MBA Math Sample Exercise

Economics: Marginal Analysis with Formulas

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

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

Solution Commentary

(3:29)

Manual Solution

Marginal Analysis

Set marginal revenue (MR) equal to marginal cost (MC) to find the optimal output level.

92=10*q

q=9.2

Total Profit is computed as Total Revenue minus Total Cost. Total Revenue is price times quantity.

Total Cost is fixed cost plus the sum of the marginal costs for each unit.

To determine the optimal integer quantity according to the marginal analysis, we check the total profit for the integer values above and below the non-integer q.

Total profit for q of 9 is $28.

Total profit for q of 10 is $20.

Thus, the marginal analysis shows that the optimal q is 9 with a corresponding profit of $28.

Consider Fixed Costs

One last check involves comparing the result from the marginal analysis with the fixed cost of producing nothing.

The result of the marginal analysis is the optimal solution.

The optimal q is 9 units.

Total Profit for the optimal quantity is $28.

Excel Solution

The Excel solution below implements a table to serve as a visual confirmation that the formula-based solution provided above is reasonable.

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.