Question

TC=8,000+3Q+0.004Q2 so its marginal cost is thus MC=3+0.008Q

Answer 1

Here, Given TC (Total Cost) and we have to show MC (Marginal Cost) is equal to 3+0.008Q

Marginal cost is the increase or decrease in total production cost if output is increased by one more unit.
The formula to obtain the marginal cost is

MC = Change in Total Cost / Change in Quantity.

Or

So as we know that TC is given here,

If TC = 8,000+3Q+0.004Q^2

So MC is just the differentiation of TC with respect to Q.

SOLVING IT

Differentiate TC with respect to Q,

We get,

0+3+2*0.004Q = MC

3+0.008Q = MC

Hence prove.