Indifference curves and budget lines · 无差异曲线与预算线
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| indifference curve/ɪnˈdɪfrəns kɜːv/ | 无差异曲线 | wú chā yì qū xiàn |
| convex/kɒnˈveks/ | 凸的 | tū de |
| marginal rate of substitution/ˈmɑːdʒɪnl reɪt ɒv ˌsʌbstɪˈtjuːʃn/ | 边际替代率 | biān jì tì dài lǜ |
| budget line/ˈbʌdʒɪt laɪn/ | 预算线 | yù suàn xiàn |
| optimum/ˈɒptɪməm/ | 最优 | zuì yōu |
| substitution effect/ˌsʌbstɪˈtjuːʃn ɪˈfekt/ | 替代效应 | tì dài xiào yìng |
| income effect/ˈɪŋkʌm ɪˈfekt/ | 收入效应 | shōu rù xiào yìng |
Mapping what you'd trade
- Would you swap two coffees for one cake? Your willingness to trade between goods can be drawn as a map of indifference curves 无差异曲线.
- Combine that map with what you can afford, and you can predict the exact bundle a rational consumer chooses.
绘制你会交易什么
- 你会用两杯咖啡换一个蛋糕吗?你在商品之间交易的意愿能被画成一张无差异曲线(indifference curves)的地图。
- 把那张地图与你买得起的结合,你就能预测一个理性消费者选择的确切组合。
An indifference curve joins all consumption bundles that give: · 无差异曲线连接所有带来：
Every point on one indifference curve yields equal utility. · 同一条无差异曲线上的每一点都产生相等的效用。
Indifference curves are usually convex to the origin (the MRS diminishes). · 无差异曲线通常向原点凸出（边际替代率递减）。
As you get more X, you'll give up less Y for each extra X — convex shape. · 随着X的增加，为了每多获得一单位X而放弃的Y会减少——呈现凸形。
Indifference curves
- An indifference curve joins all bundles giving the same satisfaction.
- They slope downward (give up some X, gain some Y) and are convex 凸的 (the marginal rate of substitution 边际替代率 diminishes).
- Curves further from the origin = higher utility.
无差异曲线
- 一条无差异曲线连接所有给出相同满足的组合。
- 它们向下倾斜(放弃一些 X,获得一些 Y)且是凸的(边际替代率递减)。
- 离原点更远的曲线 = 更高的效用。
An increase in income shifts the budget line: · 收入增加会使预算线：
More income lets you afford more of both goods → an outward parallel shift. · 更多收入意味着能负担两种商品 → 发生向外的平行移动。
The budget line 预算线
- The budget line shows all bundles a consumer can afford at given prices and income.
- Its slope is the ratio of the two prices; more income shifts it outward.
The consumer's optimum 最优 is where the budget line is tangent to the highest reachable indifference curve.
预算线
- 预算线(budget line)显示一个消费者在给定的价格和收入下能买得起的所有组合。
- 它的斜率是两个价格的比率;更多的收入把它向外移动。
消费者的最优是预算线与最高可达无差异曲线相切之处。
Budget line lab · 预算线实验室
good B = income / priceB - slope x good A · 商品B = 收入 / 价格B - 斜率 x 商品A
Move quantity of one good and see the trade-off with the other good. · 移动一种商品的数量，观察其与另一种商品的权衡关系。
The consumer's optimum bundle is where: · 消费者最优消费组合出现在：
Tangency maximises utility subject to the budget constraint. · 相切是在预算约束下实现效用最大化的条件。
At the optimum, the budget line is ______ to the highest reachable indifference curve. · 在最优点，预算线与最高可达无差异曲线______。
Tangency is the utility-maximising condition. · 相切是实现效用最大化的条件。
The optimum
- The consumer maximises utility where the budget line is tangent to the highest reachable indifference curve.
- At that point the slopes match: the rate they're willing to trade (MRS) equals the rate the market lets them (price ratio).
Income vs substitution effect 替代效应. When a price falls, the consumer buys more partly because it's now relatively cheaper (substitution) and partly because real income rose (income effect 收入效应).
最优
- 消费者在预算线与最高可达无差异曲线相切之处最大化效用。
- 在那一点斜率匹配:他们愿意交易的比率(MRS)等于市场允许他们的比率(价格比率)。
收入对替代效应。 当一个价格下降时,消费者买更多,部分因为它现在相对更便宜(替代),部分因为实际收入上升了(收入效应)。
You've got it
- indifference curves: equal-satisfaction bundles, downward-sloping and convex; further out = better
- the budget line shows affordable bundles (slope = price ratio)
- the optimum is the tangency of the budget line with the highest reachable curve
你掌握了
- 无差异曲线:相等满足的组合,向下倾斜且凸;更靠外 = 更好
- 预算线显示买得起的组合(斜率 = 价格比率)
- 最优是预算线与最高可达曲线的相切点