Marginal Analysis:

Marginal Benefit - including Marginal Revenue and Marginal Cost


At the basis of all human needs comes the desire to maximize our output from the amount of our input, basically we want to get as much as possible from the least amount possible. Discovering the correct ratio of inputs vs. outputs to receive the most benefit from the effort is the one of the most important concepts in managerial economics. The concept that assists managers in deciding this ratio is called marginal analysis. This analysis refers to the optimal ratio between the marginal benefit received and the required marginal cost resulting from a single managerial decision. This concept can be demonstrated through the example of a simple decision such as: what is the optimal amount of ram that should be put in a new workstation. To make this decision a user has to decide the benefit received from additional ram vs. the additional cost required to purchase that ram. So long as the benefit from the additional ram is greater than the cost of the ram the optimal decision is to increase the ram until cost exceeds the benefit.

Benefit in the above example relates to the net benefit received from subtracting the total cost from the total benefit. The marginal analysis is referring to the incremental benefit equating from an additional input. The marginal (incremental) benefit for the first additional input is derived from the difference between the initial total benefit and the first total benefit as is the second marginal benefit derived from the first total benefit and the second. This method can also be used toward the marginal cost using the same process but using total cost instead of total benefit.

To show these concepts in another way we will use the example of the ram we discussed earlier in this discussion. The formula we will use to show the net benefit (NB) is NB(x) (20x + x2) - 5(x)2 where the benefit is demonstrated by the (20x + x2) and the cost is shown by the 5(x)2 or this could be explained by NB(x) B(x) - C(x) where B is benefit and C is cost. The next step to this process is to discover the totals for the revenues and costs for additional units of output, which is displayed in the table below..
Marginal_Table.JPG

With closer examination of the data resulting from incrementally adding units of output to our net benefit formula you can see that after the 2nd output unit of ram, the net benefit is maximized. This level of benefit is also achieved at the 3rd output unit, which is what we are looking for but the ambiguity of the results from the totals does not give a clear answer to which level of output would maximize benefit. To achieve a maximized net benefit the output variable should be increased to the point where marginal net benefit is equal to 0. This point is also where marginal benefit is equal to marginal cost, which can be seen in the graphs or in the table above. This can now be implemented as a rule to increase the accuracy and the speed of completing a marginal analysis by simply setting the marginal benefit marginal cost (MB MC) to achieve maximum benefit. This would be rather difficult, but luckily you are fluent in calculus and you know that the when changing the original formula to the first derivative the equation then turns into a marginal formula rather than a total formula. To demonstrate this theory, the math is shown below.
MarginalEquation.JPG
As you can see the math did not give exactly 3 where marginal net benefit is equal to zero and it is not possible to create a half stick of ram. In thesesituations it is required to do a bit more math to discover which level of output would equate marginal net benefit to zero. As you can see from the table above the math has already been solved and as shown graphically below the marginal revenue and the marginal cost are equal at 25 at the same level that marginal net benefit is equal to zero.

Margin2.jpg
Questions:

What is the maximum benefit a company could receive with a benefit curve of B(x) 600x + 5x2 and a cost curve of C(x) 20x2?
A. 15
B. 17
C. 20
D. 22

At what point would a manager choose to produce to maximize the revenue?
A. Net Benefit
B. NB(x) = B(x) - C(x)
C. Marginal Revenue
D. MNB(x) = MB(x) - MC(x)

Resources:
Baye R., Michael. Managerial Economics and Business Strategy. McGraw-Hill Irwin: New York, NY 2006.
Yeager, Tim. Contemporary Topics in Economics. "Marginal Analysis: Cost and Benefit". Retrieved from:
http://sorrel.humboldt.edu/~economic/econ104/marginal/

By:
Brent Rothgerber
MBA Econ 651