What is the ‘transformation problem’ in Marxist economics?

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What is the ‘transformation problem’ in Marxist economics?

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Here is the gist:

All profit is derived from surplus labor – i.e. the value of the labor done by the worker minus the wages paid to said worker. So, for example, if a worker creates $10 of value per hour and you pay him $7 per hour, he generates $3 of surplus labor per hour and thus $3 in profit for you, the capitalist. Profit cannot be made from commodities like raw materials free of labor – you can’t buy iron for $X/lb and resell it for $X+1/lb (at least not long term). The only way to generate profit is to transform raw materials via labor.

Given that, it stands to reason that industries where more money is spent on labor should generate more profit for the capitalist (as opposed to industries where more money is spent on raw materials, machinery, etc.). Since raw materials can’t produce profit, the more you spend on the labor that transforms, the more profit you should be able to generate.

However, this is not the case. In practice, Marx found that rates of profit tended to equalize across industries regardless of what proportion of the cost was labor vs. materials.

This is the transformation problem – there is no general rule or formula where value from labor transforms the value of commodities to prices in the market – or to simplify, there is no universal translation of labor value to money (i.e. one unit of labor value = $20 profit). If there were, then we wouldn’t see equalized rates of profit across industries.

Marx’s solution was that there is a transformation factor – one unit of value = $20 * _t_ – which accounts for the difference between industries.