How do I calculate marginal cost?

Question

Link to excel Marginal calculation

I want to know if I did the calculations for the terms mentioned in the question correctly.

I am trying to see how much the organization saves in costs if the organization does mass production.

I am really awful at Maths. I am supposed to analyze a business, suggest a strategy, but as part of the analysis, I am supposed to look at discounted cash flow which I have done and now I decided to look at marginal cost with mass production.

To explain what I have done for the marginal cost. I did a change in unit produced/change in total cost.

So for sell I3 I did =($E3-$E4)/($A3-$A4). Then I did the same for each sell going down? Is that right? This looks like (£28,872-26.760)/(200-100) = £21 but on excel it equals £17,60 I don't know what I am doing wrong

I need this for an assignment due in 5 days

Thanks

Answer 1

Your definition is correct. Think of marginal cost as the cost of producing the next good. Let $C$ represent total cost and $Q$ quantity. Then, we define marginal cost ($MC$) as:

$$ MC = \frac{\Delta C}{\Delta Q} . $$

In your spreadsheet, at $Q = 100$,

$$ \Delta C = \text{E}4 - \text{E}3 , $$

$$ \Delta Q = \text{A}4 - \text{A}3 . $$

So, at $Q = 100$,

$$ MC = \frac{\text{E}4-\text{E}3}{\text{A}4-\text{A}3} . $$

Note, because of the identity $C = FC + VC$, where $FC$ is fixed cost and $VC$ is variable cost, you also have the following:

$$ MC = \frac{\Delta C}{\Delta Q} $$

$$ = \frac{\Delta (FC + VC)}{\Delta Q} $$

$$ = \frac{\Delta FC + \Delta VC}{\Delta Q} . $$

Because fixed costs are fixed for all quantities, $\Delta FC = 0$ is always true, so we can further simplify to

$$ MC = \frac{\Delta VC}{\Delta Q} $$

So, instead of using column E in your spreadsheet, you could also have used column C. You'd end up with the same answer for marginal cost.

One more note: there shouldn't be a value in cell I12, since you don't have any data on the cost of producing an additional good at a quantity of 1000. I'm also not sure where you see a value of 28,872 - in the spreadsheet, it looks like the value in cell E4 is 28,520, so the calculation in Excel is correct.