1. Finishing off Worksheet 3… Last time: 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

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

3. MR & MC Marginal Cost (MC) Is the change in Total Cost as the order size increases by 1. EX: @ q=0, MC=? MC=$6 (Since TC at 1 is $6, and at 0 is $0, so the change is $6) @ q=1, MC=? MC=ΔTC=$6 (Since TC at q=2 is $12, and at q=1 is $6, so MR at q=1 is $12-$6=$6 In fact MC is always $6 since it always takes 6 extra dollars to produce any extra tube. Marginal Revenue (MR) Is the change in Total Revenue as the order size increases by 1. EX: @ q=0, MR=? MR=$20 (Since TR at 1 is $20, and at 0 is $0, so the change is $20) @ q=1, MR=? MR=ΔTR=$12 Since TR at q=2 is $36, and TR at q=1 is $20, so MR at q=1 is $36-$20=$16 Do:

4. 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=ΔTC6 6 6 6 6 6 6 6 6

5. MR=ΔTR 16 12 8 4 0 -4 -8 -12-16 MC=ΔTC6 6 6 6 6 6 6 6 6 Question: Can we tell from MR and MC alone what quantity results in a maximal profit? If MR is positive, the Total Revenue goes up by that much if we sell one extra item. Similarly, a positive MC tells us how much the Total Cost is increasing if we produce an extra item. Profit = TR-TC, so ΔProfit= ΔTR- ΔTC=MR-MC. That is, MR> MC  ΔProfit is positive  the Profit is increasing if we produce & sell an extra item 20 36 48 60 60 56 48 36 56 6 12 18 24 30 36 42 48 56 Profit=TR-TC / / / \ \ \ \ \ \ Profit starts decreasing from q=4 on, so it’s max at q=4.

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