Chapter 6: Production Magic: Pulling a Rabbit Out of the Hat
The costs of producing a given quantity of output are minimized at the point where the production isoquant is just tangent — or, in other words, just touching — the isocost curve. This point is illustrated as point A in Figure 6-6. The cost-minimizing combination of labor and capital are the quantities L0 and K0.
Figure 6-6: Costminimizing input combination.
Now comes the easy part. At the point where you minimize costs, the production isoquant and isocost curve are tangent. This means the slopes of these two curves are equal. Therefore
Or, if you rearrange that equation
Thus, you minimize costs when the marginal product per dollar spent on each input is equal for all inputs. And this holds true no matter how many inputs you use! Economists call the preceding concept the least cost criterion, and it’s an application of the equimarginal principle. To produce goods with the lowest possible production cost, you equate the marginal product per dollar spent.
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