{"id":4135,"date":"2019-02-20T09:52:50","date_gmt":"2019-02-20T16:52:50","guid":{"rendered":"http:\/\/blogs.pugetsound.edu\/econ\/?p=4135"},"modified":"2019-02-20T11:53:43","modified_gmt":"2019-02-20T18:53:43","slug":"do-mathematicians-do-economics-better","status":"publish","type":"post","link":"https:\/\/blogs.pugetsound.edu\/econ\/2019\/02\/20\/do-mathematicians-do-economics-better\/","title":{"rendered":"Do Mathematicians do Economics Better?"},"content":{"rendered":"

In my optimization class we were talking about maximin problems. \u00a0A maximin problem is a problem that maximizes the lowest outcome (maximize f when f(x1,x2,…xn) = min{x1,x2,…xn}. \u00a0Our professor made the claim that \u201c… economics is focused on maximin problems or should be focused on\u201d. I felt like this statement grossly understated my major and the range of economics. \u00a0Even the optimization problems we face in economics have a wide variety such as profit optimization, game theoretical optimization, utility optimization, etc. not to mention the other sectors of economics that don\u2019t include optimization. \u00a0However, he does deserve some credit. Maximin problems are one way to solve a particular problems in economics.<\/span><\/p>\n

When attempting to optimize it is nice to be all to confidently say choice x >= y, but comparing isn\u2019t always this easy. \u00a0An inequality can be difficult when x and y are not numerical values. Take the saying \u201c…comparing apple and oranges\u201d for example. \u00a0The saying is conveying that the attributes of an apple(x), are in no way similar to an orange(y), making it impossible to say one is greater than the other. \u00a0Believe it or not, economists have a solution to this problem; utility functions. Utility functions focus on one attribute; the sum benefit or cost of a choice or bundle. \u00a0We are all familiar with utility functions; u(x) where x represents bundles or possible choices, and u represents the utility received for choosing x. Since u(x) usually produces one numerical value(the utility made from x decision) it is easy to compare choices (>,< or =) in the domain of u. \u00a0This enables us to compare choices, and optimize our decision x. That was one hurdle economists have faced when comparing choices, but not the one that is uses maximin.<\/span><\/p>\n

What if the outcomes are numerical, but has but as multiple sets of values. \u00a0As an economist you\u2019re trying to compare the point (2,1) and (4,0) by inequalities. \u00a0One point is not strictly greater than the other. Similarly we can use our imagination to derive a function, a function that returns one value that can be compared to another singular value. \u00a0One of the functions is a min{} function where f(x,y) = min{x,y}. This is a specific function that is used to describe specific situations. This function is also the maximin problem I was referring to. \u00a0We are trying to maximize the minimum of the set (x,y). The decision mechanism the student was referring to was dictator games; <\/span><\/p>\n

Thought Experiment: \u00a0You are at dinner eating with your friends. \u00a0You have finished eating but still have a lot of food left over, and your friends have made the mistake of getting off-campus meal plans, so they\u2019re hungry. \u00a0One\u2019s a foodie and the other not so much, they only eat out of necessity. Who do you give your food to? And in what ratio? If you give all of your food to the foodie it will be appreciated and all you\u2019ll soothe their hunger, but someone will go completely unfed. \u00a0Even though the non-foodie won\u2019t appreciate the food you can\u2019t let them starve! That\u2019s horrible! Even if the overall happiness between the two of them is highest when the foodie gets all the food. So you devise a maximin problem that says; I am only as happiest as the saddest person between them. \u00a0This would feed the non-foodie only enough so that they are not starving and the foodie the rest, because they\u2019ll appreciate it. (\u201cThe Division Problem\u201d Planet Money)<\/span><\/p>\n

This problem can be generalized to many tough problems in economics, but it cannot be generalized to all of economics…or can it? \u00a0In economics we assume all resources are scarce. This means that we face allocating those resources to people in the best way possible. \u00a0One way to compare distributions is maximin problems. Could economics be a huge, confusing, indescribable maximin problem? Another mathematician making accidental economic revelations, Nash would be proud.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

In my optimization class we were talking about maximin problems. \u00a0A maximin problem is a problem that maximizes the lowest outcome (maximize f when f(x1,x2,…xn) = min{x1,x2,…xn}. \u00a0Our professor made the claim that \u201c… economics is focused on maximin problems or should be focused on\u201d. I felt like this statement grossly understated my major and the range of economics. \u00a0Even the optimization problems we face in economics have a wide variety such as profit optimization, game theoretical optimization, utility optimization, etc. not to mention the other sectors of economics that don\u2019t include optimization. \u00a0However, he does deserve some credit. Maximin Continue reading Do Mathematicians do Economics Better?<\/span>→<\/span><\/a><\/p>\n","protected":false},"author":581,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[763,754,16],"class_list":["post-4135","post","type-post","status-publish","format-standard","hentry","category-economics","tag-division-problem","tag-optimization","tag-planet-money"],"_links":{"self":[{"href":"https:\/\/blogs.pugetsound.edu\/econ\/wp-json\/wp\/v2\/posts\/4135","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.pugetsound.edu\/econ\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.pugetsound.edu\/econ\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.pugetsound.edu\/econ\/wp-json\/wp\/v2\/users\/581"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.pugetsound.edu\/econ\/wp-json\/wp\/v2\/comments?post=4135"}],"version-history":[{"count":5,"href":"https:\/\/blogs.pugetsound.edu\/econ\/wp-json\/wp\/v2\/posts\/4135\/revisions"}],"predecessor-version":[{"id":4140,"href":"https:\/\/blogs.pugetsound.edu\/econ\/wp-json\/wp\/v2\/posts\/4135\/revisions\/4140"}],"wp:attachment":[{"href":"https:\/\/blogs.pugetsound.edu\/econ\/wp-json\/wp\/v2\/media?parent=4135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.pugetsound.edu\/econ\/wp-json\/wp\/v2\/categories?post=4135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.pugetsound.edu\/econ\/wp-json\/wp\/v2\/tags?post=4135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}