Price Discrimination

Watch the art of charging different prices for the same good. Switch between uniform pricing, third-degree, and first-degree discrimination.

Third-degree splits buyers into markets and matches marginal revenue to marginal cost in each. First-degree charges each buyer exactly their willingness to pay and turns all surplus into profit. Surprisingly, third-degree can destroy more welfare than one uniform price. Splitting markets is not always more efficient.

For example, say a stationery 🏪 shop sells ✏️ pencils. The owner charges a regular 🧑 friend 100 won but a first-time visitor 150. The friend buys happily at the low price, and the owner earns more overall. Each customer faces a different price tag.

MR1=MR2=MC(third-degree)MR_1 = MR_2 = MC \quad \text{(third-degree)}
π1st=∑i(Ai−c)22B\pi_{1st} = \sum_i \frac{(A_i - c)^2}{2B}

Part of these learning paths

Examples & Exercises

With market 1 demand P=12−q1P = 12 - q_1, market 2 demand P=8−q2P = 8 - q_2, and c=2c = 2, find the optimal third-degree prices and profit, and compare with the uniform monopoly profit.

MR1=MR2=MCMR_1 = MR_2 = MC
Third-degree — different prices per market, p1=7p_1 = 7, p2=5p_2 = 5.
Show proof

  1. Set MRi=MCMR_i = MC in each market: 12−2q1=212 - 2q_1 = 2 gives q1=5q_1 = 5, p1=7p_1 = 7.

    8−2q2=28 - 2q_2 = 2 gives q2=3q_2 = 3, p2=5p_2 = 5.

    The less elastic market 1 gets the higher price.

  2. Profit is (7−2)⋅5+(5−2)⋅3=25+9=34(7-2)\cdot 5 + (5-2)\cdot 3 = 25 + 9 = 34.

    Under the uniform price pu=6p_u = 6, profit is (6−2)⋅8=32(6-2)\cdot 8 = 32.

    Price discrimination raises profit by 22 — how the monopolist uses information to grab consumer surplus.

    π3rd=34>32=πuniform\pi_{3rd} = 34 > 32 = \pi_{uniform}

In the same example, compute the deadweight loss under the uniform price and under third-degree discrimination, and discuss whether the folk claim that discrimination raises welfare always holds.

Uniform price — DWL 1616 vs 1717 under third-degree.
Show proof

  1. Uniform price: market 1 DWL is (6−2)(10−6)/2=8(6-2)(10-6)/2 = 8, market 2 is (6−2)(6−2)/2=8(6-2)(6-2)/2 = 8 — total 1616.

  2. Third-degree: market 1 gives (7−2)(10−5)/2=12.5(7-2)(10-5)/2 = 12.5, market 2 gives (5−2)(6−3)/2=4.5(5-2)(6-3)/2 = 4.5 — total 1717.

    Third-degree discrimination lowered welfare!

    Total output is 88 in both cases, but output is misallocated — shifted from high-marginal-value market 1 to low-marginal-value market 2.

    DWL3rd=17>16=DWLuniformDWL_{3rd} = 17 > 16 = DWL_{uniform}

11. Market Power