Manny Motors, Inc., can hire auto workers for $20 per hour, whereas robot arms cost $12 per hour to operate. The horizontal (labor) intercept of Manny Motors' isocost line is 3 million, and the vertical (robot) intercept of the isocost line is 5 million. Manny Motors' operating budget must be
A) $4.5 million
B) $8 million
C) $60 million
D) $80 million
E) $120 million

Question

Quizplus · Accepted Answer

The equation for Manny Motors' isocost line can be written as:

$20L + $12R = $3,000,000 + $5,000,000

Simplifying this equation, we get:

$20L + $12R = $8,000,000

Dividing both sides by $4, we get:

$5L + $3R = $2,000,000

This equation represents all the possible combinations of labor (L) and robots (R) that Manny Motors can use to produce a total cost of $8 million.

To find Manny Motors' operating budget, we need to know how much it plans to spend on production. If we assume that Manny Motors wants to produce at the minimum possible cost, it will choose the point on the isocost line where the cost is minimized.

The minimum point on the isocost line occurs at the point where the slope of the line is equal to the slope of the production possibilities curve (PPC). The slope of the PPC is determined by the ratio of the marginal product of labor to the marginal product of robots (MPL/MPR).

Assuming that MPL = 1 and MPR = 2/3 (since each robot arm can do the work of 1.5 workers), we can write:

$20/$12 = MPL/MPR

Simplifying this equation, we get:

MPL/MPR = 5/3

Multiplying both sides by R, we get:

MPLR/MPR = 5R/3

Simplifying, we get:

MPLR = (5/3)MPR

This equation represents the PPC.

To minimize cost, Manny Motors will choose the combination of labor and robots where the PPC is tangent to the isocost line. At this point, the ratio of MPL to MPR is equal to the ratio of the prices of labor to robots, i.e., MPL/MPR = $20/$12 = 5/3.

Substituting MPL/MPR = 5/3 into the PPC equation, we get:

(5/3)R = MPL = 1

Solving for R, we get:

R = 3/5

Substituting R = 3/5 into the isocost equation, we get:

$5L + $3(3/5) = $2,000,000

Simplifying, we get:

$5L + $1,800,000 = $2,000,000

Subtracting $1,800,000 from both sides, we get:

$5L = $200,000

Dividing both sides by $5, we get:

L = $40,000

Manny Motors will need to spend $40,000 per unit of labor, and $24,000 per unit of robots, to produce at the minimum possible cost.

To find Manny Motors' operating budget, we need to know how many units of labor and robots it plans to use. Since we don't have this information, we can't calculate the exact operating budget. However, we do know that Manny Motors' operating budget must be at least $2,000,000 (since this is the total cost of production at the minimum possible cost).

Out of the given answer choices, the closest one is C) $60 million.