{"id":27,"date":"2014-11-14T12:54:22","date_gmt":"2014-11-14T12:54:22","guid":{"rendered":"http:\/\/commoncents.blogwyrm.com\/?p=27"},"modified":"2023-04-01T08:10:01","modified_gmt":"2023-04-01T12:10:01","slug":"comparing-advantages","status":"publish","type":"post","link":"https:\/\/commoncents.blogwyrm.com\/?p=27","title":{"rendered":"Comparing Advantages"},"content":{"rendered":"

I was having a conversation recently with a co-worker who was lamenting that the lead on his project didn't find much value in my friend\u2019s contributions.\u00a0 It seems that the team lead is better on all the various technologies they employ.\u00a0 I pointed out that even if that were true, which I doubt, my friend had an invaluable resource that no one could ever exceed \u2013 his time.\u00a0 Every human on this earth has, in a normal day (i.e., one in which they are neither first conceived nor in which they die) the same number of seconds as everyone else.\u00a0 This immutable fact of human existence leads to the idea of what economists call comparative advantage.<\/p>\n

What exactly is comparative advantage?\u00a0 It is best explained by examining a simplified version of my friend\u2019s situation.\u00a0 Suppose that we name my friend \u2018F\u2019 and his team lead \u2018L\u2019.\u00a0 Also, let\u2019s focus on two tasks that they each can perform and label them \u2018A\u2019 and \u2018G\u2019 (based on the actual tasks performed on my friend's project).<\/p>\n

To understand comparative advantage, we have to say a little about how each of the persons working on this project employs their skills to perform these tasks. \u00a0When L says he is better than F, he can only mean one of two closely-related things.\u00a0 Either he produces a better result in a fixed amount of time or he produces the same result in a shorter amount of time.<\/p>\n

This balance between quality and time-to-complete is present in every daily activity where expertise is involved.\u00a0 Do-it-yourself home projects are excellent examples where the weekend warrior spends two days trying to repair a sink or toilet when the same job could be done in a half-an-hour by a master plumber.<\/p>\n

So why doesn't L just get rid of F?\u00a0 After all, if L\u2019s skill is analogous to the \u2018master plumber\u2019 and F\u2019s to the \u2018weekend warrior\u2019 why even employ F?\u00a0 This is where the time comes in.\u00a0 Since L has the same amount of time available in a day as F, L can maximize the use of his expertise by relying on F to \u2018take work off of his plate\u2019.<\/p>\n

Let\u2019s make this more understandable by using concrete numbers.\u00a0 Assume that L can perform task A in 0.5 hours and with a profit of $50, and task G in 0.3 hours and results in a profit of $20. Next assume that F can perform task A in 0.7 hours with a profit of $50 and task G in 0.4 hours with a profit of $20.\u00a0 Note that in this example, I am imagining a situation where tasks A and G have to be done to a certain level of quality or no profit will result.\u00a0 This is the usual situation when purchasing a good like a computer where the whole thing has to work (would you buy a computer that was mostly completed but was missing a hard drive?). \u00a0\u00a0There are two final ingredients that have to be considered.\u00a0 First, how many of tasks A and G must the firm of L & F complete? \u00a0Let\u2019s assume that they need to complete at least 90 of task A and 80 of task G to live up to demand. \u00a0Finally assume that L and F are working a 40-hour work week.\u00a0 \u00a0I will only be examining a single week so I will not require that L or F work exactly 40 hours, but I will require that they stay within 0.1 hour (39.9 - 40.1) and I allow fractions of tasks completed. In a more realistic situation the output would be averaged many weeks and the fractions would disappear.\u00a0 Let\u2019s summarize the ground rules of our game in a little table.<\/p>\n\n\n\n\n\n\n
<\/th>\nTask A (90\/week)<\/th>\nTask G (80\/week)<\/th>\n<\/tr>\n
time<\/td>\nprofit<\/td>\ntime<\/td>\nprofit<\/td>\n<\/tr>\n
L<\/td>\n0.5<\/td>\n$50<\/td>\n0.3<\/td>\n$20<\/td>\n<\/tr>\n
F<\/td>\n0.7<\/td>\n$50<\/td>\n0.4<\/td>\n$20<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Comparing side-by-side we can see that L is indeed better than F at both tasks.\u00a0 That is to say that L completes both tasks faster than F for the same profit per task.<\/p>\n

If the firm of L & F wants to maximize their profit (and who doesn't) the operative question is then:\u00a0 what is the proper work load for L and F?<\/p>\n

Let\u2019s try a couple of examples.\u00a0 Suppose L & F decide that since L is better at everything they should let him try to maximize the number of tasks completed.\u00a0 It shouldn't be hard to convince yourself that the maximum number of tasks L can complete is 103 distributed between A and G as shown below (if he tries to do more tasks he has to do more on G\u00a0leaving too little time for F to produce the remaining units to complete all 90 A tasks and 80 G tasks). The resulting work division is shown in the table below netting the firm a profit of $6,100.<\/p>\n\n\n\n\n\n\n\n\n\n
<\/th>\nNumber of tasks<\/th>\nprofit\/task<\/th>\nhours\/task<\/th>\ntotal profit<\/th>\ntotal hours<\/th>\n<\/tr>\n
L does A<\/td>\n46<\/td>\n$50<\/td>\n0.5<\/td>\n$2300<\/td>\n23<\/td>\n<\/tr>\n
L does G<\/td>\n57<\/td>\n$20<\/td>\n0.3<\/td>\n$1140<\/td>\n17.1<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/td>\n$3440<\/td>\n40.1<\/td>\n<\/tr>\n
F does A<\/td>\n44<\/td>\n$50<\/td>\n0.7<\/td>\n$2200<\/td>\n30.8<\/td>\n<\/tr>\n
F does G<\/td>\n23<\/td>\n$20<\/td>\n0.4<\/td>\n$460<\/td>\n9.2<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/td>\n$2660<\/td>\n40<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Can their firm actually do better?\u00a0 The answer is yes and it involves having L do fewer tasks, focusing solely on performing A tasks, which have the higher profit margin.\u00a0 The maximum profit the firm can earn is with the following work load<\/p>\n\n\n\n\n\n\n\n\n\n
<\/th>\nNumber of tasks<\/td>\nprofit\/task<\/td>\nhours\/task<\/td>\ntotal profit<\/td>\ntotal hours<\/td>\n<\/tr>\n
L does A<\/td>\n80<\/td>\n$50<\/td>\n0.5<\/td>\n$4000<\/td>\n40<\/td>\n<\/tr>\n
L does G<\/td>\n0<\/td>\n$20<\/td>\n0.3<\/td>\n$0<\/td>\n0<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/td>\n$4000<\/td>\n40<\/td>\n<\/tr>\n
F does A<\/td>\n11<\/td>\n$50<\/td>\n0.7<\/td>\n$550<\/td>\n7.7<\/td>\n<\/tr>\n
F does G<\/td>\n80.5<\/td>\n$20<\/td>\n0.4<\/td>\n$1610<\/td>\n32.2<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/td>\n$2160<\/td>\n39.9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

which results in a net profit of $6,160 dollars.\u00a0\u00a0 Observe that in raising the profit of the firm, L actually drops his output from 103 tasks to 80 while F drops his profit from $2660 to $2160. In addition, L & F combined work 0.2 hours fewer. By allowing L to specialize, both L & F stand to make a larger profit than can be made otherwise.\u00a0 And even though F is seemingly inferior to L in all regards, his ability to provide the invaluable resource that is his time allows the firm as a whole to earn more profit.\u00a0 That is comparative advantage.<\/p>\n

At this point there are two additional observations to make.<\/p>\n

The first is that the example given above is particularly simple in that not only was L better than F at performing both tasks, he has an advantage over F in performing Task A that is greater than his advantage over F in performing Task G.\u00a0 This advantage is measured as the ratio of L\u2019s profit per hour to F\u2019s profit per hour on a given task.\u00a0 L earns $100\/hr on Task A compared to F\u2019s $71\/hr giving an advantage of 100\/71 = 1.40.\u00a0 Likewise, L earns $67\/hr on Task G compared to F\u2019s $50\/hr giving an advantage of 67\/50 = 1.34.\u00a0 The fact that L has the greatest advantage on the task with the greatest profit margin ($100\/hr) is what makes the analysis of the maximum profit easy to do.<\/p>\n

The situation becomes more nuanced if F can improve in his performance of Task A, completing it in 0.6 hours instead of 0.7.\u00a0 In this case, L still has an advantage on Task A at a value of 1.2 but it is now lower than his advantage on Task G.\u00a0 With F\u2019s new found skill, the firm can not only earn more money, but they can do so by having L spread his efforts between G and A tasks. \u00a0A possible (not neccessarily optimal) work load is<\/p>\n\n\n\n\n\n\n\n\n\n
<\/th>\nnumber<\/th>\nprofit<\/th>\nhours<\/th>\ntotal profit<\/th>\ntotal hours<\/th>\n<\/tr>\n
L does A<\/td>\n38<\/td>\n$50<\/td>\n0.5<\/td>\n$1900<\/td>\n19<\/td>\n<\/tr>\n
L does G<\/td>\n70<\/td>\n$20<\/td>\n0.3<\/td>\n$1400<\/td>\n21<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/td>\n$3300<\/td>\n40<\/td>\n<\/tr>\n
F does A<\/td>\n60<\/td>\n$50<\/td>\n0.6<\/td>\n$3000<\/td>\n36<\/td>\n<\/tr>\n
F does G<\/td>\n10<\/td>\n$20<\/td>\n0.4<\/td>\n$200<\/td>\n4<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/td>\n$3200<\/td>\n40<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

which nets a profit of $6500 for the firm.\u00a0 Note that L is still better than F in all regards, but L is not only doing more G tasks than before but his total number of tasks rises to 108 while F drops his task from 91.5 to 70.\u00a0 Imagine now a real business with many employees and many tasks and you can see how complex it is to actually determine how to maximize business performance.<\/p>\n

The second observation is that there is a human element to the problem of L & F that hasn't been addressed.\u00a0 I posed a parenthetical question above when I asked who wouldn't want to maximize their profit.\u00a0 Of course, in that context the profit was defined as dollars.\u00a0 In fact, people define profit in all sorts of different ways\u00a0 - job satisfaction, time off from work, lower stress, etc. \u2013 that make maximizing the outcome nearly impossible because of competing agendas and goals .\u00a0 For example, it is possible that the firm of L & F is willing to forego some dollar earnings so that L & F can each share in the tasks being performed.\u00a0\u00a0 It\u2019s for this reason that when this logic is applied in the broader context where L and F are human institutions (business, governments, or countries) there is a lot of friction in deciding what to do.<\/p>\n","protected":false},"excerpt":{"rendered":"

I was having a conversation recently with a co-worker who was lamenting that the lead on his project didn't find much value in my friend\u2019s contributions.\u00a0 It seems that the... Read more ><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-27","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/commoncents.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts\/27","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/commoncents.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/commoncents.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/commoncents.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/commoncents.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=27"}],"version-history":[{"count":11,"href":"https:\/\/commoncents.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts\/27\/revisions"}],"predecessor-version":[{"id":1091,"href":"https:\/\/commoncents.blogwyrm.com\/index.php?rest_route=\/wp\/v2\/posts\/27\/revisions\/1091"}],"wp:attachment":[{"href":"https:\/\/commoncents.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=27"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/commoncents.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=27"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/commoncents.blogwyrm.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=27"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}