Output, Price and Distribution of Output

6.3 A Model of the Rural Industrial Sector

6.3.2 Output, Price and Distribution of Output

6.3.2.1 Output

Let 𝑌 denote the real output (net value added) of the rural industries sector. Output-input relation of this sector is described using the Leontief Production Function or the fixed- coefficient production function. Rural industries have a certain number of installed

𝐿𝐹_𝑟𝑎 𝑇𝐸_𝑟𝑎2

𝑇𝐸_𝑎𝑟1

Quantity of Labour Price

of Labour

output. To increase the full capacity output both machinery and labour have to be increased in a certain proportion.

[6-3] 𝑌 = 𝑚𝑖𝑛 ( ^𝐿

𝑎, ^𝐾

𝑣)

In equilibrium in the medium run, when both 𝐿 and 𝐾 vary we get, [6-3a] ^𝐿

𝑎= ^𝐾

𝑣

[6-3b] 𝑌 = ^𝐾

𝑣

where 𝐿 and 𝐾 are labour and capital inputs respectively to the production process, 𝑎 the labour required to produce one unit of output, that is, 𝑎 is labour to output ratio, reciprocal of labour productivity. 𝑣 is the capital required to produce one unit of output, that is 𝑣 is capital to output ratio, reciprocal of capital productivity.

6.3.2.2 Price Determination

Price of industrial goods is determined using mark-up pricing. Price (𝑝) of such goods is a mark-up⁷⁹ (𝜆) over short run unit cost that is, the price is cost-determined [6-4a]. We assume that marginal cost equals average cost. Short-run unit cost or marginal cost (𝜇) is the sum of marginal costs of material⁸⁰ (𝑏. 𝑐) and labour (𝑎. 𝑤_𝑛) .

[6 − 4𝑎] 𝑝 ₌ 𝑎. 𝑤_𝑛+ 𝑏. 𝑐 + 𝜆(𝑎. 𝑤_𝑛+ 𝑏. 𝑐)

[6 − 4𝑏] 𝑝 ₌ (1 + 𝜆)(𝑎. 𝑤_𝑛+ 𝑏. 𝑐)

[6 − 4𝑐] 𝑝 ₌ 𝜇(1 + 𝜆)

80Given Lee’s(1984) exhaustive work on pricing procedures, when talking about 𝜆, a mention of Lee’s(1984) views may not be out of place,. Lee had reservations about the widespread use of mark-up pricing in macroeconomic models. His argument was that most industries were large corporations, where mark-up method of pricing was not prevalent; it was a method of pricing adopted in smaller firms (Lavoie, 2016). As rural organised sector manufacturing industries in India certainly qualify in the genre of smaller industries than mega corps, we are possibly exempted from Lee’scriticism.

where 𝑤_𝑛 is the money value of the rural industrial wage rate that is, price of rural industrial labour, 𝑐 is the unit cost of material. 𝑤_𝑛 and 𝑐 are determined by factors external to the industrial sector. As mentioned earlier, 𝑤_𝑛 is decided by 𝑤_𝑎 and 𝑃_𝑓 , 𝑐 is decided by technological requirements of inputs per unit of output in the production process. The capitalist determines the mark-up keeping in mind the competitor’s price and the quantum of returns he expects⁸¹. In order to stay competitive firms may reduce mark-up when there is a significant rise in the industrial wage rate and vice-versa, thereby restricting variation in 𝑝. Thus, 𝜆 could be thought of as a function of wage rate.

[6 − 5] 𝜆 = 𝜆(𝑤_𝑛), In our model, ^{𝜕𝜆(𝑤𝑛)}

𝜕𝑤_𝑛 < 0 ⁸². For 𝜆 = 𝜆(𝑤_𝑛), price of industrial goods depends on the capitalist’s tweaking of 𝜆 with change in 𝑤_𝑛. Accordingly⁸³,

∆𝑝 𝑝

∆𝑤𝑛 𝑤𝑛

, the elasticity of industrial price with respect to wage rate, can be positive, negative or equal to zero.

81This is in line with Eichner’s theory on determinants of mark-up. There are different views on determinants of mark-up. Sawyer (1998) neatly sums up the Kaleckian view on mark-up. He states that in Kalecki’s early work (1954, cited in Sawyer 1998) degree of monopoly determined the extent of mark-up; however, in a later paper (1971b, cited in Sawyer,1998), Kalecki presented a different view: trade unions influenced mark-up of prices over costs and mark-up decided the real wage for a given ratio between material costs and costs. Thus, Kalecki moved from mark-up being decided by product market considerations to it being decided by both labour and product market considerations. Eichner (1976, cited in Lavoie, 2016) also advocated that mark-up over unit costs set prices; but he had a different take than Kalecki on what determines the degree of mark-up. For Eichner, mark-up was determined by the firm’s requirement to finance its output expansion and research and development. Lavoie (2016) points out that this view of deciding costing margin is popular as it links micro-economic pricing behaviour of the firm with macroeconomic growth model, where profit share rises with increase in growth rate of output due to increase in capital stock. Increase in mark-up augments profit share, whereas an increase in wage rate augments wage share. In Eichner’s framework, income required by capitalists drives mark-up.

Thus, the latter Kaleckian view that extent of mark-up is influenced by trade unions appears to be contrary to Eichner’s view.

82 Rotemberg and Woodword (1999) in their empirical analysis of data of American industries found that during a boom, variation in mark-up is counter-cyclical whereas variation of marginal cost, which is proportional to the average labour cost in their analysis, is

6.3.2.3 Distribution of Output

Let 𝑦_𝑛 denote the money value of net value added per unit of output viz. (the money value of unit output – material cost per unit of output).

[6 − 6] 𝑦_𝑛 = 𝑝 − 𝑏. 𝑐

For every unit of output produced, 𝑦_𝑛 gets shared between capitalists (second R.H.S.

term of [6-6b]) and labourers (first R.H.S. term of [6-6b]).

[6 − 6𝑎] 𝑦_𝑛 = 𝑊𝑎𝑔𝑒𝑏𝑖𝑙𝑙 + 𝑃𝑟𝑜𝑓𝑖𝑡𝑠, per unit of output [6 − 6𝑏] 𝑦_𝑛 = 𝑎. 𝑤_𝑛+ 𝜆(𝑎. 𝑤_𝑛+ 𝑏. 𝑐), from [6 − 4𝑎]

[6 − 6𝑐] 𝑦_𝑛 = 𝑎. 𝑤_𝑛+ 𝜆. µ, from [6 − 4𝑐]

The distribution of output between capitalists and labourers determines demand patterns for various goods and services. Put simply, rise in capitalists income will increase demand for goods and services required by capitalists. This in turn will lead to growth in output of industries manufacturing such goods and services. A closer examination of [6 − 6𝑏] indicates that change in capitalists income depends on quantum of change in 𝑎 and 𝑤_𝑛. We obtain capitalist’s income as a share of total income viz. profit share (𝜃) in terms of 𝜆 and unit cost as,

[6 − 7] 𝜃 = ^{𝜆(𝑎.𝑤𝑛+𝑏.𝑐)}

𝑎.𝑤𝑛+𝜆(𝑎.𝑤𝑛+𝑏.𝑐)) , 𝜃 = ^𝜆

𝜆+ ^{𝑎.𝑤𝑛} 𝑎.𝑤𝑛+𝑏.𝑐

𝜃 = ^𝜆

𝜆+^{𝑎.𝑤𝑛} µ

[6 − 7𝑎] 𝜃 = 𝜃(𝑤_𝑛, 𝑎) , follows from [6 − 6𝑏]

And labourers share (1 − 𝜃) as,

[6 − 8] (1 − 𝜃) = 1 − ^𝜆

𝜆+ ^𝑎𝑤𝑛 𝑎.𝑤𝑛+𝑏.𝑐

,

(1 − 𝜃) =

𝑎.𝑤𝑛 𝑎.𝑤𝑛+𝑏.𝑐 𝜆+ ^{𝑎.𝑤𝑛}

𝑎.𝑤𝑛+𝑏.𝑐

(1 − 𝜃) =

𝑎.𝑤𝑛 µ 𝜆+^{𝑎.𝑤𝑛}_µ

[6 − 8𝑎] (1 − 𝜃) = (1 − 𝜃)(𝑤_𝑛, 𝑎) , follows from [6 − 6𝑏]