Question

uppose the cost function is given by \( C(Q)=100+5 Q+2 Q^{5} \) and the output level is 10 . What is the marginal cost at the current output lever?"

Answer 1

the marginal cost at the current output level (Q = 10) is 10,005.

Step-by-step explanation:

To find the marginal cost at the current output level, we need to calculate the derivative of the cost function with respect to output (Q) and then substitute the current output level (Q = 10) into the derivative.

The cost function is given as:

C(Q) = 100 + 5Q + 2Q^5

To find the marginal cost, we differentiate the cost function with respect to Q:

C'(Q) = d/dQ (100 + 5Q + 2Q^5)

Differentiating each term separately:

C'(Q) = 0 + 5 + 10Q^4

Simplifying the derivative:

C'(Q) = 5 + 10Q^4

Now, we substitute the current output level Q = 10 into the derivative:

C'(10) = 5 + 10(10^4)

= 5 + 10,000

= 10,005