## Core of Economics

1. Optimization: (Postulate of Rational Choice) \begin{align} {\text{maximize}} \quad&\text{value}(\text{choice}; \text{others' choice}) \\ \text{subject to} \quad&\text{choice} \in \text{alternatives} \end{align}
2. Competition:
3. Trade: (The Law of Demand)
4. Production: (The Law of Diminishing Marginal Productivity)
• $\mathbf{e}' \cdot \nabla^2 f \cdot \mathbf{e} < 0$: diminishing marginal productivity;
• $\nabla^2 f \cdot \mathbf{r} = \mathbf{0}$: isolines of marginal productivity;
• $\mathbf{x}' \cdot \nabla^2 f \cdot \mathbf{y} > 0$: marginal productivity of complementary factors increase;

### Postulates of economics

Like Variational Principles of physical systems, the fundamental principle of social systems is the postulate of rational choice. But instead of a single optimality/stationarity, the dynamics of social systems are usually outcomes of multiple competing objectives, which requires game theoretic analysis.

Postulate of rational choice is stated in two parts:

1. Postulate of individual choice: All human behaviors originate from individual choice, which can be inferred.
• Implicit postulate: Individuals are the fundamental unit for all economic analysis.
2. Postulate of constrained maximization (rational choice; rationality as optimization): All individuals aim to obtain their maximum value under constrained options.
1. Constraint (rule/institution): delimitation of property and individual rights, such as private property rights, regulation, custom, religion;
2. Payoff functions (竞争准则): value, cost; market price, queuing, seniority, force, etc;

Three categories of economic inference (经济学的三范畴):

1. Choice of institution 游戏规则/局限条件的形成;
2. Payoff mechanism under institution 竞争准则;
3. Equilibrium: individual behavior (e.g. resource allocation), payoff distribution (e.g. income/wealth distribution);

### Laws of economics

• The Law of Demand:
• For any economic goods, demand increases if and only if its price decreases;
• Proof: As the use value of any goods never decrease when quantity increases, its dual representation $q(p) = \arg\sup_{q \ge 0} { u(q) - \langle p, q \rangle }, \forall p \ge 0$ is not trivial and never increases; there's no need to assume the use value function is concave;
• There shall be no Giffen goods (demand increases as price rises, and vice versa, {Marshall1890});
• Demand and supply curves are the save curve with opposite quantity axes: an individual acts as a supplier when holding more than the equilibrium quantity, a demander when holding less;
• Every individual in the market has (almost) the same marginal use value of the goods as its market price;
• 只要需求定律的验证含意不被事实推翻，其它的不变因素愈少愈好，其它可变量愈多愈好：凡是直接影响价格的其它因素皆可变；凡是直接影响需求量的其它因素皆不可变；价格转变引起的其它间接影响需求量的因素皆可变。
• The Law of Diminishing Marginal Productivity (边际产量下降定律; law of diminishing returns, 回报率下降定律): {von-Thunen1826, Marshall1890}
• When multiple factors of production are used, increasing the quantity of one factor while keeping others unchanged will increase the total production, but the increase rate will diminish while total production peaks and falls.
• 以竖线为边际产量横线为部分生产要素的量，部分生产要素的边际产量曲线向右下倾斜且可以为负。
• 边际产量曲线开头可以有上升的部分，可以归因于生产方法转变。
• 若一种生产要素增加时其平均产量下降(边际产量低于平均产量)，另一种要素的边际产量必定上升。
• 部分生产要素的总产量曲线呈倒扣碗形。
• 生产要素的量可以换成比例；生产要素不限于两种。
• 边际产量下降定律适用于物品生产，不事生产的物品交换依然满足需求定律。
• 需求定律可以替代边际产量下降定律，但好些情况下不如它好用，因为原则上边际产量可以观察。
• Coase Theorem 科斯定律:
1. Condition of market transaction:
• The delimitation of rights is an essential prelude to market transactions {Coase1959}; 权利界定是市场交易必要的先决条件;
• Without the establishment of this initial delimitation of rights there can be no market transactions to transfer and recombine them. {Coase1960}; 市场交易不是物品交换那么简单，而是权利的买卖;
2. (Invariance Theorem): But the ultimate result (which maximises property rent/value) is independent of the legal position if the pricing system is assumed to work without cost {Coase1960}; 只要权利有明确界定，不论属谁，资源使用的效率不变且由市场决定;
3. (Introduction of transaction costs): 权利的界定与市场没有交易费用的运作会满足经济效率; 如果交易费用是零，不需要资产权利界定和市场，资源的使用总会达到最高的价值。

Other important results:

• Fundamental Theorem of Exchange (交易定理): Voluntary exchange benefits all parties involved.
• Say's Law {Say1803}: Supply creates its own demand;
• The law of comparative advantage (比较优势定律) {Ricardo1817}:
• Trade can benefit both parties if they specialize (专业生产) in producing the product they are best at, even if one of them is better at producing everything than the other.
• 不同的生产单位（个人、企业、国家），生产同样的物品，只要生产要素的比例不同，就会有不同的成本，各自选择成本较低的来专业生产，然后在市场交易可以互相得益。
• Absolute advantage in doing something compares across production units, while comparative advantage compares within each unit.
• Laffer Curve {Keynes1972}: No tax revenue will be raised at the extreme tax rates of 0% and 100% and that there must be at least one rate which maximizes government taxation revenue;
• The Law of Contractual Performance (履行定律), 选择定律; 四二均衡定律——引进交易费用的市场一般均衡;

Other results by Cheung:

• 成本定律：直接成本是按量度产量而支付的费用。
• 玉石定律：需要专家鉴证的物品，自私自利的行为会增加讯息传达的费用，但没有这种费用的增加那些物品不会有贵重的市场。 （没有专家翡翠不值钱）
• 摊数定律：物品的讯息费用上升，在竞争市场出售的摊档数量会增加，但讯息费用升到某一点摊档的数量会下降。
• 权利定律：人与人之间的权利不可能平等，因为先天与后天的局限不同；如果我们要产权平等，人权的不平等一定要增加；如果我们要人权平等，产权的不平等一定要增加。
• 捆绑定律
• 欺骗定律: 一个艺术家不能持久地欺骗所有的人。 (造价的人一般谨慎)
• 一般均衡：任何经济分析，衡量所有局限，如果有应该消散但没有消散的租值存在，该分析一定错。
• 产权分派的生产定理
• 价格分歧、座位票价、隔离收费、全线逼销、上头成本、挤迫效应、
• 类聚定律、仓库理论

Main interpretations:

1. 权利谁属谁较富有。
2. 只要权利有明确界定，不论属谁，资源使用的效率不变且由市场决定。

### Criticism on mainstream economics

1. The law of comparative advantage {Ricardo1817} 比较优势定律一团糟，因为汇率一团糟，而且专业生产还有其它重要的决定因素（分工合作、熟能生巧、知识累积）;
2. Gresham’s law {Macleod1858} 格拉森定律(劣币逐良币)是谬论: 劣币良币可以共存; 如果劣币大劣, 良币会把劣币逐出市场;
3. General equilibrium {Walras1874} 瓦尔拉斯的一般均衡理念没有经济内容; 芝加哥的奈特、弗里德曼与施蒂格勒见解一致;
4. Welfare economics {Pigou1920} 福利经济学毫无解释或推断功能;
5. Price discrimination {Robinson1933} 传统的价格分歧理论（价格分歧源于需求弹性系数差异）不知世事错得离谱, 应解释为资源空置。
6. Keynesian macroeconomics {Keynes1936} 传统宏观经济学有严重的失误：不深入调查个人选择的局限，国民收入没有算消费者盈余且不适合用于国际比较，只要回报有盈余政府财政赤字原则上可以无限大，失业没有从公司合约解释; 意同 Alchian "There is no such thing as macroeconomics." {Allen2010};
7. IS-LM model of general equilibrium {Hicks1937}
• (产品市场均衡曲线——意图投资与意图储蓄永远相等) 投资与储蓄是同一回事;
• (货币市场均衡曲线——货币的需求与供应永远均衡) 货币何物与币量应该怎样算到今天还争议不休，真实世界利率受到管制;
8. "Second law of demand" {Alchian, Stigler} 需求第二定律(需求的价格弹性随时间增加)不能成立;
9. Game theory {Cheung1969} 博弈理论的变数（比如人的意图——偷懒、卸责、欺骗、恐吓、勒索）可能存在但往往无从观察，因而无从验证;

## Basic Concepts

### Goods & Property

Preference is an individual's subjective ordering of one thing over another. Symbolically, an individual's preference is a binary relation $\succeq$ on subsets of the universe $U$: ignoring equivalent expressions, $\forall A, B \subseteq U$, an individual may

1. weakly prefer $A \succeq B$,
2. (strictly) prefer $A \succ B \iff A \succeq B \land \lnot B \succeq A$,
3. be indifferent $A \sim B \iff A \succeq B \land B \succeq A$, or
4. regard as incomparable $A \parallel B \iff \lnot (A \succeq B \lor B \succeq A)$; comparability is denoted by $A \perp B$.

Goods (物品) are any physical subject an individual prefers to have than not (有胜于无): $x \succ \emptyset$.

Scarcity (缺乏) is a state of supply which an individual prefers more of, regardless of the current amount; (多胜于少). Abundance is a state of supply that is not scarce. Economic goods (经济物品) are goods scarce to an individual who would sacrifice somewhat in exchange for more of it: $A \cup x \succ A$, where $A$ denotes the individual's all personal asset. Free goods (免费物品) are any non-economic good to an individual, who does not need to sacrifice anything to obtain more of it.

Competition is a situation where more than one individual regard a subject as economic goods. Property (物产) is any competitive economic good.

Goods ⊃ Scarcity ⊃ Economic Goods ⊃ Property

### Value & Quantity 价与量

Consider a population of $n$ individuals: $N = \{ 1, \dots, n \}$, and assume all goods in the world can be categorized into distinct groups indexed by $g \in G$, each homogeneous within itself. Each individual $i$ may have various ways, indexed by $m \in M_i$, to use goods in the world and find value in the outcome. Let the $m$-th way for individual $i$ to use goods take multiple units of $a_m = \{ m_g \mid g \in G \} \subseteq U$, and find value in the way of use: $u_{im} : a_m \mathbb{R}_{\ge 0} \to \mathbb{R}_{\ge 0}$. Function $u_{im}$ shall be non-decreasing: $\forall k > l \ge 0, u_{im}(a_m k) \ge u_{im}(a_m l)$.

Let $A_i \subseteq U$ be the asset of individual $i$, the use value of asset the individual can get (without trade), $u_i: 2^U \to \mathbb{R}_{\ge 0}$, is the maximum total value by partitioning the asset for different ways of use: $u_i(A_i) = \max_{x_m \in P_{A_i}} \sum_m u_{im}(x_m)$, where $P_{A_i} = \{ x_m \mid m \in M_i \}$ denotes a partition of asset $A_i$ so that $\forall m \in M_i, \exists k \ge 0, x_m = k a_m$, and $\cup_m x_m = A_i$. Function $u_i$ shall be non-decreasing in the lattice ordered by subset inclusion: $\forall X \subset Y \subseteq U, u_i(X) \le u_i(Y)$.

The use value of additional asset $x = \{ x_g \mid g \in G \}$ to individual $i$ is the increase in use value of asset (without trade): $\delta_x u_i(A_i) = u_i(A_i \cup x) - u_i(A_i)$. The use value of differential asset to individual $i$ is the gradient/difference in in use value of asset (without trade): $\nabla_g u_i(A_i)$, or $\text{D}_g u_i(A_i)$. If additional asset $x$ is small, we can write $\nabla_g u_i(A_i) \cdot x = \delta_x u_i(A_i)$.

For individuals $i,j$ to voluntarily trade goods $x,y$ where $x \cap y = \emptyset$ and no currency is involved, it is necessary that the trade benefits both parties: \begin{align} \Delta u_i(A_i) &= \nabla u_i(A_i) \cdot (-x, y) \ge 0 \\ \Delta u_j(A_j) &= \nabla u_j(A_j) \cdot (x, -y) \ge 0 \end{align}

Figure: Illustration of trade in the goods spaces of two individuals.

The exchange value of $x$ to individual $i$ while sacrificing $y$ (without currency) is the sacrificed use value of asset: $\varepsilon_{x,y} u_i(A_i) = u_i(A_i \cup x) - u_i((A_i \setminus y) \cup x)$. The condition of trade can also be expressed as: the use value of the additional asset is no less than its exchange value. $\delta_x u_i(A_i) \ge \varepsilon_{x,y} u_i(A_i)$.

Figure: Illustration of Nash equilibria in trade. $p_i, p_j$ are the NE if one party has absolute negotiation power.

Let the monetary value of goods (single location) be $q: 2^A \to \mathbb{R}_{\ge 0}$, consumer price index (CPI) at the location is the monetary value of a basket of goods $B = \{ b_g \mid g \in G \}$: $\text{CPI} = \sum_g q(b_g)$. Inflation at the location is the increase rate of consumer price index: $\frac{\Delta \text{CPI}}{\Delta t}$.

Currency exchange value (single location) is the use value of additional asset that can be purchased by unit currency: $v = \frac{\nabla u_i(A_i) \cdot B}{\text{CPI}} = \frac{\nabla u_i(A_i) \cdot x}{q(x)}$. At economic equilibrium, the marginal use value of goods for every individual should equal the exchange value of their market price at that location: $\frac{\partial u_{im}}{\partial x_m} = v \frac{\text{d} q}{\text{d} x_m}, \forall i \in N, \forall m \in M$. This implies that: deflation causes hoarding of physical assets; market price decrease of a good causes hoarding of that good; market price increase of a good causes dumping and production of that good.

The exchange value of goods $x$ in trade (single location) is the exchange value of price, $\varepsilon_{x,q} = v q$, in case of paying money; it is the use value of sacrificed asset to the individual, $\varepsilon_{q,x;i} = | \delta_{-x} u_i(A_i) |$, in case of earning money. The use value of asset and money (single location) is the sum of use value of physical asset and the exchange value of savings: $u_i(A_i \cup Q_i) = u_i(A_i) + v Q_i$.

The use value of asset and money (inter-regional)...

The use value (用值) of some goods is the maximum value (nominal number) the holder can extract from it, or from the opposite perspective, the maximum value the individual willing to sacrifice to obtain it: $u(x) = \| \mathbf{u}(x) \|_\infty$; $u(x) \ge u(y) \iff A \setminus y \succeq A \setminus x$. The exchange value (换值) of some goods is the use value the individual sacrificed for obtaining it: $v_i(x) = \min \{ u_i(y) \mid y \subseteq A, \max_j \{ u_j(x) - u_j(y) \} \ge 0 \}$. If a market exists for the goods, exchange value equals its market price (市价);

These definitions of value are based on exchange, which is perfectly acceptable when trade is the only concern. However, common sense understanding of use value is far from close to its economic definition. Consider a situation where milk and bread are both scarce goods to you, do you consider their use values comparable? In general, goods are of different kinds, which is equivalent to say they are of different types of use value. Within each well-defined value type, goods can be totally ordered, sometimes even admitting a metric. But any goods can have multiple or infinite types of use value to an individual, which include the exchange-based use value. Use value defined in economics shall be understood as exchange value, and exchange value be understood as exchange value of the other in a transaction; the two shall be exactly the same in an ideal transaction.

From this perspective, legal tenders have emerged as the only kind of goods with pure exchange value, that is, it has no use value other than exchange value in any scenario for any individual. Since exchange is reciprocal (symmetric and transitive), exchange values are . Monetary value embodies exchange value, and has been adopted by economists as the universal measure of use values across goods and individuals.

From this broader perspective, the postulate of economics asserts that individuals' choices can be inferred as if their only objective is the exchange value of their asset.

Quantity 数量:

• Demand 需求量: 在某价格下某人意图获取的量。
• Supply 供应量: 在某价格下某人意图舍弃的量。

### Equilibrium & Disequilibrium 均衡／不均衡

Economic equilibrium is the choices where value gets maximized under the constraints: $s^* = \arg\max_{s \in S} u(s)$.

Equilibrium can also be interpreted as the equality of marginal values, e.g. marginal cost equals marginal return. Marginal (边际量) is a qualifier that refers to the differential of a variable.

If an economic model properly represents the real world phenomenon, economic equilibrium should always coincide with observation. 均衡可以阐释为经济分析有足够的局限界定，因而推出可以被事实验证的假说，即有机会被事实推翻; Disequilibrium 不均衡是指局限界定不足，没有可以被事实验证的假说，即是没有理论: 不均衡所谓的剩余或短缺不会出现. 经济学的均衡和不均衡都只是概念，不存在于真实世界，无从观察, 不要跟物理学的均衡混为一谈。

The classic result of market equilibrium should be stated as: when a good reaches market equilibrium, its marginal use value to all individuals are the same, represented by its market price. Together with the conservation of quantity under trade, this condition uniquely determines the distribution of the good within the population. Market equilibrium shall never be understood as when supply equals demand, which at best restates the conservation of quantity, and at worst dismisses this practical restriction altogether for some fictional understanding of demand and supply.

### Income & Cost 收入与成本

Income is a series of events. {Fisher1930} 收入是一连串的事件; 收入永远是流动的，有时间性. $\dot{C}(t) = \frac{\text{d} u(A)}{\text{d} t}$.

Return 利润是成本投资的利息回报，也即是市场给予的收入。 均衡意味着成本与收入看齐.

return = income

Profit (windfall) 盈利是意外的收入, 盈利是不能折现的收入。 事前不知道会发生，事后也不知何日君再来的盈利，是不会影响行为的。 意外所得不算资产，不可提前享用或出售。

The cost of an event is the highest-valued opportunity necessarily forsaken; 成本是无可避免的最高代价. 代价(sacrifice)是放弃选择的用值: $c = \min_s \max_{s' \in S \setminus \{s\}} u(s')$. Direct costs (prime costs) 直接成本是指那些不生产就不需要支付的费用，由市价决定。

Economic rent (租值) 是指收入变动而某角度资源使用不变的那部分的资产价值: $r = u(s^*) - c$. 只要考虑所有的选择，租值是成本的一部分。(?) 专利所赚到的、在生产要素成本以上的钱，因为不会被竞争者消灭，称为专利租值（monopoly rent）。

Overhead 上头成本是各直接成本以上的盈余之和，要视为租值。 Historical cost（通译“历史成本”）不是成本: 历史投资不直接算入生产单位租值极大化的选择。 Social cost 社会耗费（通译“社会成本”）也不是成本。

rent = overhead = return - direct costs

### Investment & Interest 投资与利息

Interest is not a part of income, but the whole of income. {Fisher1930}

Interest (利息) is a value determined by impatience to spend income and opportunity to invest it. {Fisher1930} 利息是提前享用或预先投资资产的价，由市场竞争决定。

return = income = interest

Interest rate is the ratio of interest to the present value of a property; 利息率是利息与现值的比率。 从社会整体的角度看，市场的利率是由投资或做生意的真实回报率决定的。 现实世界利息率多得五花八门，有两个原因：其一是通货膨胀，其二是风险或说是交易费用。 通胀或通缩是指未来日子的货币贬值或升值，这是由市场的预期促成的。 风险其实是执行借贷合约的费用，或是投资的未来回报（可视为讯息费用，但难处理）。

Wealth is the net present value (NPV) of an individual's lifetime income; 财富是全部收入的净现值. 财富是所有收入减却成本，以利率折现而得的现值. 财富是现值，本身没有时间，是静止的。 Annuity (permanent income, 年金收入)：财富乘以年利率。

Investment is the balancing of consumption over time; 投资是消费在时间上的权衡轻重。 放弃今天的消费来换取明天的消费. 储蓄与投资是同一回事，不管意图不意图，只是角度看法不同。 投资在边际上回报率不要低于市场的利息率。 投资与消费的社会均衡：社会通过利率的指引与市场的运作带来不同投资项目的边际回报率相等，以及不同消费者的时间边际意欲相等。

savings = investment

Capital asset (资产) 凡是可以导致收入的物产都是资产。 所有生产要素都是资产。 Capital value is the net present value (NPV) of an individual's future income; 资本是未来收入的净现值. 资本是未来收入折现后的现值，也是资产的市值; $C = u(A)$. 视现在无限短，则资本与财富相同。

unit time -> 0: capital value -> wealth

Separation Theorem 分离定律: 在有市场且交易费用够低的情况下，一个人的投资与消费可以分开来作决策。

## Efficiency: Social Cost, Rent dissipation, External Effects, Market failure, Transaction cost

Efficiency is a comparative concept between equilibria under different settings/mechanisms/institutions, measured in total payoff (aka social income).

［效率(efficiency) = 总租值最大化］ (Cheung's use of Pareto optimality shall be understood as Hicks optimality, which maximizes social income/surplus, sometimes even game theoretic solution concepts.) 解释行为所需要指定的局限不一定满足帕累托。 如果所有局限条件都放进分析，至善点一定得到满足；无效率或浪费的出现，是因为某些局限没有放进分析。 给定局限，租值一定会最大化(Not total rent)；只是不同局限下租值有高低，相比而言即是租值消散了。

## Institution & Contract 局限及其转变——合约理论

### Property rights 资产权利

Four aspects of property rights:

1. Ownership right 所有权: 所有权不重要;
2. Right to use 使用权: 收入没有主人，物主或业主不会热衷于监管或执行他的使用权利;
3. Right to earn income 收入权: 资源使用赚取租值的权利可以转到使用者的本领那边去; 价格管制(price control)、分成率管制(share control)，或与租值无干的分配财富的税务(tax for wealth redistribution)，一般会削弱(attenuate)收入权的界定从而出现租值消散;
4. Right to transfer 转让权: 转让权的存在是市场合约出现的一个先决条件; 转让权含意着该资产有私有的使用权与收入权，但倒转过来不成立;

• 两种生产要素，土地与劳力，各适其主，如果土地的一部分收入没有界定为谁属，在竞争下劳力投入相对土地的比率会上升，含意着劳力的边际产值下降与土地的边际产值上升。
• 如果没有界定的土地收入继续上升，劳力的边际产值会再下降。
• 当土地收入完全没有界定为谁属时，平均产值 = 平均成本, 劳力的边际产值可能是负值。

Private property (私产) is any property the holder has the right to transfer; 凡是人与人之间有转让权的资产。

Public and private goods:

1. Private goods (私用品)： The consumption of the goods is exclusive to one person. 私用品的市场需求曲线是个人需求曲线向右横加而成的：每价加个别需求者的需求量。 (horizontal stack)
2. Public goods (共用品) {Samuelson}： The goods allow concurrent use; 凡是享用人数增加而物品的量不增加属共用品. 共用品的市场的需求曲线是个别享用者的需求边际用值向上直加而成：每量加需求者的边际用值。 (vertical stack)

### Transaction / Institution cost 交易费用／制度费用

Transaction cost 交易费用是市场招致的费用: 市价的采用与厘定要付出产权界定、讯息传达、量度监管、合约磋商、风俗法律等费用。 公司的有形之手或经理人的收入全部是交易费用。 量度是以数字排列次序，而量度的精确性只能从不同观察者的认同性衡量; 交易费用起码在边际上（转变量）可以量度且不需要用基数——用序数排列高低足够，只要不同的观察者会作出同样的排列。

The Law of Contractual Performance 履行定律:

• 如果物品或生产要素指定是以某量作价成交，购买的人需要付出的监管费用会因为该量被算了价而下降，但没有被量度作价的其他量的监管费用会上升。
• 任何市场交易，因为讯息费用的存在，个人争取利益会出现不履行承诺的行为，或言而无信，甚或瞒骗，但量度了而作价的量，出售者会倾向于履行协议，因为量度费用（也是交易费用）是付出了的。

Institution cost includes costs that arise as a result of any arrangement used to conduct economic activities which involve two or more individuals. {Cheung1998} 凡是在一人世界不存在的费用，都是制度费用. 制度费用是广义的交易费用，还包含其他所有约束招致的费用： 现存制度的运作费用; 讯息费用：要知道其他制度怎样运作及效果如何的费用; 改制费用/抗拒费用：要说服或强迫那些认为改制会受到损害的人的费用，尤其是对于那些在以等级排列权利制度中的优胜者。

Interpretation of economic inefficiency:

• 以交易费用的角度看市场运作的合约最适当，因为是最直接的。
• 以制度费用的角度看市场之外的问题（例如风俗、宗教、论资排辈等）比较适当，因为是一般性的约束。
• 以租值消散的角度解释竞争行为最适用，因为其处理市场与非市场的竞争皆容易。
Rent dissipation = Transaction cost = Institution cost

### Contractual arrangement 公司理论

1. 件工合约: 市场之内的任何要素，只要量够大（commodity）都可以用件工合约; 但是过于零散而又变化多的工作难用件工，多人合作难以划分贡献的情况难用件工，产品质量容易有争议的难用件工。
2. 时间合约: 生产要素以时间算价; 这时要素市场与产品市场出现了分离。
3. 分成合约: 生产要素以产品价格分成算价; 分成合约的出现主要是因为参与的人不知产品的量; 不可以用风险规避(risk averse)、卸责(shirking)、偷懒来解释分成合约。

1. 分工合作带来的增产利益，在边际上要跟交易费用的边际上升相等。
2. 同样的产出贡献，合约选择的均衡是基于不同合约的交易费用在边际上相等。

### Price control 价格管制

1. 合约转变: 价格管制下市价作为决定竞争胜负的准则被压制，制度费用上升最少的其他竞争准则会出现;
2. 使用转变: 拥有资产使用权的参与者也可能选择资产价值下降最少的其他用途;

## Resource Allocation 资源分配

At societal level, efficient use of existing resources necessitates equal marginal products of each resource across all sectors it gets used. (See conclusion of {Cheung1969 6.B})

But this is only a necessary condition for economic equilibrium and does not guarantee maximum value.

Price searching 觅价 = monopoly pricing 垄断价格 逻辑上，觅价需要出售者面对向右下倾斜的需求曲线。 讨价还价显然是觅价，购买者与出售者皆觅价，面对个别出售者的需求曲线显然是向右下倾斜的了。 可以退货拿钱，讨价还价的行为当然难以出现。

Price taking 受价{Alchian} = perfect competition; 竞争市场决定了市价，生产者就跟着市价出售自己的产出。 潜在的竞争者要算进去，而不管潜在不潜在，竞争出售的人数不需要很多。 受价需要出售者面对的需求是平线。 平均成本等于平均收入，即是总成本等于总收入，没有盈利（profit），但有利润(return)。

Social choice theory {Arrow1951}

Public-choice theory {Black1958}

## Theory of the state 国家理论

1. 处理产权(property rights)与人权(human rights)的界定;
2. 处理收入分配与再分配;
3. 人民要共享一个共同的文化(ethics);

1. 讯息与监管还钱的费用存在, 富人借钱的利息率一般比穷人的低, 同样的投资回报可赚较多的钱, 而且富人容易借较多的钱，因而有较多的投资选择;
2. 通货膨胀下工资的调校一般比资产的币值提升慢, 富人多持有非劳力资产, 受到的损害比不富的少, 二战之后通胀的日子远比通缩的多;
3. 政府腐败贪污的回报率高, 可观的财富转到有钱的贿赂者与受贿者或他们的亲属那边;
4. 有钱人子女的求学际遇远胜穷人，粗下工作的收入难以糊口;