1. Good Morning Today: WS 3 & 4, Friday: WS 5
Thursday: Activity 1 in quiz section plus Homework 1 collected.
Office hours:
Today 1:30-2:30 in MSC (CMU B-006)
Today 2:30-3 in PDL C-326

2. One of my last quarter’s students writes:
“The only thing I would suggest is to be even more forceful in encouraging students to use the MSC and telling them more about it (professors, TA's, tutors, free help!). I think many students see it as just a "nerd-club" and have no idea how much help it can be. ”

3. Tentative MSC Schedule

4. Worksheet 3, Review & Continued
TR=q x price 20 36 48 56
TC=q x cost
Profit=TR-TC

5. Max Profit is at q=4 (since largest vertical distance with TR above)
Negative profit (loss)
Profit for an order of q=2 tubes is $24
Profit for an order of q=1 tube is $14

6. MR & MC Marginal Revenue (MR) Marginal Cost (MC)
Is the change in Total Revenue as the order size increases by 1.
(MR=ΔTR for Δq=1)
EX:
at q=0, MR=$20-$0=$20.
(Since TR=$20 at q=1, and TR=$0 at q=0)
at q=1, MR=ΔTR=$36-$20=$16
(Since TR=$36 at q=2,
and TR=$20 at q=1)
Marginal Cost (MC)
Is the change in Total Cost as the order size increases by 1.
(MC=ΔTC for Δq=1)
EX:
at q=0, MC=$6-$0=$6
(Since TC=$6 at q=1, and
TC=$0 at q=0,
so the change is $6)
at q=1, MC=ΔTC=$12-$6=$6 (Since TC=$12 at q=2,
and TC=$6 at q=1,
so MR at q=1 is $12-$6=$6
In fact, MC is always $6 in this problem, since it always takes 6 extra dollars to produce any extra tube.
Do: <fill Row 4 with values of MR, and Row 6 with the values of MC>

7. Important to Remember: MR and MC always “look one quantity ahead”!
TR=q x p 20 36 48 56
TC=q x cost
Profit=TR-TC
MR=ΔTR
MC=ΔTC
Important to Remember: MR and MC always “look one quantity ahead”!

8. Profit starts decreasing from q=4 on,
Question: Can we tell from MR and MC alone what quantity q results in the maximal profit?
Recall : if the Marginal Revenue (MR) is positive, the Total Revenue goes up by that much if we sell one extra item.
Similarly, a positive Marginal Cost (MC) tells us how much our Total Cost increases if we produce an extra item.
Profit = TR-TC, so ΔProfit= ΔTR- ΔTC, i.e ΔProfit =MR-MC (when Δq=1)
So: MR> MC  ΔProfit is positive  the Profit is increasing from q to q+1
& MR< MC  ΔProfit is negative  the Profit is decreasing from q to q+1 20 36 48 56
MR=ΔTR
MC=ΔTC
Profit=TR-TC
/ / /
\ \ \ \ \ \
Profit starts decreasing from q=4 on,
so it’s max at q=4.

9. Conclusion:
The max profit occurs at the first quantity q at which the Marginal Revenue MR falls at or below the Marginal Cost MC.