MBA Math Sample Exercise

Economics: Marginal Analysis with Tables

Moving well beyond generic GMAT aptitude questions, the MBA Math sample exercises allow prospective MBA students to self assess their proficiency with the quantitative building blocks of the MBA first year curriculum.

MBA focused, time efficient, and convenient, the MBA Math online course builds your quantitative skills. Furthermore, the MBA Math transcript provides a concise summary for admissions officers that you are up to speed.

Visit www.mbamath.com to learn more!

Exercise

Global Corp. sells its output at the market price of $13 per unit. Each plant has the costs shown below:

Units of Output	Total Cost ($)
0	6
1	9
2	15
3	24
4	36
5	51
6	69
7	90

How much output should each plant produce?

Solution

Solution Commentary

(5:36)

Manual Solution

Each plant should produce the quantity that generates the greatest profit.

This solution shows two approaches.

Solution Approach 1

We can find the most profitable quantity by adding columns for Total Revenue and Total Profit to the original table.

Total Revenue is the price times the number of units. Total Profit is the difference between Total Revenue and Total Cost.

Units of Output	Total Cost ($)	Total Revenue ($)	Total Profit ($)
0	6	0	-6
1	9	13	4
2	15	26	11
3	24	39	15
4	36	52	16
5	51	65	14
6	69	78	9
7	90	91	1

The optimal quantity is 4 and the corresponding profit is $16.

Solution Approach 2

Alternately, and equivalently, we can find the most profitable quantity by adding columns for Marginal Cost, Marginal Revenue, and Marginal Profit to the original table.

Marginal Cost for a given quantity is the change in Total Cost from the previous unit to the current unit.

Marginal Revenue in this case is the price, which is the same for each unit.

Marginal Profit for a given quantity is the difference between Marginal Revenue and Marginal Cost.

Units of Output	Total Cost ($)	Marginal Cost ($)	Marginal Revenue ($)	Marginal Profit ($)
0	6	N/A	N/A	N/A
1	9	3	13	10
2	15	6	13	7
3	24	9	13	4
4	36	12	13	1
5	51	15	13	-2
6	69	18	13	-5
7	90	21	13	-8

We want to produce as long as the marginal profit of each successive unit is not negative.

As in the first approach, the optimal quantity is 4.

Excel Solution

Peter Regan teaches decision science courses at Dartmouth’s Tuck School and Duke’s Fuqua School. He also teaches pre-term quantitative skills courses at Tuck and Cornell’s Johnson School. He created the MBA Math self-paced, online pre-MBA quantitative skills course covering finance, accounting, economics, statistics, and spreadsheets.