1. Good Morning! 1) Office hrs: 1:30-2:30 in PDL C-326 3-4 in PDL C-326
2) Midterm 1 on Thursday (Prologue + WS 1-9)
In-class Review: Tuesday & Wednesday (Please print last quarter’s midterm from our class website and bring to quiz section tomorrow)
Out-of-class review: Wednesday 2:30-4 (room TBA)
3) Webpage has been updated with: rules, review file & direct link to Exam Archive

2. Recap of last time (Worksheet 8)
Given a specific Total Cost vs. quantity produced q, recall:
The Breakeven Price (BEP): Is the special price that satisfies:
If p < BEP, the producer never makes a profit
If p > BEP, the producer makes some profit, for some quantities

3. $ TC Breakeven Price = slope of the lowest diagonal line tangent to TC
Recall Computing BEP:
Breakeven Price
= slope of the
lowest diagonal line
tangent to TC
Draw this line &
Pick a good point
(450, 1100)
BEP
=1100/450=2.44
($ per hat)
hats

4. What is the Average Cost$
What is the Average Cost
at q=50?
AC(50) = TC(50)/50 =
=800/50
=slope of diagonal to TC
(at q=50)
Slope of this diagonal=
AC(200)
(lower than previous!)
Slope of this diagonal=
AC(400)
(lower still!)
What is the minimum AC?
Note:
BEP = minimum AC
hats

5. Also, recall:
The Shutdown Price (SDP): Is the special price that satisfies:
If p < SDP, the producer never makes a profit AND loses more money than the fixed costs if he/she produces any hats. One should shut down and produce nothing!
If p > SDP, the producer will at least recover some of the fixed cost FC, for some quantities, so it’s best to stay open a while.

6. $ Shutdown Price = slope of the VC lowest diagonal line tangent to VC
Recall: Computing SDP:
Shutdown Price
= slope of the
lowest diagonal line
tangent to VC VC
Draw this line &
pick a good point
on this line: (600, 900)
Our SDP
=900/600=1.5
($ per hat)
hats

7. $ Similarly to the situation for BEP: VC SDP= minimum AVC hats
Shutdown Price = slope of the lowest diagonal line (but this time tangent to VC)
So:
SDP= minimum AVC
hats

8. Worksheet 9: Analysis of Cost (Part II)
<Please retrieve the handout for WS 9>

9. TR
First, draw TR for a market price of p=$2.50 per paperweight.
slope=2.5=2.5/1=25/10=250/100=500/200  a good point on the line is (200, 500)

10. Part I of WS 9: Three methods to compute max profit, from graphs:
Given the graphs of TR and TC recall that the max profit occurs where we see the maximum vertical distance between the graphs of TR and TC (with TR on top).
Rolling ruler: hold ruler vertical and move across, searching for the largest “gap”.
Looks like max profit occurs at about q=650 paperweights.

11. Now, some PREPARATION FOR THE NEXT 2 METHODS:
From WS 3, recall that our profit is maximized at the first quantity where we go from MR>MC (increasing profit) to MR<MC (decreasing profit).
So we’re looking for q where MR=MC.
In our case, MR=$2.50, always, because you make $2.50 from selling any extra item.
How about MC?
Recall that MC=ΔTC for Δq=1, and MC = the slope of a secant line thru TC’s graph at points q and q+1.
Problem: The scale of our graph is too big to “see” a Δq of 1 paperweight!
Solution: When the scale for the x-axis is in large # of items (10’s,100’s, etc) we approximate MC(q) by: MC(q) = slope of the tangent line at q (line that “brushes” the graph at q, symmetrically, but without crossing).

12. 1. Draw the tangent line at q=200
.625 ?
Example:
MC (200)=?
1. Draw the tangent line at q=200
2. Pick 2 easy to read points:(350, 1000) & (750, 1250)

13. Method 2 for finding the quantity that maximizes Profit,
given the graphs of TR and TC (and large scale for q):
Since the max profit occurs when MR=MC (switching from MR>MC to MR<MC), we get max profit:
when the graphs for TR and TC have parallel tangent lines
(since “matching slopes” means that MR=MC)

14. Method 2: look for matching slopes (parallel tangent lines) at the same q.
In our example, since TR is already a straight line, its slope (MR) is always 2.5.
Align the ruler with TR and move it parallel until it becomes tangent to TC
Find the quantity q where the slopes match (MR=MC):
Once again, looks like max profit occurs at about 650 paperweights.

15. Method 3: If you’re given the graphs of MR and MC,
simply look for their intersection point.
Note: If MR greater than MC before, and smaller after, that q gives max profit. Otherwise it gives max loss.
Look at your handout: The graph of MC is given. How do we draw the graph of MR?
MR is always 2.5
MR(q)=2.5
MR=MC MR
So max profit is at q=640 (note: more accurate answer!)

16. WS9, Part II: Reading BEP from graphs of AC & MC
Reading SDP from graphs of AVC & MC

17. Reading BEP from MC/AC:
On the TC graph:
BEP corresponds to 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 locate BEP at the point where MC equals (crosses) AC. (y-coordinate)
BEP=1.8

18. Reading SDP from MC/AVC :
Similarly: on the graph of VC vs q: the SDP corresponds to 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 locate SDP by looking where MC equals (crosses) AVC.
(y-coordinate!)
SDP=0.9

19. 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

20. 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)

21. 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)