1. Today’s lecture notes will be available
on the website, in PowerPoint format
Announcements:
Next Week: WS 11-13
Tues: Activity 3
Fri: Hwk 3 (WS )
Finish WS 8 & 9, and do WS10 this weekend.
We expect to return your midterms on Tues.
Office hrs today 2:30-3:30 by appointment

2. WS9, Part II: Reading BEP from graphs of AC & MC
Reading SDP from graphs of AVC & MC
First -- a recap of MC, AC, and AVC as slopes
(No need to write, just to watch)

3. q
100
200
300
400
500
600
700
800
900
1000 MC
1.88
0.68
0.08
3.68
6.08
9.08
12.68 AC
7.73
4.48
2.90
2.33
1.93
1.81
1.94
2.30
2.88
AVC
2.73
1.98
1.43
1.08
0.93
0.98
1.14
1.68
3.18
200

4. Amounts ($) Tangent Slopes ($/item) q 100 200 300 400 500 600 700 800
900
1000 MC
1.88
0.68
0.08
3.68
6.08
9.08
12.68 AC
7.73
4.48
2.90
2.33
1.93
1.81
1.94
2.30
2.88
AVC
2.73
1.98
1.43
1.08
0.93
0.98
1.14
1.68
3.18
($ per item)

5. Diagonal Slopes ($ / item)
Amounts ($) q
100
200
300
400
500
600
700
800
900
1000 MC
1.88
0.68
0.08
3.68
6.08
9.08
12.68 AC
7.73
4.48
2.90
2.33
1.93
1.81
1.94
2.30
2.88
AVC
2.73
1.98
1.43
1.08
0.93
0.98
1.14
1.68
3.18
Diagonal Slopes ($ / item)
($ per item)

6. Now for the punchline:
(write down, understand, and remember)

7. Reading BEP from MC/AC:
On the TC graph:
BEP = the slope of the lowest diagonal line which is tangent to the graph of TC.
Lowest AC MC
So on the graph of MC vs q we can read BEP
as the y-coordinate of the point where MC equals (crosses) AC.
(Note that this also is the lowest value of AC!)
BEP=1.8

8. Reading SDP from MC/AVC :
Similarly: on the graph of VC vs q: SDP = the slope of the lowest diagonal line which is tangent to VC.
Lowest AVC MC
So: on the graph of MC vs q we can read SDP by looking at the y-coordinate
of the point where MC equals (crosses) AVC.
SDP=0.9

9. Worksheets 10, 11 & 12: LINEAR ANALYSIS
NEW MINDSET:
We’ll be using functional notation and algebra from now.
At first, the functions will be linear: f(x)=ax+b
f(x) means f is a function of (depends on) x.
x is the independent variable, f is the dependent
The graph of such a linear expression is a line
of slope = a
and y-intercept = b

10. Example:
TC(q)=mq+c
The Total Cost TC is a function of the quantity you produce, q.
Its graph will be a line of slope m and y-intercept c
What if we write this:
TC(q)=z+qm?
Same thing:
The functional notation clearly shows that
the Total Cost TC is a function of the quantity you produce, q.
So its graph is a line of slope m and y-intercept z.
TC(q)=z+qm=mq+z

11. WS 10: Breaking Even Story I: You make and sell toothbrushes.
The market price (aka selling price) is $3.50 per toothbrush.
You have fixed costs of $200,
and the marginal cost is always $1
Let’s start with something familiar: Describe the graphs of TR and TC.
Since the selling price p=$3.5 is constant for all q,
MR(q)=p=3.5
TR(q)=pq=3.5q
So the graph of TR is a diagonal line of slope 3.5.
Since the marginal cost is always $1, VC(q)=1xq=q, so
TC(q)=VC(q)+FC=q+200
So the graph of TC is a line of slope 1 and y-intercept 200.

12. TR=3.5q
TC=q+200 ??
GOAL: To determine the quantity q for which we break even
Meaning: profit=loss=0

13. We’ll start to solve things using algebraic expressions and getting more
accurate answers!
Since TR(q)=3.5q
& TC(q)=q+200
& we break even when profit=0, i.e when TR=TC:
we can set TR=TC and solve for q
Do it! What do you get?
Answer: q=80

14. Story II: Same setup, but
your marginal cost is doubled: it now takes $2 per toothbrush
TR(q)=pq=3.5q
TC(q)=VC(q)+FC=2q+200
We break even when TR=TC, so 3.5q=2q+200. Solve for q.
Answer: q=133.33

15. Story, generalized: Same setup, but everything is in letters now
The market price (aka selling price) is $p per toothbrush.
You have fixed costs of $c
and the marginal cost is always $m.
TR(q)=pq
TC(q)=VC(q)+FC=mq+c
We break even when TR=TC, so pq=mq+c. Solve for q.
pq=mq+c
First, separate all terms involving the variable q:
pq-mq=c
Now, factor out the variable q on the left:
(p-m)q=c
Answer: q=c/(p-m)

16. Yay, we obtained our first formula! : q=c/(p-m)
Why the excitement?
Since we made a general formula to fit our story problem
we can now plug in any numbers for
the fixed cost c, market price p & the marginal cost m
and very quickly compute the quantity at which we’ll break even
without having to redo all the work each time!
Algebra Rocks!