"The only 'equations' which would have to be 'solved' [under socialism] would be those of the consumers and the managers of production. These are exactly the same 'equations' which are 'solved' in the present economic system and the persons who do the 'solving' are the same also. Consumers 'solve' them by spending their income so as to get out of it the maximum total utility; and the managers of production 'solve' them by finding the combination of factors that minimizes average cost and the scale of output that equalizes marginal cost and the price of the product. They 'solve' them by a method of trial and error, making (or imagining) small variations at the margin, as Marshall used to say, and watching what effect those variations have either on the total utility or on the cost of production. And only a few of them have been graduated in higher mathematics. Professor Hayek and Professor Robbins themselves 'solve' at least hundreds of equations daily, for instance, in buying a newspaper or in deciding to take a meal in a restaurant, and presumably they do not use determinants or Jacobians for that purpose." (page 88).The title of this post is meant to highlight that I find more to agree with with Lange on capitalism here than I have to agree with him about socialism, but I've conveniently cut off the quote before he got into socialism.
This is an issue I posed to my students in my history of economic thought class when we went over Walras, Jevons, and Menger (and it is perhaps easiest to see with Jevons and Menger precisely because they are not presenting the problem so formally as Walras). Do you need to know and use calculus to make decisions for the theory of the marginalists to be useful? If not, why not?
Well if you do then surely marginalism is not useful, because even those of us proficient in calculus don't use it in the vast majority of our decision making. My view is that you don't need calculus and marginalism is nevertheless very useful for modeling human decision making (and "modeling" here is the key). In the end, all the constrained optimization framework says is "keep doing X until doing more X makes you worse off". It requires very little behaviorally. The greatest burden imposed by marginalism is not in the area of behavior, it's in assumptions about the structure of preferences. We usually impose a few rules here. I've argued elsewhere that they are not very burdensome and fine as an approximation in the absence of anything better. Furthermore, there's no indication that loosening these assumptions qualitatively changes the results. Its only apparent effect is to make the math harder.
As Lange points out, we don't care about the math in everyday life. The purpose of the math is to generate models to study.