✏ Determine TC when given MC and FC

✏️ Of the following two TC functions, you can solve the MC of one of them but not the other. Which one can you find the MC of? What is the MC?

$$TC = 3q^2 + 7q + 15$$$$TC = 7q + 15$$

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✔ We can only find the MC of the second one. You can not find the MC of the first one. Bruce knows this and would never ask you.

q	TC	$MC = \frac{\Delta TC}{\Delta q} = \frac{7}{1} = 7$
0	15
1	22	7
2	29	7
3	36	7
4	43	7

$MC = 7$

With a TC like this, know that it is special and that you can immediately analyze it.  ✅

✏️ $TC = 32q + 150{,}000$
What is FC, AFC, VC, AVC, MC?

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✔ $FC = 150{,}000$
$AFC = \frac{150{,}000}{q}$
$VC = 32q$
MC = 32 ← the focus of this page.
$AVC = \frac{32q}{q} = 32$
With a linear functional form $MC = AVC$.
There is a lot of intuition behind this. Imagine you are the entrepreneur. The picture is that you pay 150,000 to get started, and every time you produce a new widget, it costs $32 ($MC = \$32$). Therefore, every widget costs you $32 (ie $AVC = \$32$).

Let’s examine AFC.

q	1	2	3	4	5	10	100	10,000	1,000,000
AFC	150,000	75,000	50,000	37,500	30,000	15,000	1,500	15	.15

Clearly, it is good to sell these things at scale, because you can spread your FC across millions of units.
Takeaway: FC always declines as q increases. Bruce demonstrates this on the following slide:

 ✅

✏️Suppose for a given product and given firm, marginal cost is always $2 and Fixed cost is always $20,000. What is the Total Cost function?

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✔ TC = ______←variable + ______←fixed.
$TC = 2q + \$20{,}000 \quad\text{✅}$

This will apply broadly.