Euler, Leonhard (1707-83)

Updated: Aug 20, 2021

Economists have found that certain propositions in pure mathematics developed by Leonhard Euler, a Swiss mathematician, can be usefully applied to problems in economic theory. The most notable application concems a theory of distribution based on marginal productivity. This theory states that factors of production (i.e. land, labour and capital) will each earn an income corresponding to the value of OUTPUT produced by the last unit of the factor employed. For instance, if a firm employs nineteen workers at an average wage of £20 per week, it will be willing to employ an additional worker as long as his output is worth more than £20. Moreover, if the twentieth worker yields, say, £21 per week it will be worthwhile to pay him more than £20 to attract him. The firm cannot, however, pay its workers different wages if they have the same skill, and therefore must pay all of them more than £20 per week. The earnings of each worker are therefore made equal to that at which it is just worthwhile to the firm to employ one more worker. A similar argument is applied to other factors of production and for the total national output as well as for a single firm. However, total output must, by definition, equal total income. National output is distributed among the three basic factors of production: land, labour and capital. No arithmetical reasons, however, could be thought of as to how the different factor incomes, derived from marginal productivities, could necessarily add up to the same as total output. Euler’s Theorem resolved the problem by showing what assumptions about the nature of the production function (which describes how the factors of production are combined to produce outputs) had to be made in order for the equality between the sum of incomes and the sum of outputs to be achieved.

Reference: The Penguin Dictionary of Economics, 3rd edt.

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