Answer to Question #127984 in Microeconomics for Surya Salur

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.

What amount of engineers should be hired?

a. 2

b. 4

c. 6

d. 8

What amount of technicians should be hired?

a. 4

b. 2

c. 6

d. 8

Answer 1

The output is maximized, when $MPe/Pe = MPt/Pt$ and $4,000×E + 2,000×T = 28,000.$

$MPe = Q'(E) = 20 - 2E,$

$MPt = Q'(T) = 12 - T.$

$\frac{20 - 2E} {4,000} = \frac{12 - T} {2,000}$

E = T - 2,

$4,000×(T - 2) + 2,000T = 28,000,$

T = 6, E = 6 - 2 = 4.

So, the correct answers are:

b. 4 and c. 6.