Marginal cost function

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Consider that the total cost to produce a $x$ units of a product is given by the function

$$C(x) = 2000 + 3x + 0,01 x^2 + 0,0002 x^3$$

(a) Calculate the marginal cost at the production level $x=100$

(b) Calculate the cost to produce the product of number 101. Compare this result with the one obtained at item (a)

I calculated the marginal as $C'(100)$ but I don't know how to obtain the cost of the product number 101. Can I have some help?

thanks in advance!

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2 Answers

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a. The marginal cost at $x = 100$ is $C'(100)$.

$C'(x) = 3 + 0.02x + 0.0006x^2 \Rightarrow C'(100) = 3 + 0.02\cdot 100 + 0.0006\cdot 100^2 = 11$.

b. The cost to produce the $101$th unit is: $C(101) - C(100) = 11.07$.

They are not the same, and the difference between them is $0.07$ dollars = $7$ cents.

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To make $100$ units costs $2000+3\cdot 100 + 0.01\cdot100^2+ 0.0002\cdot100^3$.

To make $101$ units costs $2000+3\cdot 101 + 0.01\cdot101^2+ 0.0002\cdot101^3$.

If you have those two numbers, you can figure out how much the $101$th unit costs.

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