Cost Minimizing Input Combination and Productive Efficiency

When firms are looking to minimize costs, they want to make the best use of their inputs (labor and capital). If you look at a graph of a production function, the outward bending curve shows you all of the ways you could most efficiently allocate your inputs. Anywhere outside that line is not possible, and anywhere under the line means you could be producing more output with the inputs you have. Every option on the line is a cost minimizing input combination (you’ve got options).

When firms are producing efficiently, that’s where their average total costs are at their minimum point. If you look at a firm’s costs on a “theory of a firm” graph, one of the lines will be ATC, or average total costs...a swooping “U” shape. The lowest point is where firms are producing most efficiently.

Think about it: wouldn’t you want your average costs as low as they can be? Producing at a quantity to the left on the graph would mean you could keep producing more, driving your average costs down. Producing at a quantity to the right on the graph would mean your average costs are going up when you’re producing more, which means you’re losing money by making more.

The low point is the sweet spot. This is also where ATC crosses with MC, or marginal cost (yes, always, and yes, there’s only one option here).

In theory, firms take both cost minimizing input combinations and productive efficiency into account. The first helps them create products efficiently, and the second helps them decide the quantity to make, and what price to sell it for.