2. Every item is sold at a different price, so TR is the area under the demand curve out to where MC=MR(=D). $ 0 Q MC AC AR MR=D (a la Pigou)

3. This is very theoretical and implies much monopoly power (not to mention a utilometer). $ 0 Q MC AC AR MR=D (a la Pigou)

4. Second degree discrimination is similar to the block rate in public utilities. There is a commercial electricity rate and a household rate. It can capture some consumer surplus as profit. $ 0 Q PcPc CS Household P > Commercial price. (Revenues, shaded, reduce CS, but increase NR for the firm. (a la Pigou) PhPh

5. For 3 rd degree price discrimination, we will assume (for simplicity) only two markets. So draw 2 sets of revenue curves. $ 0 Q (a la Pigou) AR 2 MR 2 MR 1 AR 1

6. $ 0 Q (a la Pigou) AR 2 MR 2 MR 1 AR 1 2. Sum MR curves (  MR). Above this p, there’s only one MR  MR

7. $ 0 Q (a la Pigou) AR 2 MR 2 MR 1 AR 1 2. Sum MR curves (  MR). Another  MR point. One point on  MR line.

8. d2d2 MR 2 MR 1 d1d1 If each MR curve (at the horizontal line where the two intersect) is one half way out to its respective demand curve, the two demand curves are just twice as far out from the vertical axis where they will also intersect. Horizontally, MR 1 = 1/2 d 1, and MR 2 = 1/2 d 2 since 1/2 + 1/2 = 1, MR 1 + MR 2 = d 1 = d 2 =  mr

9. Now, simply connect the two points shown and get the  mr we have been looking for. $ 0 Q (a la Pigou) AR 2 MR 2 MR 1 AR 1 Another  mr point. One point on  MR  MR

10. (a la Pigou) $ 0 Q AR 2 MR 2 MR 1 AR 1  mr 3. Add MC and AC curves… and find the output where MC =  MR. MC AC QtQt r

11. (a la Pigou) $ 0 Q ar 2 mr 2 mr 1 ar 1  mr 1. Assume two markets (draw 2 sets of revenue curves). 2. Sum MR curves (  MR). 3. Add MC and AC curves… and find the output where MC =  MR. mc ac QtQt 4. Find MR 1 = MC (= r) Find MR 2 = MC (= r) r q1q1 p1p1 q2q2 p2p2

12. (a la Pigou) $ 0 Q ar 2 mr 2 mr 1 ar 1  mr Profit in market 1: TR 1 - TC = NR 1 or... mc ac QtQt q1q1 q2q2 p1p1 p2p2 p 1 (q 1 ) - c(q 1 ) = NR 1 or the shaded area c

13. (a la Pigou) $ 0 Q ar 2 mr 2 mr 1 ar 1  mr Profit in market 2: TR 2 - TC = NR 2 or... mc ac QtQt r q1q1 q2q2 p1p1 p2p2 c the shaded area, p 2 (q 2 ) - c(q 2 ) = NR 2

14. (a la Pigou) $ 0 Q ar 2 mr 2 mr 1 ar 1  mr Total NR: NR 1 + NR 2 = p 1 q 1 - cq 1 + p 2 q 2 - cq 2 or, the shaded areas. mc ac QtQt r q1q1 q2q2 p1p1 p2p2 c

15. (a la Pigou) But wait! There is a simpler method for wimps!

16. (a la Pigou) 1. Determine MC for total output, MR1D1 MR2D2 MC

17. (a la Pigou) 2. Equate MC to MR in each market to find the correct output for each market, Q1Q2 MR1D1 MR2D2 MC

18. (a la Pigou) 3. The output line extended up to the D curve indicates each market’s price. Q1 Q2 P1 P2 MR1D1 MR2D2 MC