Why Productivity Matters

Bloomberg’s Shift: The Commission on Work, Workers, and Technology report tried to address the problems workers face with technological innovation. It did, however, praise technological advances because increased productivity is the only real way to advance our quality of life. Here’s why:

Consider the most basic model of a firm selling a single product in a competitive market. That means the firm can sell as much as it can produce at the market price, p. The firm’s inputs are labor, L, and capital, K. For simplicity, we’ll assume capital is fixed in the short-run. (It doesn’t affect the result.) The firm’s objective is to maximize profit, so it will produce efficiently. That means it will produce on its production function, f(L, K), a function that defines maximum output for given levels of inputs, L and K.

The firm’s objective is to maximize profit which equals revenue minus cost. Price times output (production function) is total revenue. Costs are wage (w) times labor and rental cost of capital (r) times capital. To keep the math simple, assume competitive input markets as well, so w and r are constant. The firm’s objective function is


This is a simple, unconstrained optimization problem with a single decision variable, L. (The bar over K is to denote that capital is constant.) To solve the problem, take the derivative with respect to the single decision variable (L) and set it equal to zero:


The result: pMPL = w, where MPL is the marginal product of labor (the derivative of the production function with respect to labor).

So, if we define our quality of life based on our income (wage), we want to increase w. That can only be done by increasing p or MPL. The former will raise wage, but not effectively increase real purchasing power because the increased wage will be offset by the higher price. Increasing MPL, however, will increase wage and allow workers to purchase more product (i.e., higher quality of life).

Note that this analysis also explains why you can’t simply mandate a higher wage. Product prices will rise to effectively negate the wage increase. The only real way to advance our quality of life (as mentioned in the Shift report) is to increase productivity.


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