Excludability and Rivalry

  • Excludability: 排他性
    • Non-excludable goods: Cannot exclude non-payers (e.g., national defense, radio signals).
    • Excludable goods: Can exclude non-payers (e.g., jeans, paid e-books).
  • Rivalry: 竞争性
    • Rival goods : Use by one person reduces availability for others.
    • Non-rival goods : One person’s use does not diminish availability for others.
Excludability Rivalry Type Examples
Excludable Rival Private Goods Jeans, hamburgers, gasoline
Excludable Non-rival Nonrival Private Wi-Fi, satellite TV
Non-excludable Rival Common Resources Timber in public land, bluefin tuna
Non-excludable Non-rival Public Goods National defense, lighthouses

四种商品类型

Private Goods

  • 可以直接高效地进入竞争市场
    • 因为 rival，所以 excludable 不导致 inefficiency
    • 因为 excludable，所以有 incentive 去消费和生产
  • 经典微观经济学的假设：
    1. 所有生产成本由生产者承担
    2. 所有消费收益由消费者享受

Public Goods

  • Under-provision : Free-rider problem leads to insufficient supply.
  • Collective Action : Difficult to negotiate joint purchases, especially with large groups.
  • 需要政府介入
    1. Taxes to buy public goods (e.g., streetlights, highways).
    2. Optimal quantity determined where Marginal Social Benefit (MSB) = Marginal Social Cost (MSC) .
    3. MSB curve: 分段加和

Non-rival Private

Common Resources

私人决策的低效性

个人在做决策的时候，指针方针仅考虑私人的边际收益和私人的边际成本

MB(Qi)≥MC(Qi) MB(Q_i)\ge MC(Q_i)

然而从社会的角度看，社会成本 == 私人成本 ++ 外部成本，导致市场均衡产量 QmktQ_{mkt} 远大于社会均衡产量 QsocQ_{soc}.

为防止 Tragedy of the Commons 需要政府干预：

核心思想

当前的 quantity 为 QmktQ_{mkt}，其满足

MB(Qmkt)=MC(Qmkt) MB(Q_{mkt})=MC(Q_{mkt})

既然想让它达到 QsocQ_{soc} 的水平，那么我们可以列出两个式子

{MB(Qsoc)=MC(Qsoc)MC(Qsoc)=MC(Qmkt)+Extra Cost \begin{cases} MB(Q_{soc})=MC(Q_{soc})\\ MC(Q_{soc})=MC(Q_{mkt})+\text{Extra Cost} \end{cases}

那么我们只需要限制 Extra Cost\text{Extra Cost} 的范围即可。

通过税收干预

通过 Tradable Permit 干预

例题

2020 Fall Final

Q1

Please refer to the background information below to answer the following three questions.

Factory X produces 1010 tons of wastewater every day. Each ton of wastewater caused 17.517.5 (in thousand dollars) worth of damage to nearby residents. It costs the factory n2n^2 (in thousand dollars) to remove pollutants from nn tons of wastewater. Suppose nn can only take integer numbers.

  1. If pollution is unregulated and negotiation is impossible, Factory X will discharge [ Answer38 ] tons of untreated wastewater to the sea every day.

  2. It is socially efficient for Factory X to treat [ Answer39 ] tons of wastewater.

  3. Consider levying a tax on wastewater. In order to achieve the socially efficient outcome, the minimum amount of tax should be [ Answer40 ] thousand dollars per ton of wastewater.

【解答】
我们不妨
38. 由于工厂并不对环境污染负责，所以其 cost 仅由废水处理构成 arg min⁡xx2\argmin_x x^2，所以 x=0x=0，即不处理任何污水

  1. 考虑社会环境效益，假设工厂处理 xx 吨废水，则社会的成本由废水处理和废水污染构成，即 arg min⁡xx2+17.5(10−x)\argmin_x x^2+17.5(10-x)，因为 x∈Zx\in \Z 故 x=9x=9

  2. 仅考虑工厂的成本，工厂的成本由废水处理和税构成，假设处理 xx 吨废水其余排放，每吨废水收税 pp，则成本为 arg min⁡xx2+p(10−x)\argmin_x x^2+p(10-x)，现在要求达到社会最大效益，即这个二次函数的最小值在 x=9x=9 取到。所以解得 p≥17p\ge 17

Q2

Please refer to the background information below to answer the following three questions.

There is a small public beach in Utopia. The residents of Utopia, in total 20 of them, love to go to the beach but prefer not to when it is too crowded. In particular, if n people share the beach together, each individual gets an economic surplus of 10.5 − n dollars. Suppose n can only take integer numbers.

  1. If the residents make their decisions individually, then [ ] residents will go to the beach in equilibrium.

  2. The socially optimal number of beach occupants is [ ].

  3. If the government charges an entrance fee of $2.62, [ ] residents will go to the beach in equilibrium.