The MBA Math Monday series helps prospective MBA students to self assess their proficiency with the quantitative building blocks of the MBA first year curriculum.
The first MBA Math economics exercise explained that marginal analysis discovers a firm’s optimal production quantity and profit. Marginal analysis problems can be posed equivalently in terms of tables, formulas,or charts. The first exercise used data in tables. This exercise uses formulas but without invoking calculus.
Economics is tricky because it takes awhile to internalize the necessary chain of reasoning. Of course, it also has its own terminology (qth unit?) that is confusing at first. The goal is generally clear, at least in intro economics exercises. In this exercise, we want to know what level of production yields the highest profit. The challenge is to build a chain of reasoning from the problem as stated to the goal.
Once you’ve got a clear solution path in your head, the rest is simple algebra. Starting with algebra before you know where you’re headed is a common form of flailing for beginning (or returning) students.
Working with data in tables is more intuitive for many beginning students but, if you can accept that formulas represent the same information in shorthand, you can get more quickly to an answer with formulas. This one takes about 5 seconds once you know what you’re doing.
The last step in a marginal analysis is to introduce fixed costs to determine whether the optimal strategy results in a true profit or loss. This has been the Twilight Zone world of U.S. car companies recently. However much they’ve (debatably) been closing the gap in quality and marginal production costs, the industry-wide drop in demand combined with their massive fixed cost burdens put them in the position of working like hell to lose the least amount possible.
Exercise:
Suppose that you can sell as much of a product as you like at $92 per unit. Your marginal cost (MC) for producing the qth unit is given by:
MC=10q
If fixed costs are $350, what is the optimal output level?
Solution (with audio commentary): click here
Prof. Peter Regan created the self-paced, online MBA Math quantitative skills course and teaches live MBA courses at Dartmouth (Tuck), Duke (Fuqua), and Cornell (Johnson).