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Price Discrimination. (a la Pigou). First Degree Price Discrimination. (a la Pigou). Every item is sold at a different price, so TR is the area under the demand curve out to where MC=MR(=D). $. AR. MC. AC. MR=D. 0. Q. First Degree Price Discrimination. (a la Pigou).
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Price Discrimination (a la Pigou)
First Degree Price Discrimination (a la Pigou) Every item is sold at a different price, so TR is the area under the demand curve out to where MC=MR(=D). $ AR MC AC MR=D 0 Q
First Degree Price Discrimination (a la Pigou) This is very theoretical and implies much monopoly power (not to mention a utilometer). $ AR MC AC MR=D 0 Q
$ 0 Q Second Degree Price Discrimination (a la Pigou) Household P > Commercial price. (Revenues, shaded, reduce CS, but increase NR for the firm. 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. Ph CS Pc
$ 0 Q Third Degree Price Discrimination (a la Pigou) For 3rd degree price discrimination, we will assume (for simplicity) only two markets. So draw 2 sets of revenue curves. AR2 AR1 MR2 MR1
AR2 AR1 MR2 MR1 Third Degree Price Discrimination (a la Pigou) Above this p, there’s only one MR $ MR 2. Sum MR curves (MR). 0 Q
Third Degree Price Discrimination (a la Pigou) $ One point on MR line. Another MR point. 2. Sum MR curves (MR). AR1 MR2 AR2 MR1 0 Q
d1 d2 MR2 MR1 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, MR1 = 1/2 d1, and MR2 = 1/2 d2 since 1/2 + 1/2 = 1, MR1 + MR2 = d1 = d2 = mr
$ MR 0 Q Third Degree Price Discrimination (a la Pigou) Now, simply connect the two points shown and get the mr we have been looking for. One point on MR Another mr point. AR1 AR2 MR2 MR1
$ 0 Q Third Degree Price Discrimination (a la Pigou) 3. Add MC and AC curves… and find the output where MC = MR. MC AC r AR1 AR2 MR2 MR1 mr Qt
$ mc ac ar2 r ar1 mr2 mr1 0 Qt Q Third Degree Price Discrimination (a la Pigou) 1. Assume two markets (draw 2 sets of revenue curves). 3. Add MC and AC curves… and find the output where MC = MR. p2 2. Sum MR curves (MR). 4. Find MR1 = MC (= r) Find MR2 = MC (= r) p1 mr q2 q1
$ p2 mc p1 ac ar2 mr2 0 q2 q1 Qt Q Third Degree Price Discrimination (a la Pigou) Profit in market 1: TR1 - TC = NR1or... p1(q1) - c(q1) = NR1 or the shaded area c ar1 mr1 mr
$ p2 mc p1 ac ar2 r ar1 mr2 mr1 0 q2 q1 Qt Q Third Degree Price Discrimination (a la Pigou) Profit in market 2: TR2 - TC = NR2 or... c the shaded area, p2(q2) - c(q2) = NR2 mr
$ p2 mc p1 ac ar2 r ar1 c mr2 mr1 0 q2 q1 Qt Q Third Degree Price Discrimination (a la Pigou) Total NR: NR1 + NR2 = p1q1 - cq 1 + p2 q2 - cq 2 or, the shaded areas. mr
Third Degree Price Discrimination (a la Pigou) But wait! There is a simpler method for wimps!
Third Degree Price Discrimination (a la Pigou) MC MR2 D2 MR1 D1 • 1. Determine MC for total output,
Third Degree Price Discrimination (a la Pigou) MC MR2 D2 MR1 D1 Q1 Q2 • 2. Equate MC to MR in each market to find • the correct output for each market,
Third Degree Price Discrimination (a la Pigou) P1 P2 MC MR2 D2 MR1 D1 Q1 Q2 • 3. The output line extended up to the D • curve indicates each market’s price.
