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NemiM [27]
3 years ago
10

The production function is f (L, M) = 5L1/2M1/2, where L is the number of units of labor and M is the number of machines. If the

amounts of both factors can be varied and if the cost of labor is $9 per unit and the cost of using machines is $64 per machine, then the total cost of producing 12 units of output is________.
a. $438.
b. $108.
c. $576.
d. $115.20.
e. $57.60.
Business
1 answer:
Anton [14]3 years ago
6 0

Answer:

The correct answer is option d.

Explanation:

The production function is given as:

f (L, M) =5L^{1/2} M^{1/2}

The total cost will be

= wL + rM

Here, w is the cost of labor or wages and r is the cost of capital or rent.

The cost of labor is given as $9 per unit and the cost of using machine is $64 per machine.

MPl

= \frac{dQ}{dL}

= \frac{5}{2}\frac{M}{L}^{1/2}

MPm

= \frac{dQ}{dM}

=  \frac{5}{2}\frac{L}{M}^{1/2}

\frac{MPl}{MPm} = \frac{9}{64}

\frac{M}{L} = \frac{9}{64}

M = \frac{9}{64}L

f (L, M) = 5L^{1/2} M^{1/2}

12 = 5L^{1/2} \frac{9}{64}L^{1/2}

12 = \frac{15L}{8}

L = \frac{96}{15}

L = 6.4

M = \frac{9}{64}\times 6.4

M = 0.9

Total cost

= wL + rM

= 6.4 \times 9 + 0.9 \times 64

= 57.6 + 57.6

= $115.2

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