Answer to Question #119611 in Microeconomics for harish

Question

Consider the Beiswanger Company, a small firm engaged in engineerng analysis. Beiswanger’s president has estimated that the firm’s output per month (Q) is related in the following way to the number of engineers € and technicians used (T): Q = 20E – E^2 + 12T – 0.5T^2 . The monthly wage of an engineer is $4,000, and the monthly wage of a technician is $2,000. President allots $28,000 per month for the combined wages of engineers and technicians.

Question 3: If the president is to maximize output, he must choose a bundle of engineers and technicians such that
a. MP^e / P^e = MP^t / P^t
b. MP^e / P^t = MP^t / P^e
c. MP^t / P^e = MP^e / P^t
d. None of the above

Answer 1

Correct answer: (A): MP^e / P^e = MP^t / P^t

Analysis

The optimal number of engineers and technicians to employ can be maximized by choosing a bundle of engineers and technicians such that MP^e / P^e = MP^t / P^t. The values of number of engineers € and technicians used (T) at which the marginal products per dollar spent on engineers and technicians are identical and this can be obtained by differentiating the firm’s output per month (Q) with respect to E and T. The marginal products of engineers and technicians are given by:

$MP_{E} = \varDelta Q / \varDelta E = 20 – 2E$

$MP_{T} = \varDelta Q / \varDelta T= 12 – T$

$MP_{E} /P_{E} = (20-2E) / 4,000 = (12 – T) / 2,000 = MP_{T} / P_{T}$