# 进入、退出与产业资本投入

倒推进入的弱均衡集合，区分零利润多解、进入上限、项目建设与退出选择。

Entry: zh-ei08 | Node: EI-08 | Language: zh | Editorial revision: 2026-09-21

## Teaching instructions
你正在教 EI-08《进入、退出与产业资本投入》。使用同源正文、真实EIA时点和教学输入。
先实际读取核心 required_readings。读者选择research分支时，才实际读取正式33页AER的§I.A–F、Table1、Figure4。把读取日志从空数组按实填写，未读图表不能称已核。
诊断让读者解释K=900时为什么{2,3}而非唯一3。先推经营阶段非负Cournot数量、价格与变动利润，再倒推进入者和非进入者的偏离激励。默认K800->{3}、压力350->{5}；所有成本收益同一经营期单位。
检查cap0->{0}；到cap不检查不存在的下一家；a<=c选零产量续局，K>0只0、K=0全0..cap；无成交没有成交价。不把最大N选择规则藏进弱不等式。
让读者将EIA的2025已新增53GW与2026当时计划86GW放回2026-02-20文章，不计算同批兑现率或把GW当企业数。用沉没/可回收/未来可避免支出解释退出例，清楚区分进入前与进入后。
研究分支只采用有样本和模型条件的对数就业方差约85%/约40%及age20外推；原文引言90%+不混入，绝不转成成功概率。
最后迁移到三年后投产项目：必须指出当前订单、未来竞争、付款承诺与可回收价值各负责哪一步，并选下一项新证据。
以当前 selected_branch 和 required_readings 为准；共同正文必读，选中分支的完整单元同时成为必读。保留完整同源正文一次及附带静态说明、输入和解析；runtime_reading_log 本次从空开始。

Before substantive teaching, actually retrieve every required reading unit for the selected scope. Read its complete designated section, including necessary assumptions, tables and footnotes. A working URL or an editorial access date is not a runtime reading receipt. Record the actual version, location, scope and what it supports. If unavailable, use a previously verified equivalent source; if the required unit remains unavailable, identify that gap rather than teach it from memory. Start runtime_reading_log empty. Once reading is complete, use a substantive diagnostic or follow the reader's request for direct explanation. Advance one complete reasoning task at a time; skip mastered basics. Distinguish original facts, supplied teaching assumptions and inference.

## Required readings and runtime protocol
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        "verified_access_at": "2026-09-21"
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        "locator": "slides3–4",
        "scope": "Cournot设定与一阶条件",
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      "supports": "静态Cournot、Bertrand和Hotelling的条件与一阶条件；本包无退出选项的覆盖市场、数值和角点验证为教学改写，并非会员公司参数估计。",
      "version": "MIT 14.271 Fall 2022; Lecture 5",
      "id": "EI08-READ-01",
      "title": "Static Competition and Models of Differentiation, Part 1",
      "authors": [
        "Glenn Ellison"
      ],
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      "source_id": "EIBC-S02",
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        "verified_access_at": "2026-09-21"
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        "locator": "slides2–3",
        "scope": "二阶段进入与纯策略弱条件",
        "purpose": "检验零利润多解和有限上限"
      },
      "supports": "两阶段进入的纯策略弱条件；零利润边界不唯一。有限上限、N=0及无产量情形按本包完整明示的教学续局计算。",
      "version": "MIT 14.271 Fall 2022; Lecture 16",
      "id": "EI08-READ-02",
      "title": "Entry",
      "authors": [
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        "locator": "文章全文及开篇数据期",
        "scope": "2026-02-20固定短文",
        "purpose": "计划与实现的资料身份"
      },
      "supports": "固定文章报告2026计划新增86 GW与2025已新增53 GW。两值分属不同年度和状态，不是同批项目兑现率。",
      "version": "Published 2026-02-20",
      "id": "EI08-READ-03",
      "title": "New U.S. electric generating capacity expected to reach a record high in 2026",
      "authors": [
        "U.S. Energy Information Administration"
      ],
      "branch": "common"
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        "uri": "https://www.eia.gov/electricity/data/eia860m/index.php",
        "verified_access_at": "2026-09-21"
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        "locator": "工作簿列表前方法说明全文",
        "scope": "preliminary、修订与capacity commitments",
        "purpose": "理解观测范围和承诺区别"
      },
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      "version": "Methods webpage accessed 2026-09-21",
      "id": "EI08-READ-04",
      "title": "Preliminary Monthly Electric Generator Inventory",
      "authors": [
        "U.S. Energy Information Administration"
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        "verified_access_at": "2026-09-21"
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        "locator": "§I.A–F; Table1; Figure4; introduction p.548 comparison",
        "scope": "正式版印刷pp.550–559，包含样本、估计、图注和85/90文本差异",
        "purpose": "事前异质性的有限结论"
      },
      "supports": "§I平衡面板对数就业横截面方差分解；正文age0约85%、age20约40%，后者为外推。与引言90%+不一致。只作进入异质性选读，不作成功概率或项目校准。",
      "version": "AER 111(2), 2021, pp.547–579; 33-page version of record",
      "branch": "research",
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      "id": "EI08-READ-05",
      "title": "The Nature of Firm Growth",
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        "Petr Sedláček",
        "Benjamin Pugsley"
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      "supports": "静态Cournot、Bertrand和Hotelling的条件与一阶条件；本包无退出选项的覆盖市场、数值和角点验证为教学改写，并非会员公司参数估计。",
      "version": "MIT 14.271 Fall 2022; Lecture 5",
      "id": "EI08-READ-01",
      "title": "Static Competition and Models of Differentiation, Part 1",
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        "purpose": "检验零利润多解和有限上限"
      },
      "supports": "两阶段进入的纯策略弱条件；零利润边界不唯一。有限上限、N=0及无产量情形按本包完整明示的教学续局计算。",
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        "scope": "2026-02-20固定短文",
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      },
      "supports": "固定文章报告2026计划新增86 GW与2025已新增53 GW。两值分属不同年度和状态，不是同批项目兑现率。",
      "version": "Published 2026-02-20",
      "id": "EI08-READ-03",
      "title": "New U.S. electric generating capacity expected to reach a record high in 2026",
      "authors": [
        "U.S. Energy Information Administration"
      ],
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      "version": "Methods webpage accessed 2026-09-21",
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      "title": "Preliminary Monthly Electric Generator Inventory",
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        "purpose": "事前异质性的有限结论"
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      "title": "The Nature of Firm Growth",
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        "Petr Sedláček",
        "Benjamin Pugsley"
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        "version": "MIT 14.271 Fall 2022; Lecture 5",
        "id": "EI08-READ-01",
        "title": "Static Competition and Models of Differentiation, Part 1",
        "authors": [
          "Glenn Ellison"
        ],
        "branch": "common"
      },
      {
        "source_id": "EIBC-S02",
        "access": {
          "kind": "pdf_full_text",
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          "verified_access_at": "2026-09-21"
        },
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          "locator": "slides2–3",
          "scope": "二阶段进入与纯策略弱条件",
          "purpose": "检验零利润多解和有限上限"
        },
        "supports": "两阶段进入的纯策略弱条件；零利润边界不唯一。有限上限、N=0及无产量情形按本包完整明示的教学续局计算。",
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        "title": "Entry",
        "authors": [
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        "access": {
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          "verified_access_at": "2026-09-21"
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          "locator": "文章全文及开篇数据期",
          "scope": "2026-02-20固定短文",
          "purpose": "计划与实现的资料身份"
        },
        "supports": "固定文章报告2026计划新增86 GW与2025已新增53 GW。两值分属不同年度和状态，不是同批项目兑现率。",
        "version": "Published 2026-02-20",
        "id": "EI08-READ-03",
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```

## Supplied entry
> 建议学习时间：18–20 分钟。共同部分完成“进入数量—利润—项目时点”的重建；企业异质性研究作为选读。先修只要求理解数量、单价、成本和利润，文中的进入模型会从头推导。

<div data-reading-branch-controls aria-label="选择阅读分支">
<button type="button" data-select-reading-branch="common">共同主线</button>
<button type="button" data-select-reading-branch="research">研究选读</button>
<button type="button" data-select-reading-branch="all">全部展开</button>
</div>

<a id="ei08-process"></a>

## 一、进入者买的是未来经营机会

在[竞争、差异化与利润分配](https://ou-liu-red-sugar.github.io/zh/notebook/competition-differentiation-profit/)中，我们暂时固定了企业集合。现在把潜在进入者放进来。它看到的高利润来自现有企业，而自己要先付出投入，再在未来面对客户和竞争对手。因此，进入不是“看到利润就立即增产”，而是**用当前投入换取未来有条件的经营机会**。

把过程按经济含义写出来：预期需求与竞争 → 决定是否进入 → 支付或承诺投入 → 建设与调试 → 投运 → 在当时条件下生产。进入后还可能扩张、暂停或退出。技术建成与经济可行也各有自己的门槛：设备具备生产能力，并不保证届时每单位销售都能覆盖应承担的费用。

这条时间线里要区分三种投入。可以通过转卖或其他用途回收的部分，会影响退出选择；一旦支付无法回收的部分，成为沉没投入；尚未支付的继续经营支出，则仍能通过暂停或退出避免。它们都可能在进入前影响决策，但进入后不应再以相同方式处理。

<a id="ei08-cournot"></a>

## 二、先把未来竞争算出来

MIT 的进入讲义采用两阶段结构：第一阶段选择进入并支付成本 $K$，第二阶段由已进入企业竞争。我们先用一个只有一个经营期的教学版本，明确 $K$ 与经营利润采用同一货币单位；这里没有跨多年贴现，也没有把 $K$ 校准成电厂成本。[^entry]

本篇在每个进入数量下采用下述对称经营续局，第一阶段的进入集合以这个续局为条件。

设有 $\bar N$ 家潜在企业。若 $N\ge1$ 家进入，它们生产同质产品，边际成本均为 $c\ge0$，同时选择非负数量。需求在正价格区域为 $P=a-Q$，$Q=\sum_iq_i$，$a\ge0$；价格下界为0。先处理 $a>c$ 的正产量情形。给定其他企业总产量 $Q_{-i}$，企业 $i$ 选择 $q_i$，其经营期变动利润为

$$
\pi_i^v=(a-Q_{-i}-q_i-c)q_i.
$$

一阶导数为 $a-c-Q_{-i}-2q_i$，二阶导数为 $-2$。在正产量均衡中，所有企业取相同数量 $q$，于是 $Q_{-i}=(N-1)q$。代回一阶条件：

$$
a-c-(N+1)q=0,\qquad
q_i^*=\frac{a-c}{N+1}.
$$

再由价格定义得到

$$
Q^*=\frac{N(a-c)}{N+1},\qquad
P^*=c+\frac{a-c}{N+1},\qquad
\pi^v(N)=\frac{(a-c)^2}{(N+1)^2}.
$$

这是经营阶段扣除可变成本、**尚未扣进入成本**的利润。企业增加时，每家数量和价差都下降，故每家利润比数量下降得更快。对称结果落在非负数量、正价格区域；偏离到零产量只得0，偏离到总供给使价格为0也不会改善正利润结果。这是讲义 Cournot 框架的完整数值化教学例。[^pricing]

<a id="ei08-entryset"></a>

## 三、倒过来判断谁愿意进入

现在回到第一阶段。若已有 $N$ 家进入，每家净所得为 $\pi^v(N)-K$。一组进入决定要稳定，必须同时满足两件事：已进入者不因改选不进入而获得更高所得，未进入者也不能因成为第 $N+1$ 家而获得严格正净所得。因此，在 $0<N<\bar N$ 时：

$$
\pi^v(N)\ge K,\qquad \pi^v(N+1)\le K.
$$

这是**弱最优条件**。等号时，一家企业可能进入，也可能不进入。我们寻找的是所有满足条件的企业数构成的集合，不是自动选最大整数。[^entry]

取 $a=120,c=0,\bar N=10$。先列出经营利润，再放入进入成本：

| 已进入企业数 $N$ | 每家产量 | 均衡价格 | 每家变动利润 $\pi^v(N)$ |
|---:|---:|---:|---:|
| 1 | 60 | 60 | 3,600 |
| 2 | 40 | 40 | 1,600 |
| 3 | 30 | 30 | 900 |
| 4 | 24 | 24 | 576 |
| 5 | 20 | 20 | 400 |
| 6 | 17.142857 | 17.142857 | 293.877551 |

当 $K=800$ 时，三家进入各有100净利润，第四家若进入只得 $576-800<0$。两家并不稳定，因为第三家进入仍可获利；四家也不稳定，因为已有企业愿意改为不进入。均衡企业数集合因此是 $\{3\}$。

把 $K$ 降到350，五家时每家有50净利润，第六家则亏损，集合变为 $\{5\}$。需求和技术没有变，仅进入成本改变，就使未来竞争和利润空间改变了。

边界同样有经济内容。$K=900$ 时，若已有两家，第三家净利恰为0，它可以选择不进入，因此两家稳定；若三家都进入，各家也都无意以退出换取更高所得。故集合是 $\{2,3\}$。同理，$K=400$ 给 $\{4,5\}$。

| $K$ | 弱均衡企业数集合 | 含义 |
|---:|---|---|
| 800 | $\{3\}$ | 唯一默认例 |
| 350 | $\{5\}$ | 较低进入成本 |
| 900 | $\{2,3\}$ | 第三家零净利，进入与否均可 |
| 400 | $\{4,5\}$ | 第五家零净利，进入与否均可 |

**潜在企业上限也必须进入判断。** 当 $N=\bar N$ 时，只检查现有企业不亏，不再检查不存在的下一家。若上限只有2而 $K=800$，两家都不亏，结果就是受上限约束的 $\{2\}$。若 $\bar N=0$，直接得到 $\{0\}$；若上限大于0，零家进入稳定的条件是第一家单独进入也没有严格正净利，即 $\pi^v(1)\le K$。

还有一个数量角点：当 $a\le c$ 时，我们采用各企业不生产的经营阶段续局，变动利润为0，不允许内点公式生成负销量。此时 $K>0$ 只剩 $\{0\}$；$K=0$ 则从0到 $\bar N$ 的所有进入数都无差异。$a=c=0$ 的退化情形同样采用不生产续局，绝不把无价、无需求支持的产量称为正经营机会。没有成交时，界面不展示“实际成交价”。

<a id="ei08-experiment"></a>

## 四、让进入成本改变竞争，而不是只改变一行费用

<div data-experiment-slot="exp-ei08-entry"></div>

先用800与350两个默认情形，看企业数、每家数量和净所得怎样一起变化；再切到900，观察集合为什么出现两个元素。最后把潜在进入上限改成2，看看“没人还能进入”和“下一家进入不赚钱”是两种不同约束。

这个模型没有主张现实行业存在可直接填入的统一 $K$。它让我们知道收集什么资料：谁有可能进入、这些主体要支付什么不可回收投入、投产后会用什么方式竞争。进入成本若只是把资金从今天移到明天的会计标签，而未改变真实承诺和资源，就不能直接套用这里的比较。

<a id="ei08-capital"></a>
<a id="CASE-EI08-EIA-GENERATOR-PLAN-2026"></a>

## 五、电力资料中的计划、建设与有效供给

EIA 在2026年2月20日的文章中，依据当时的月度发电机组资料报告：开发商和运营商计划在2026年新增86 GW公用事业规模电力容量，措辞保留“若实现”；文章同时报告2025年新增约53 GW。860M说明月度数为初步估计、可能修订，公布容量也不构成设施的容量承诺。[^eia][^inventory]

| 同一篇历史文章中的数值 | 材料期间 | 状态 | 本例用途 |
|---|---|---|---|
| 53 GW | 2025年 | 文章报告的已新增量 | 回看上年交付 |
| 86 GW | 2026年 | 当时计划量，尚待实现 | 识别未来潜在供给 |

53与86不属于“同批项目的计划与完成”分子分母，不能相除得到兑现率。这里也没有从86 GW推导企业数：一种是设备容量，另一种是进入主体数量。

把现实项目放入下面的静态过程，就能定位每一项资料：

```text
预期需求与未来竞争
      │ 形成投资理由
      ▼
投资决定 ──资金、许可、设备和场址安排──▶ 建设、调试
                                            │ 达到运行条件
                                            ▼
                                        投入运行
                                            │ 原料、人员、网络与运行状态
                                            ▼
                                        可用供给
```

建设时点很重要。新增项目可能在看到需求信号时就启动，等几年后投运才改变供给；期间需求、成本和其他进入者都可能变化。因此，今天利润高和几年后利润低并不矛盾。反过来，只有纸面计划增加，也不足以判断近端紧张已经解除。逐项目跟踪时应分开记录当时预计的投入、关键进度和实际投运；本例只使用已核的计划／实现身份，不假定一套通用状态码。

退出的判断则从“现在还能改变什么”开始。一个明确虚构的单期例子：过去已付且收不回的建厂费为900；从现在继续到期末可取得营业净现金流120、残值30；现在清算可取得100。所有数值已折成同一决策时点单位，忽略其他义务。继续价值为150，高于立即退出的100，所以继续有利，尽管最初900尚未赚回。若未来净现金流改为40，继续价值70低于100，退出更有利。900影响最初是否应建厂，却不会因今天继续或退出而改变；可回收残值和未来可避免支出才改变当前选择。

<section data-reading-branch="research">
<a id="ei08-research"></a>
<details>
<summary>选读：真实进入者为什么未必像模型中一样</summary>

模型故意给所有企业相同成本与能力。Sterk、Sedláček、Pugsley 的2021年正式 AER 论文，则用美国企业纵向数据研究企业起点差异与后续冲击如何影响**对数就业的横截面方差**。基准估计使用观察到年龄0–19的存活企业平衡面板；§I.E与Figure 4中，事前异质性份额在年龄0约85%，年龄20约40%，后者属于估计区间外的参数外推。它不是创业成功概率。[^sterk]

这项结果提示我们把进入者能力、目标规模和成本分布列入现实证据，而不应给所有潜在企业同一个经营利润。它没有替我们估计电力项目的成本。原文引言的“超过90%”与正文约85%存在差异；本例引用正文和图表，不把两个数拼成一条年龄曲线。

**小练习。** “85%的企业命运在成立时已决定”错在哪里？它把一个特定样本和统计模型中的方差分解，改成对每家企业成败的判断，又忽略存活面板和外推边界。可保留的结论是：起点异质性在该模型中解释了相当部分企业规模差异，因此同质进入模型有明确适用边界。

</details>
</section>

<a id="ei08-exercises"></a>

## 六、从进入集合迁移到一个建设项目

**任务一：重建多解，而不是记住答案。** 取 $a=120,c=0,K=400,\bar N=10$，逐一解释4家与5家为何都稳定，再说明6家为什么不稳定。

**解析。** 四家现有企业各得 $576-400=176$，第五家进入后的净利润为0，因此可以不进。五家现有企业各得0，第六家只能得 $293.877551-400<0$。六家时已有企业亏损，改为不进入所得0更好。因此集合为 $\{4,5\}$。若只保留最大值5，相当于另外规定零净利润的潜在企业一定进入，而不是原弱条件自动给出的结论。

**任务二：没有正产量时，进入与生产还一样吗？** 取 $a=20,c=30,\bar N=3$，比较 $K=10$ 与 $K=0$。

**解析。** 非负数量最优续局为0，变动利润0。$K=10$ 时任何进入都亏10，集合为 $\{0\}$。$K=0$ 时进入与不进入所得相同，集合为 $\{0,1,2,3\}$，但各自都没有正产量。进入主体数与已形成的有效供给要分开。

**迁移题。** 某工业企业称“当前订单利润率高，已宣布一座三年后投产的新厂”。专用安装无法回收，设备可二手转售，投入尚未全部支付。请写出进入前、建设中、投运后三个不同问题，并给一项下一步证据。

**解析。** 进入前比较未来竞争条件下的经营价值与全部投入承诺，不能用当期利润率直接乘三年。建设中比较从当前继续的增量价值、尚可避免的付款以及暂停／转售所得；已付专用安装费属于沉没部分。投运后还需核订单交付、可用资源与边际经营收益。下一步可选设备采购合同及付款节点、项目调试进展，或能约束投运后需求的客户承诺。证据应对应所讨论的时点；“宣布了项目”不能代替三个时点的全部判断。

本篇把进入条件放回未来竞争和资本形成。[库存周期、产能周期与结构变化](https://ou-liu-red-sugar.github.io/zh/notebook/inventory-capacity-dynamics/)接着区分另一类更快的过程：订单、交货和库存可以在新厂尚未建成时就已经发生显著变化。

[^entry]: EIBC-S02，Glenn Ellison，MIT 14.271 Fall 2022，Lecture 16《Entry》，slides2–3为两阶段进入和弱条件；slide11只作学习／退出的概念背景。[原讲义](https://ocw.mit.edu/courses/14-271-industrial-organization-i-fall-2022/mit14_271_f22_lec16slides.pdf)。
[^pricing]: EIBC-S01，MIT Lecture5，slides3–4的Cournot数量竞争设置。本篇 $a,c,K,\bar N$ 和所有数值为教学假设，不是现实项目校准。[原讲义](https://ocw.mit.edu/courses/14-271-industrial-organization-i-fall-2022/mit14_271_f22_lec5slides.pdf)。
[^eia]: EIBC-S05A，EIA，2026-02-20《New U.S. electric generating capacity expected to reach a record high in 2026》，正文开篇及图的数据期注释。此处固定文章当时的历史信息，不将其计划值改称截至现在已实现容量。[原文](https://www.eia.gov/todayinenergy/detail.php?id=67205)。
[^inventory]: EIBC-S05B，EIA《Preliminary Monthly Electric Generator Inventory》，页面方法说明与“not meant to be capacity commitments”段；这里不使用未读工作簿状态码。[方法原页](https://www.eia.gov/electricity/data/eia860m/index.php)。
[^sterk]: EIBC-S06，Vincent Sterk、Petr Sedláček、Benjamin Pugsley，《The Nature of Firm Growth》，AER 111(2)，2021，正式33页版。§I.A–F、Table1、Figure4（印刷pp.550–559）；引言p.548与正文p.558的百分比差异按原文保留。没有重新估计受限微观数据，也未采用§II完整结构模型。[开放正式版](https://discovery.ucl.ac.uk/id/eprint/10109806/1/Sterk_aer.20190748.pdf)。

<script src="/notebook/labs/ei-b/reader-adapter.js" defer></script>


## Additional teaching material
### 本篇实验静态等价与计算说明

a=120,c=0，潜在上限10，默认K=800。
N=1..6变动利润：3600,1600,900,576,400,293.877551。
均衡集合：K800->{3}；350->{5}；900->{2,3}；400->{4,5}。
默认N3时每家q30，价格30，变动利润900，净利润100；
K350时N5，每家q20，价格20，变动利润400，净利润50。

算法枚举N=0..cap。a,c,K、cap均为合法范围内整数。
g=max(a-c,0)，正N变动利润g²/(N+1)²。
现有企业条件：N=0或g²>=K(N+1)²。
外部条件：N=cap或g²<=K(N+2)²。
用整数BigInt比较，保留零净利润等号。
cap0->{0}；a<=c,K>0->{0}；a<=c,K0->{0,1,...,cap}，采用零产量续局。
无成交时成交价null，不显示未发生的交易价格。
a/c合法0..200，K0..20000，cap0..20。到cap不再检查不存在的下一家。

EIA静态卡：2026-02-20文章报告2025新增53GW、2026当时计划86GW。不能当同批兑现率，不能当模型N或K。
退出例：过去沉没900；继续现金120+残值30=150，立即清算100，选择继续；
未来现金降为40时，继续70<100，选择退出。各值已统一决策时点的教学单位。


## Experiment inputs and static equivalents
```json
[
  {
    "id": "exp-ei08-entry",
    "title": "进入、退出与产业资本投入：机制实验",
    "anchor": "ei08-experiment",
    "description": "g=max(a-c,0); var_profit(N)=g^2/(N+1)^2. Enumerate 0..cap; incumbent g^2>=K*(N+1)^2; outsider g^2<=K*(N+2)^2 only when N<cap.",
    "inputs": {
      "input_version": "2026-09-21-review-v2",
      "facts": {
        "eia": {
          "source_ids": [
            "EIBC-S05A",
            "EIBC-S05B"
          ],
          "article_date": "2026-02-20",
          "rows": [
            {
              "year": 2025,
              "capacity_gw": 53,
              "status": "reported_realized_additions"
            },
            {
              "year": 2026,
              "capacity_gw": 86,
              "status": "plan_if_realized"
            }
          ]
        }
      },
      "models": {
        "entry": {
          "identity": "teaching_assumption",
          "defaults": {
            "a": 120,
            "c": 0,
            "K": 800,
            "cap": 10
          },
          "ranges": {
            "a": [
              0,
              200,
              1
            ],
            "c": [
              0,
              200,
              1
            ],
            "K": [
              0,
              20000,
              1
            ],
            "cap": [
              0,
              20,
              1
            ]
          },
          "presets": [
            {
              "K": 800,
              "expected": [
                3
              ]
            },
            {
              "K": 350,
              "expected": [
                5
              ]
            },
            {
              "K": 900,
              "expected": [
                2,
                3
              ]
            },
            {
              "K": 400,
              "expected": [
                4,
                5
              ]
            }
          ],
          "conditions": [
            "finite identical potential entrants; one operating period",
            "weak entry incentives, no maximal-N selection",
            "cap=0 -> {0}",
            "a<=c -> zero-output continuation; if K=0 every N from 0..cap indifferent",
            "no trades -> no transaction price"
          ]
        },
        "exit": {
          "identity": "teaching_assumption",
          "unit": "same-date decision units",
          "past_sunk": 900,
          "continue_cash": 120,
          "future_salvage": 30,
          "salvage_now": 100,
          "stress_cash": 40
        }
      },
      "default_outputs": {
        "entry": {
          "a": 120,
          "c": 0,
          "K": 800,
          "cap": 10,
          "equilibrium_set": [
            3
          ],
          "rows": [
            {
              "N": 0,
              "q_each": null,
              "Q": 0,
              "price": null,
              "variable_profit": null,
              "net_profit": null,
              "incumbentOK": true,
              "outsiderOK": false,
              "next_exists": true,
              "equilibrium": false,
              "cap_bound": false,
              "entry_tie": false,
              "incumbent_tie": false
            },
            {
              "N": 1,
              "q_each": 60,
              "Q": 60,
              "price": 60,
              "variable_profit": 3600,
              "net_profit": 2800,
              "incumbentOK": true,
              "outsiderOK": false,
              "next_exists": true,
              "equilibrium": false,
              "cap_bound": false,
              "entry_tie": false,
              "incumbent_tie": false
            },
            {
              "N": 2,
              "q_each": 40,
              "Q": 80,
              "price": 40,
              "variable_profit": 1600,
              "net_profit": 800,
              "incumbentOK": true,
              "outsiderOK": false,
              "next_exists": true,
              "equilibrium": false,
              "cap_bound": false,
              "entry_tie": false,
              "incumbent_tie": false
            },
            {
              "N": 3,
              "q_each": 30,
              "Q": 90,
              "price": 30,
              "variable_profit": 900,
              "net_profit": 100,
              "incumbentOK": true,
              "outsiderOK": true,
              "next_exists": true,
              "equilibrium": true,
              "cap_bound": false,
              "entry_tie": false,
              "incumbent_tie": false
            },
            {
              "N": 4,
              "q_each": 24,
              "Q": 96,
              "price": 24,
              "variable_profit": 576,
              "net_profit": -224,
              "incumbentOK": false,
              "outsiderOK": true,
              "next_exists": true,
              "equilibrium": false,
              "cap_bound": false,
              "entry_tie": false,
              "incumbent_tie": false
            },
            {
              "N": 5,
              "q_each": 20,
              "Q": 100,
              "price": 20,
              "variable_profit": 400,
              "net_profit": -400,
              "incumbentOK": false,
              "outsiderOK": true,
              "next_exists": true,
              "equilibrium": false,
              "cap_bound": false,
              "entry_tie": false,
              "incumbent_tie": false
            },
            {
              "N": 6,
              "q_each": 17.142857142857142,
              "Q": 102.85714285714286,
              "price": 17.142857142857142,
              "variable_profit": 293.8775510204082,
              "net_profit": -506.1224489795918,
              "incumbentOK": false,
              "outsiderOK": true,
              "next_exists": true,
              "equilibrium": false,
              "cap_bound": false,
              "entry_tie": false,
              "incumbent_tie": false
            },
            {
              "N": 7,
              "q_each": 15,
              "Q": 105,
              "price": 15,
              "variable_profit": 225,
              "net_profit": -575,
              "incumbentOK": false,
              "outsiderOK": true,
              "next_exists": true,
              "equilibrium": false,
              "cap_bound": false,
              "entry_tie": false,
              "incumbent_tie": false
            },
            {
              "N": 8,
              "q_each": 13.333333333333334,
              "Q": 106.66666666666667,
              "price": 13.333333333333334,
              "variable_profit": 177.77777777777777,
              "net_profit": -622.2222222222222,
              "incumbentOK": false,
              "outsiderOK": true,
              "next_exists": true,
              "equilibrium": false,
              "cap_bound": false,
              "entry_tie": false,
              "incumbent_tie": false
            },
            {
              "N": 9,
              "q_each": 12,
              "Q": 108,
              "price": 12,
              "variable_profit": 144,
              "net_profit": -656,
              "incumbentOK": false,
              "outsiderOK": true,
              "next_exists": true,
              "equilibrium": false,
              "cap_bound": false,
              "entry_tie": false,
              "incumbent_tie": false
            },
            {
              "N": 10,
              "q_each": 10.909090909090908,
              "Q": 109.09090909090908,
              "price": 10.909090909090908,
              "variable_profit": 119.00826446280992,
              "net_profit": -680.99173553719,
              "incumbentOK": false,
              "outsiderOK": true,
              "next_exists": false,
              "equilibrium": false,
              "cap_bound": true,
              "entry_tie": false,
              "incumbent_tie": false
            }
          ],
          "nonpositive_margin_corner": false,
          "zero_output_continuation": false,
          "no_potential_entrants": false
        }
      }
    },
    "outputs": {
      "entry": {
        "a": 120,
        "c": 0,
        "K": 800,
        "cap": 10,
        "equilibrium_set": [
          3
        ],
        "rows": [
          {
            "N": 0,
            "q_each": null,
            "Q": 0,
            "price": null,
            "variable_profit": null,
            "net_profit": null,
            "incumbentOK": true,
            "outsiderOK": false,
            "next_exists": true,
            "equilibrium": false,
            "cap_bound": false,
            "entry_tie": false,
            "incumbent_tie": false
          },
          {
            "N": 1,
            "q_each": 60,
            "Q": 60,
            "price": 60,
            "variable_profit": 3600,
            "net_profit": 2800,
            "incumbentOK": true,
            "outsiderOK": false,
            "next_exists": true,
            "equilibrium": false,
            "cap_bound": false,
            "entry_tie": false,
            "incumbent_tie": false
          },
          {
            "N": 2,
            "q_each": 40,
            "Q": 80,
            "price": 40,
            "variable_profit": 1600,
            "net_profit": 800,
            "incumbentOK": true,
            "outsiderOK": false,
            "next_exists": true,
            "equilibrium": false,
            "cap_bound": false,
            "entry_tie": false,
            "incumbent_tie": false
          },
          {
            "N": 3,
            "q_each": 30,
            "Q": 90,
            "price": 30,
            "variable_profit": 900,
            "net_profit": 100,
            "incumbentOK": true,
            "outsiderOK": true,
            "next_exists": true,
            "equilibrium": true,
            "cap_bound": false,
            "entry_tie": false,
            "incumbent_tie": false
          },
          {
            "N": 4,
            "q_each": 24,
            "Q": 96,
            "price": 24,
            "variable_profit": 576,
            "net_profit": -224,
            "incumbentOK": false,
            "outsiderOK": true,
            "next_exists": true,
            "equilibrium": false,
            "cap_bound": false,
            "entry_tie": false,
            "incumbent_tie": false
          },
          {
            "N": 5,
            "q_each": 20,
            "Q": 100,
            "price": 20,
            "variable_profit": 400,
            "net_profit": -400,
            "incumbentOK": false,
            "outsiderOK": true,
            "next_exists": true,
            "equilibrium": false,
            "cap_bound": false,
            "entry_tie": false,
            "incumbent_tie": false
          },
          {
            "N": 6,
            "q_each": 17.142857142857142,
            "Q": 102.85714285714286,
            "price": 17.142857142857142,
            "variable_profit": 293.8775510204082,
            "net_profit": -506.1224489795918,
            "incumbentOK": false,
            "outsiderOK": true,
            "next_exists": true,
            "equilibrium": false,
            "cap_bound": false,
            "entry_tie": false,
            "incumbent_tie": false
          },
          {
            "N": 7,
            "q_each": 15,
            "Q": 105,
            "price": 15,
            "variable_profit": 225,
            "net_profit": -575,
            "incumbentOK": false,
            "outsiderOK": true,
            "next_exists": true,
            "equilibrium": false,
            "cap_bound": false,
            "entry_tie": false,
            "incumbent_tie": false
          },
          {
            "N": 8,
            "q_each": 13.333333333333334,
            "Q": 106.66666666666667,
            "price": 13.333333333333334,
            "variable_profit": 177.77777777777777,
            "net_profit": -622.2222222222222,
            "incumbentOK": false,
            "outsiderOK": true,
            "next_exists": true,
            "equilibrium": false,
            "cap_bound": false,
            "entry_tie": false,
            "incumbent_tie": false
          },
          {
            "N": 9,
            "q_each": 12,
            "Q": 108,
            "price": 12,
            "variable_profit": 144,
            "net_profit": -656,
            "incumbentOK": false,
            "outsiderOK": true,
            "next_exists": true,
            "equilibrium": false,
            "cap_bound": false,
            "entry_tie": false,
            "incumbent_tie": false
          },
          {
            "N": 10,
            "q_each": 10.909090909090908,
            "Q": 109.09090909090908,
            "price": 10.909090909090908,
            "variable_profit": 119.00826446280992,
            "net_profit": -680.99173553719,
            "incumbentOK": false,
            "outsiderOK": true,
            "next_exists": false,
            "equilibrium": false,
            "cap_bound": true,
            "entry_tie": false,
            "incumbent_tie": false
          }
        ],
        "nonpositive_margin_corner": false,
        "zero_output_continuation": false,
        "no_potential_entrants": false
      }
    },
    "algorithm": {
      "formula": "g=max(a-c,0); var_profit(N)=g^2/(N+1)^2. Enumerate 0..cap; incumbent g^2>=K*(N+1)^2; outsider g^2<=K*(N+2)^2 only when N<cap.",
      "algorithm": "engine.entry; BigInt exact integer comparisons keep weak equality; zero-output continuation",
      "boundary_tests": [
        "K800/350 unique",
        "K900/400 weak sets",
        "K3600 {0,1}",
        "cap0",
        "cap bound",
        "a<=c K0 all counts"
      ],
      "static": "readers/EI-08.reader.md#ei08-entryset; static/static-equivalents.md second unit"
    },
    "static_equivalent": {
      "markdown": "https://ou-liu-red-sugar.github.io/notebook/labs/ei-b/static-equivalents.md",
      "in_entry": "ei08-experiment",
      "text": "/ ei08-experiment\n\na=120,c=0，潜在上限10，默认K=800。\nN=1..6变动利润：3600,1600,900,576,400,293.877551。\n均衡集合：K800->{3}；350->{5}；900->{2,3}；400->{4,5}。\n默认N3时每家q30，价格30，变动利润900，净利润100；\nK350时N5，每家q20，价格20，变动利润400，净利润50。\n\n算法枚举N=0..cap。a,c,K、cap均为合法范围内整数。\ng=max(a-c,0)，正N变动利润g²/(N+1)²。\n现有企业条件：N=0或g²>=K(N+1)²。\n外部条件：N=cap或g²<=K(N+2)²。\n用整数BigInt比较，保留零净利润等号。\ncap0->{0}；a<=c,K>0->{0}；a<=c,K0->{0,1,...,cap}，采用零产量续局。\n无成交时成交价null，不显示未发生的交易价格。\na/c合法0..200，K0..20000，cap0..20。到cap不再检查不存在的下一家。\n\nEIA静态卡：2026-02-20文章报告2025新增53GW、2026当时计划86GW。不能当同批兑现率，不能当模型N或K。\n退出例：过去沉没900；继续现金120+残值30=150，立即清算100，选择继续；\n未来现金降为40时，继续70<100，选择退出。各值已统一决策时点的教学单位。"
    },
    "implementation_files": [
      "/notebook/labs/ei-b/inputs.json",
      "/notebook/labs/ei-b/inputs.js",
      "/notebook/labs/ei-b/engine.js",
      "/notebook/labs/ei-b/ui.js",
      "/notebook/labs/ei-b/interactions.html"
    ],
    "state": "staging_only_awaiting_Lead_UI",
    "local_url": "/notebook/labs/ei-b/interactions.html?experiment=exp-ei08-entry"
  }
]
```

## Sources
- [Static Competition and Models of Differentiation, Part 1](https://ocw.mit.edu/courses/14-271-industrial-organization-i-fall-2022/mit14_271_f22_lec5slides.pdf): 静态Cournot、Bertrand和Hotelling的条件与一阶条件；本包无退出选项的覆盖市场、数值和角点验证为教学改写，并非会员公司参数估计。
- [Entry](https://ocw.mit.edu/courses/14-271-industrial-organization-i-fall-2022/mit14_271_f22_lec16slides.pdf): 两阶段进入的纯策略弱条件；零利润边界不唯一。有限上限、N=0及无产量情形按本包完整明示的教学续局计算。
- [New U.S. electric generating capacity expected to reach a record high in 2026](https://www.eia.gov/todayinenergy/detail.php?id=67205): 固定文章报告2026计划新增86 GW与2025已新增53 GW。两值分属不同年度和状态，不是同批项目兑现率。

本批采用：计划容量并非实际投运或MWh发电，不计算两年度的项目兑现率。
- [Preliminary Monthly Electric Generator Inventory](https://www.eia.gov/electricity/data/eia860m/index.php): 月度存量/计划资料可修订，容量不等于设施承诺。仅用方法正文，不采用未读状态码或当前工作簿字段。

本批采用：月度库存含现有与拟建项目，估计可修订；没有读取状态码就不造状态码交互。
- [The Nature of Firm Growth](https://discovery.ucl.ac.uk/id/eprint/10109806/1/Sterk_aer.20190748.pdf): §I平衡面板对数就业横截面方差分解；正文age0约85%、age20约40%，后者为外推。与引言90%+不一致。只作进入异质性选读，不作成功概率或项目校准。

## Content relations
```json
[
  {
    "from": "zh-ei08",
    "relation": "part_of",
    "to": "industry-structure",
    "reason": "主要 topic 归属"
  },
  {
    "from": "ei08-capital",
    "relation": "illustrated_by",
    "to": "CASE-EI08-EIA-GENERATOR-PLAN-2026",
    "reason": "固定期间的真实材料，保留单位与统计对象",
    "at_section": "ei08-capital"
  },
  {
    "from": "ei08-cournot",
    "relation": "supported_by",
    "to": "EIBC-S01",
    "reason": "静态Cournot、Bertrand和Hotelling的条件与一阶条件；本包无退出选项的覆盖市场、数值和角点验证为教学改写，并非会员公司参数估计。",
    "locator": "slides 3–4 Cournot; slide 5 Bertrand; slides 6–7 Hotelling",
    "scope": "指定采用单元，不等于整部报告",
    "at_section": "ei08-cournot"
  },
  {
    "from": "ei08-entryset",
    "relation": "supported_by",
    "to": "EIBC-S02",
    "reason": "两阶段进入的纯策略弱条件；零利润边界不唯一。有限上限、N=0及无产量情形按本包完整明示的教学续局计算。",
    "locator": "slides 2–3; slide 11 learning/exit background",
    "scope": "指定采用单元，不等于整部报告",
    "at_section": "ei08-entryset"
  },
  {
    "from": "ei08-capital",
    "relation": "supported_by",
    "to": "EIBC-S05A",
    "reason": "固定文章报告2026计划新增86 GW与2025已新增53 GW。两值分属不同年度和状态，不是同批项目兑现率。",
    "locator": "Article opening, source period and planned/realized statements",
    "scope": "指定采用单元，不等于整部报告",
    "at_section": "ei08-capital"
  },
  {
    "from": "ei08-capital",
    "relation": "supported_by",
    "to": "EIBC-S05B",
    "reason": "月度存量/计划资料可修订，容量不等于设施承诺。仅用方法正文，不采用未读状态码或当前工作簿字段。",
    "locator": "Methods text above yearly workbook lists; Capacity commitments paragraph",
    "scope": "指定采用单元，不等于整部报告",
    "at_section": "ei08-capital"
  },
  {
    "from": "ei08-research",
    "relation": "supported_by",
    "to": "EIBC-S06",
    "reason": "§I平衡面板对数就业横截面方差分解；正文age0约85%、age20约40%，后者为外推。与引言90%+不一致。只作进入异质性选读，不作成功概率或项目校准。",
    "locator": "§I.A–F, printed pp.550–559; Table 1; §I.E p.558; Figure 4 p.559; introduction p.548 conflict",
    "scope": "指定采用单元，不等于整部报告",
    "at_section": "ei08-research"
  },
  {
    "from": "ei08-cournot",
    "relation": "uses_method",
    "to": "zh-ei07",
    "reason": "进入后的产品市场竞争决定变动利润",
    "at_section": "ei08-cournot"
  },
  {
    "from": "ei08-capital",
    "relation": "uses_method",
    "to": "zh-ei04",
    "reason": "资本投运后还受有效供给条件约束",
    "at_section": "ei08-capital"
  },
  {
    "from": "ei08-capital",
    "relation": "informs",
    "to": "zh-ei09",
    "reason": "资本形成时间轴；与供应链交期分开",
    "at_section": "ei08-capital"
  },
  {
    "from": "ei08-experiment",
    "relation": "illustrated_by",
    "to": "exp-ei08-entry",
    "at_section": "ei08-experiment",
    "reason": "g=max(a-c,0); var_profit(N)=g^2/(N+1)^2. Enumerate 0..cap; incumbent g^2>=K*(N+1)^2; outsider g^2<=K*(N+2)^2 only when N<cap."
  }
]
```

## Related entries

## Optional reading path
读懂一个行业: step 5/10
先求经营续局与进入集合，再区分计划、投入、投运和退出。
资本形成连接着上下游；先用投入产出表追踪生产需要，再研究交付与库存的时间。
Next: [产业链、投入产出与上下游联系](https://ou-liu-red-sugar.github.io/zh/notebook/input-output-and-production-linkages/)