Marginal Analysis in Real World

Economists possess a variety of tools in their toolbox for assisting them in taking optimal decisions. One of the most important ones is marginal analysis. Marginal analysis can be defined as "A technique used in microeconomics by which very small changes in specific variables are studied in terms of the effect on related variables and the system as a whole." (Investowords.com). Marginal analysis is a method used by economists to determine the optimal level of activity in an organization. It observes the changes in the values of some variable, which are called marginal changes and studies the effects of the change in the values of a depended variable. Following this methodology, marginal analysis attempts to determine the maximum marginal benefit, which derives from the values of the two variables and where the activity is optimized.

Marginal analysis is based on fundamental principles of optimization theory. Thomas and Maurice state that "These principles of optimal decision making turn out to be nothing more than a formal presentation of commonsence ideas that you already apply, probably without knowing it in your everyday decisions." (Thomas and Maurice, 2008, p.83). This is a true statement and can be proved if we analyze our daily activities and the decision process we follow to take a decision. We apply unconsciously marginal analysis whenever we decide to work or not, to buy something or produce it at home, even to attend an event or not. I will explain in the following paradigms how marginal analysis concepts are used by anyone for decision making and that it is effective in most of the cases even if most of us conclude to different decisions than others. The main reason behind this is not that we failed to apply correctly optimization techniques but that each one tried to optimization the marginal benefit of different variables.

Continuing, I will provide as example for using marginal analysis concepts on real decisions, the decision of a news vendor about the optimal number of newspapers he must obtain daily to resell. The news vendor is responsible to refill his daily inventory. For any inventory level, if it is found that its expected marginal profit equals, or exceeds its expected marginal loss, then an additional unit must be added. If we set p to be the probability that the demand will be greater than or equal to a given supply, then the expected marginal profit (MP) can be easily found by multiplying p by the marginal profit obtained for every unit sold. Similarly, the expected marginal loss is determined by multiplying the marginal loss (ML) by (1 - p). The optimal decision may be simplified to the following inequality, p ≥ ML/MP+ML. The above inequality means that, as long as the value of p exceeds the ratio on the right-hand side, any additional unit must be kept in stock. For this example we will suppose that the marginal profit for each newspaper is 1 and the marginal loss for each one is 3. Now, lets also suppose that the news vendor has performed observations about the levels of sales during the previous periods and has concluded the following probabilities. The probability to sell 40 newspapers per day is 35%, to sell 50 newspapers is 40%, to sell 60 newspapers is 15% and to sell 70 newspapers is 10%. Solving the p ≥ ML/MP+ML inequality with the provided data we find that p, the probability that the demand to be greater or equal to a given supply, is p ≥ 0.75. Proceeding with this example and analyzing the probability distribution of the daily newspaper sales we will see that the probability of selling up to 60 newspapers is 75% which is the same with the p value so it can be proposed as optimal. As a conclusion, the news vendor must be supplied with 60 newspapers per day.

Moving on, marginal analysis can be used in several daily decisions for maximizing the efficiency of different kind of activities. Another example where we can use marginal analysis for optimizing an activity is the attempt to determine the level of a car's engine activity. Using the method of the first example, we can gather statistical data and determine the optimal car's speed where the km/Lt variable is optimized.

Then, marginal analysis can be used not only to find the optimal level of an activity but also to determine if it should be increased or not. We can use this rationale to decide how many hours to work per day. Let's suppose that our active hours are 16 per day. During these 16 we have to accomplish various activities. We do not mind working a few hours per day since we have 16 hours and we still have a lot of time to do other things that we have in mind. However, when we begin to increase out working hours per day this results to the reduction of the number of hours we can spend the other things. We need to start giving up more and more valuable opportunities to work those extra hours. So each extra hour of work cost more than the previous one. Now let's consider that we value the first working hour $2 and we add to each subsequent hour $1. If the we are paid $12 per hour, then applying simple marginal analysis concepts we can see that we should work up to 10 hours per day. This is because from the 11th working hour on the marginal cost equals and exceeds the marginal benefit. The above rationale is applied throughout our daily lives and enforces our decision making. We use marginal analysis methods for decisions like the quantity of food to cook, the amount of time we leave our car in the parking space or the even in our daily diet.

Closing, marginal analysis is a method used to optimize various decisions but is not a method that is dedicated to scientists and managers only. It used unconsciously by all of us in our daily actions and decisions. Economists just provide a solid background and strong foundations to this method in order to be successfully used to solve much more complicated optimization problems than the ones we face daily.

References

Marginal Analysis. (n.d.). Retrieved September 5, 2009, from Investowords.com website: http://www.investorwords.com/‌5652/‌marginal_analysis.html

Thomas, C. A.,&Maurice, C. (2008). Managerial Economics. McGraw-Hill .