📚 Income and Substitution Effects of a Price Change Using Indifference Curves | 用无差异曲线分析价格变化的收入效应与替代效应
A price change alters both the relative price of a good and the consumer’s real purchasing power. Indifference curve analysis separates these two forces into the substitution effect and the income effect. This distinction is essential for explaining why demand curves usually slope downwards, and why they can occasionally slope upwards in the case of Giffen goods.
价格变化既改变商品的相对价格，也改变消费者的实际购买力。无差异曲线分析将这两种力量分解为替代效应和收入效应。这一区分对于解释需求曲线为何通常向下倾斜，以及为何在吉芬商品情况下偶尔会向上倾斜至关重要。
1. Utility Maximisation and the Budget Constraint | 效用最大化与预算约束
Consumers are assumed to rank bundles of two goods, X and Y, by utility. An indifference curve shows all combinations of X and Y that give the same total utility; higher curves represent higher satisfaction. Indifference curves are downward sloping and convex to the origin because of diminishing marginal rate of substitution.
消费者被假定能够对两种商品 X 和 Y 的组合进行效用排序。无差异曲线表示能带来相同总效用的所有 X 和 Y 组合；越高的曲线代表满足程度越高。由于边际替代率递减，无差异曲线向下倾斜并凸向原点。
The budget line shows affordable bundles given money income M and prices Px, Py. Its equation is M = Px·X + Py·Y, so its intercepts are M/Px and M/Py and its slope is –Px/Py.
预算线表示在货币收入 M 与商品价格 Px、Py 给定的条件下可以负担的商品组合。其方程为 M = Px·X + Py·Y，因此横纵截距分别为 M/Px 和 M/Py，斜率为 –Px/Py。
M = Px·X + Py·Y, slope = –Px/Py
2. Initial Consumer Equilibrium | 初始消费者均衡
The consumer maximises utility at the point where the budget line is tangent to the highest attainable indifference curve. At this optimum, the marginal rate of substitution of X for Y equals the price ratio: MRS = Px/Py. This point is labelled A in the standard diagram.
消费者在预算线与可达到的最高无差异曲线相切处实现效用最大化。在最优选择点，X 对 Y 的边际替代率等于价格比率：MRS = Px/Py。该点在标准图形中标为 A。
At A, the consumer has no incentive to reallocate spending: the rate at which they are willing to trade X for Y equals the rate at which the market allows that trade.
在 A 点，消费者没有重新分配支出的动机：他们愿意用 X 交换 Y 的比率，恰好等于市场允许交换的比率。
3. How a Price Change Pivots the Budget Line | 价格变化如何使预算线旋转
Suppose the price of X falls while money income and Py stay constant. The consumer can now buy more X at every given amount of Y. The budget line pivots outward around the Y-intercept because M/Py is unchanged, while the X-intercept M/Px increases. Its slope becomes flatter because Px/Py falls.
假设 X 的价格下降，而货币收入和 Py 保持不变。消费者现在在任意给定 Y 数量下都能购买更多 X。由于 M/Py 不变而 X 轴截距 M/Px 增大，预算线围绕纵截距向外旋转。由于 Px/Py 下降，其斜率变得更平坦。
A price fall therefore creates two simultaneous changes: X becomes relatively cheaper, and the consumer’s real income rises. These two changes are exactly what the substitution and income effects isolate.
因此，价格下降同时带来两个变化：X 变得相对更便宜，并且消费者的实际收入上升。这两个变化正是替代效应和收入效应所要分别分离的内容。
4. The Total Price Effect: From A to C | 总价格效应：从 A 到 C
After the price fall, the consumer moves from the original optimum A on indifference curve IC₁ to a new optimum C on a higher indifference curve IC₂. The total change in the quantity of X demanded, from X₁ to X₃, is the price effect of the fall in Px.
价格下降后，消费者从无差异曲线 IC₁ 上的原最优选择 A，移动到更高无差异曲线 IC₂ 上的新最优选择 C。X 需求量从 X₁ 到 X₃ 的总变动，就是 Px 下降的价格效应。
This total change can be positive or negative depending on the nature of the good. To understand why, we must break the movement from A to C into two parts.
这一总变化可能是正的，也可能是负的，具体取决于商品的性质。为了理解原因，我们必须把从 A 到 C 的移动分解为两个部分。
5. Hicksian Decomposition: Holding Real Income Constant | 希克斯分解：保持实际收入不变
To isolate the substitution effect, we draw a hypothetical budget line that is parallel to the new budget line but tangent to the original indifference curve IC₁. This hypothetical line keeps utility constant at the original level, so it removes the real income gain caused by the price fall.
为了分离替代效应，我们画一条假设预算线：它与新预算线平行，但与原无差异曲线 IC₁ 相切。这条假设线使效用保持在原水平，因此剔除了价格下降带来的实际收入增加。
The tangency point on IC₁ is labelled B. Because the hypothetical budget line has the same slope as the new budget line, it reflects the new relative price ratio, but without any increase in real income.
假设预算线与 IC₁ 的切点标为 B。由于这条假设预算线与新预算线斜率相同，它反映的是新的相对价格比率，但没有实际收入的增加。
6. Substitution Effect in Detail | 替代效应详解
The substitution effect is the movement from A to B along the same indifference curve. Since X is now relatively cheaper, the consumer substitutes X for Y, so the quantity of X demanded increases from X₁ to X₂.
替代效应是沿同一条无差异曲线从 A 到 B 的移动。由于 X 现在相对更便宜，消费者用 X 替代 Y，因此 X 的需求量从 X₁ 增加到 X₂。
For a convex indifference curve, the substitution effect always works in the opposite direction to the price change. A fall in Px always increases the quantity of X demanded through the substitution effect, while a rise in Px always reduces it.
对于凸向原点的无差异曲线，替代效应总是与价格变化方向相反。通过替代效应，Px 下降总是增加 X 的需求量，而 Px 上升总是减少 X 的需求量。
7. Income Effect in Detail | 收入效应详解
The income effect is the movement from B to C. The fall in Px raises real income because the same money income can buy more goods. For a normal good, this higher real income increases the quantity of X demanded from X₂ to X₃; for an inferior good, it reduces quantity demanded.
收入效应是从 B 到 C 的移动。Px 下降提高了实际收入，因为相同货币收入可以购买更多商品。对于正常商品，实际收入上升使 X 的需求量从 X₂ 增加到 X₃；对于劣等商品，则使需求量减少。
Along the movement from B to C, relative prices are held constant because the two budget lines are parallel. This is why B to C is interpreted as a pure income effect.
在从 B 到 C 的移动中，由于两条预算线平行，相对价格保持不变。因此 B 到 C 被解释为纯粹的收入效应。
8. Normal, Inferior and Giffen Goods | 正常商品、劣等商品与吉芬商品
The sign and size of the income effect determine whether the good is normal, inferior or Giffen. For a fall in Px, the substitution effect always raises the quantity of X demanded. The income effect may raise it further (normal), reduce it slightly (inferior), or reduce it so much that total quantity falls (Giffen).
收入效应的符号和大小决定商品是正常商品、劣等商品还是吉芬商品。当 Px 下降时，替代效应总是增加 X 的需求量。收入效应可能进一步增加需求量（正常商品），轻微减少需求量（劣等商品），或大幅减少需求量使总需求量下降（吉芬商品）。
| Good type 商品类型 | Substitution effect 替代效应 | Income effect 收入效应 | Total effect 总效应 | Demand curve 需求曲线 |
|---|---|---|---|---|
| Normal 正常 | Qx ↑ | Qx ↑ | Qx ↑ | Downward sloping 向下倾斜 |
| Inferior 劣等 | Qx ↑ | Qx ↓ smaller 较小 | Qx ↑ if SE dominates 若替代效应占优 | Downward sloping 向下倾斜 |
| Giffen 吉芬 | Qx ↑ | Qx ↓ larger 较大 | Qx ↓ | Upward sloping 向上倾斜 |
A Giffen good is therefore an extreme type of inferior good. Its negative income effect is so strong that it outweighs the substitution effect, causing quantity demanded to fall when the price falls and rise when the price rises.
因此，吉芬商品是一种极端的劣等商品。其负收入效应非常强，以至于超过了替代效应，导致价格下降时需求量减少，价格上升时需求量增加。
9. Worked Diagram Application | 图解应用示例
Suppose a consumer has initial optimum A with X₁ = 5 units. After Px falls, the final observed optimum is C with X₃ = 10 units, so the total price effect is +5 units of X. The hypothetical Hicksian point B might lie at X₂ = 7 units.
假设消费者初始最优选择 A 处 X₁ = 5 单位。Px 下降后，最终观察到的最优点 C 处 X₃ = 10 单位，因此总价格效应为 X 增加 5 单位。假设希克斯分解点 B 位于 X₂ = 7 单位。
Therefore the substitution effect is +2 units (A to B) and the income effect is +
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