-versa.

B. Change in 𝜃 with change in 𝑎 ^𝜕𝜃91

𝜕𝑎= −𝜆. ^{𝑏.𝑐.𝑤𝑛}

𝑎.𝑤_𝑛+𝜆(𝑎𝑤_𝑛+𝑏𝑐)

The result is on expected lines. As labour productivity increases that is labour to output ratio declines, profit share increases and vice versa. This is so as increased labour productivity decreases labour per unit of output, which leads to lower labour cost per unit of output. Thus, the capitalist’s share of output rises.

For 𝜆 = constant, [6 − 18𝑏] can be rewritten as

[6 − 18𝑐] ∆𝑔 = 𝛾₂ . [−

𝜆. 𝑎𝑏𝑐 (𝑎𝑤_𝑛 + 𝑏𝑐)² (𝜆 + 𝑎. 𝑤_𝑛

𝑎. 𝑤_𝑛 + 𝑏𝑐 )²

. ∆𝑤_𝑛− 𝜆. 𝑏. 𝑐. 𝑤_𝑛

𝑎. 𝑤_𝑛+ 𝜆(𝑎𝑤_𝑛+ 𝑏𝑐). ∆𝑎 ]

−𝛾₃ . ∆𝑣,

For = 𝜆(𝑤_𝑛), [6 − 18𝑏] can be rewritten as

[6 − 18𝑑] ∆𝑔 = 𝛾₂ . [𝜆. 𝑎

𝑎𝑤_𝑛 + 𝑏𝑐[𝑒 − 𝑏𝑐

(𝑎𝑤_𝑛+ 𝑏𝑐)] . ∆𝑤_𝑛

− 𝜆. 𝑏. 𝑐. 𝑤_𝑛

𝑎. 𝑤_𝑛+ 𝜆(𝑎𝑤_𝑛+ 𝑏𝑐). ∆𝑎 ]

As 𝑒 < 0, it follows that ^𝜕𝜃 < 0, for 𝜆= 𝜆(𝑤 ).

We tabulate the obtained results in Table 6-2.

Table 6-2 Results: Change in Medium-Run Growth in Output Case

No.

Case Description Result

1 Case 1

Change in profit share (𝜃) with change in the rural industrial wage rate (𝑤_𝑛), for 𝜆 = constant

Profit share increases with decrease in wage rate of rural industrial workers(𝑤_𝑛). Thus, ^𝜕𝜃

𝜕𝑤_𝑛< 0 for 𝜆 = constant

1 Case 2

Change in profit share (𝜃) with change in the rural industrial wage rate (𝑤𝑛), for 𝜆 = 𝜆(𝑤)

Profit share increases with decrease in wage rate of rural industrial workers(𝑤_𝑛) .Thus, ^𝜕𝜃

𝜕𝑤_𝑛< 0 for 𝜆 = 𝜆(𝑤)

2 Change in profit share (𝜃) with change in labour per unit of output (𝑎).

Profit share increases with a decline in labour per unit of output. Thus, ^𝜕𝜃

𝜕𝑎< 0

3 Case 1

Change in output growth rate (𝑔) with change in capital productivity and profit share for 𝜆 = constant

Output growth rate increases with increase in profit share for 𝜆 = constant and increase in capital productivity. Profit share increases with decline in rural industrial wage rate and decline in labour per unit of output.

3 Case 2

Change in output growth rate (𝑔) with change in capital productivity and profit share for = 𝜆(𝑤).

Output growth rate increases with increase in profit share for 𝜆 = 𝜆(𝑤) and increase in capital productivity. Profit share increases with decline in rural industrial wage rate and decline in labour per unit of output.

Empirically we found that output growth increased (∆𝑔 > 0), rural industrial wage rate increased (∆𝑤_𝑛 > 0), the labour productivity of rural industrial labour increased (∆ (¹

𝑎) > 0), i.e, 𝑎 declined and rural industrial capital productivity increased (∆ (¹

𝑣) >

0).

To understand the mechanism underlying this empirical observation, a relook at [6 − 18𝑐].

[6 − 18𝑐] ∆𝑔 = 𝛾₂ . [−

𝜆. 𝑎𝑏𝑐 (𝑎𝑤_𝑛 + 𝑏𝑐)² (𝜆 + 𝑎. 𝑤_𝑛

𝑎. 𝑤_𝑛 + 𝑏𝑐 )²

. ∆𝑤_𝑛− 𝜆. 𝑏. 𝑐. 𝑤_𝑛

𝑎. 𝑤_𝑛+ 𝜆(𝑎𝑤_𝑛+ 𝑏𝑐). ∆𝑎 ]

−𝛾₃ . ∆𝑣,

By our behavioural assumptions, the rate of growth in output (𝑔) increases with an increase in profit share and capital productivity; whereas profit share increases with decreases in wage rate (^𝜕𝜃

𝜕𝑤𝑛 < 0) and increase in labour productivity ( ^𝜕𝜃

𝜕𝑎< 0).

Empirically we have observed that profit share as well as wage rate are increasing. To reconcile this with the result obtained from the model, the inference is that the decline in 𝜃 consequent to the rise in 𝑤_𝑛 is offset by rise in 𝜃 associated with the decline in 𝑎.

Added to this is the positive impact of the last term (^𝜕𝑗

𝜕𝑣 . ∆𝑣) on the R.H.S. This accounts for the rise in capital productivity, which is bound to have a positive impact of profit rate and hence investment. The combined impact results in higher growth rate of output, i.e.

∆𝑔 > 0 .