👨‍🏫 Notes on E-1000 Lecture 6

Summary of Costs

	Total	Fixed	Variable	Equation
Total (all items)	TC	TFC=costs that do not vary with q	TVC=costs that do vary with q	TC = TFC + TVC
Average (per item)	AC = ATC = TC / q	AFC = TFC/q	AVC = TVC/q	AC = AFC + AVC
Marginal (additional item)	$MC = \frac{\Delta TC}{\Delta q}$	$MFC=\frac{\Delta TFC}{\Delta q}$ = 0	$MVC=\frac{\Delta TVC}{\Delta q}$ =MC	MC = 0 + MVC

Cost graphs

• AFC always slopes downward. It gets closer and closer to the X axis. $(AFC = FC/q)$.
• Advanced: Because $AC = AFC + AVC$, AFC is also the distance between AC and AVC.

MC goes through the lowest points in AC and AVC. Advanced: When MC<AC, AC slopes down. Likewise, when MC>AC, AC slopes up. Advanced: When MC<AVC, AVC slopes down. Likewise, when MC>AVC, AVC slopes up.

✏️ Costs Fill-In-The Blanks Example

Fill in the empty cells in this diagram. The cells with a ❌ are not defined (ie there is no marginal cost or average costs for the zeroth unit) and you can skip the cells with a ➖.

q	MC	AC	AVC	AFC	TC	FC	VC
0	❌	❌	❌	❌	100
1	4	104	4		104		4
2	3			50	107
3	2	36.33	3	33.33	109	➖	9
4	1	➖	➖	➖		➖	10
5	2	➖	➖	➖	112	➖	12
6	3	➖	➖	➖	115	➖
7	4					➖	19
8	6					➖
9	8	➖	➖	➖	133	➖	33
10	11	➖	➖	➖		➖	44
11	15	➖	➖	➖	159	➖
12	20	➖	➖	➖		➖	79

✔ Click here to view answer

Answers with hints:

q	MC	AC	AVC	AFC	TC	FC	VC
0	❌	❌	❌	❌	100	TC=FC at 0	Always 0
1	4	104	4		104		4
2	3	TC/q = 53.5	VC/q =AC-AFC =3.5	50	107	10	TC-FC=7
3	2	36.33	3	33.33	109	➖	9
4	1	➖	➖	➖		➖	10
5	2	➖	➖	➖	112	➖	12
6	3	➖	➖	➖	115	➖	TC-FC= 15
7	4	119/7	19/7	100/7	FC+VC=119	➖	19
8	6	125/8	25/8	100/8	119+6=125	➖	19+6=25
9	8	➖	➖	➖	133	➖	33
10	11	➖	➖	➖	133+11	➖	44
11	15	➖	➖	➖	159	➖	44 +15
12	20	➖	➖	➖	159+20	➖	79

Advanced: Two special cases

Bruce included two special cases in the slides. These sometimes help on homework or on the exams! I’m happy to explain them in section, but you can skip them if you like as they are advanced.

Identifying Fixed and Variable Cost from a formula
Variable cost is the part of the formula that varies.

If,

$$TC=4q^2+3q+7, \text{ then } VC=4q^2+3q \text{ and } FC=7$$

✏️ Suppose that $TC=47q^2+542q+7+3q^4$. What are FC and VC?

✔ Click here to view answer

Clearly, $FC = 7, \text{so } VC=47q^2+542q+3q^4$
NOTE: you’ll never have to solve an equation like this!

When marginal cost is constant
Suppose MC=10, then
⇨ $TC = 10q + FC$ and (a straight line)
In general, if MC is constant, then $TC = MC×q + FC$

✏️ Suppose that $MC=\$37$ and $FC=\$123455$. What are TC and VC?

✔ Click here to view answer

$TC=37q+123455$
Using the trick from the previous problem: $VC=37q$

⇨ If $FC = 0$, then $AC = VC/q = 10q/q = 10$
The following two slides illustrate this special case:

The following example illustrates the constant marginal cost special case from above.

What is FC, AFC, VC, AVC, MC?

FC = 150,000
AFC = 150,000/q
VC = 32q
MC = 32 (when MC is a constant number like this, TC will be a straight line, like above)
AVC = 32q/q=32

Intuition/how to think about TC in the above example: 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).

q	1	2	3	4	10	100	10,000
TC	150,032	150,064	150,096	150,128	150,320	153,200	182,000

Let’s examine AFC from this example:

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 large 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: