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

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. ”

Tentative MSC Schedule

Worksheet 3, Review & Continued TR=q x price 20 36 48 56 60 60 56 48 36 TC=q x cost 6 12 18 24 30 36 42 48 56 Profit=TR-TC 14 24 30 32 30 24 14 0 -18

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

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>

Important to Remember: MR and MC always “look one quantity ahead”! TR=q x p 20 36 48 56 60 60 56 48 36 TC=q x cost 6 12 18 24 30 36 42 48 56 Profit=TR-TC 14 24 30 32 30 24 14 0 -18 MR=ΔTR 16 12 8 4 0 -4 -8 -12-16 MC=ΔTC 6 6 6 6 6 6 6 6 6 Important to Remember: MR and MC always “look one quantity ahead”!

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 60 60 56 48 36 MR=ΔTR 16 12 8 4 0 -4 -8 -12-16 6 12 18 24 30 36 42 48 56 MC=ΔTC 6 6 6 6 6 6 6 6 6 Profit=TR-TC / / / \ \ \ \ \ \ Profit starts decreasing from q=4 on, so it’s max at q=4.

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