📚 AP Microeconomics: Key Formulas Summary and Analysis | AP微观经济：重要公式归纳与解析
Mastering key formulas is essential for success in AP Microeconomics. These formulas serve as analytical tools to understand market behavior, elasticity, production costs, and profit maximization. This article provides a comprehensive summary and detailed explanations of the most important equations, ensuring you can apply them confidently on the exam.
掌握关键公式对于AP微观经济学的成功至关重要。这些公式是分析市场行为、弹性、生产成本和利润最大化的工具。本文对最重要的方程进行了全面总结和详细解析，确保你在考试中能自信地运用它们。
1. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand quantifies how sensitive quantity demanded is to a change in price. It is defined as the percentage change in quantity demanded divided by the percentage change in price.
需求价格弹性量化了需求量对价格变化的敏感程度。它被定义为需求量的百分比变化除以价格的百分比变化。
Using the midpoint method for arc elasticity, the formula is:
PED = ((Q₂ – Q₁) / ((Q₁+Q₂)/2)) ÷ ((P₂ – P₁) / ((P₁+P₂)/2))
使用中点法计算弧弹性的公式为：
PED = ((Q₂ – Q₁) / ((Q₁+Q₂)/2)) ÷ ((P₂ – P₁) / ((P₁+P₂)/2))
If the absolute value of PED is greater than 1, demand is elastic; if it equals 1, demand is unit elastic; and if it is less than 1, demand is inelastic. The total revenue test links elasticity to revenue changes: when demand is elastic, a price decrease raises total revenue; when inelastic, a price decrease lowers total revenue.
如果PED的绝对值大于1，需求富有弹性；等于1，为单位弹性；小于1，则缺乏弹性。总收入检验将弹性与收入变化联系起来：当需求富有弹性时，价格下降会增加总收入；缺乏弹性时，价格下降会减少总收入。
2. Income Elasticity of Demand (YED) | 需求收入弹性
Income elasticity of demand measures how quantity demanded responds to a change in consumer income. The formula is:
需求收入弹性衡量需求量对消费者收入变化的反应程度。公式为：
YED = %ΔQd ÷ %ΔIncome
YED = %ΔQd ÷ %Δ收入
A positive YED indicates a normal good, while a negative YED signifies an inferior good. For normal goods, if YED is greater than 1, the good is a luxury; if between 0 and 1, it is a necessity.
正的YED表示正常品，负的YED意味着是劣等品。对于正常品，如果YED大于1，该商品是奢侈品；如果介于0到1之间，则是必需品。
3. Cross-Price Elasticity of Demand (XED) | 需求交叉价格弹性
Cross-price elasticity of demand captures the effect of a price change in one good on the quantity demanded of another good. The formula is:
需求交叉价格弹性反映一种商品价格变化对另一种商品需求量的影响。公式为：
XED = %ΔQd of Good A ÷ %ΔP of Good B
XED = 商品A的需求量百分比变化 ÷ 商品B的价格百分比变化
A positive XED means the two goods are substitutes; a negative XED means they are complements. A value close to zero suggests the goods are unrelated.
正的XED表示两种商品互为替代品；负的XED表示它们为互补品。数值接近零则表明商品之间不相关。
4. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply quantifies how responsive quantity supplied is to a change in price. Using the midpoint formula:
供给价格弹性量化了供给量对价格变化的反应程度。使用中点公式：
PES = ((Q₂ – Q₁) / ((Q₁+Q₂)/2)) ÷ ((P₂ – P₁) / ((P₁+P₂)/2))
PES = ((Q₂ – Q₁) / ((Q₁+Q₂)/2)) ÷ ((P₂ – P₁) / ((P₁+P₂)/2))
Key determinants of PES include the time horizon, the flexibility of production, and the availability of inputs. The longer the time period, the more elastic supply tends to become.
PES的关键决定因素包括时间跨度、生产灵活性和投入品的可获取性。时间越长，供给往往变得越富有弹性。
5. Utility Maximization Rule | 效用最大化法则
Consumers maximize total utility when the marginal utility per dollar spent is equal across all goods. The equi-marginal principle is expressed as:
当花费在每种商品上的每美元边际效用都相等时，消费者实现了总效用最大化。等边际原理表示为：
MUₓ/Pₓ = MUᵧ/Pᵧ
MUₓ/Pₓ = MUᵧ/Pᵧ
If the per-dollar marginal utilities differ, the consumer reallocates spending toward the good with the higher ratio until equality is restored. This rule assumes the entire budget is spent.
如果每美元的边际效用不同，消费者会将支出重新分配到该比率较高的商品上，直到恢复相等。该法则假设所有预算都被花完。
6. Cost Formulas | 成本公式
Production costs form the foundation for supply decisions. Below is a summary table of the essential cost equations:
生产成本是供给决策的基础。以下是基本成本方程的汇总表：
| English Formula | 中文公式 |
|---|---|
| TC = TFC + TVC | 总成本 = 总固定成本 + 总可变成本 |
| AFC = TFC ÷ Q | 平均固定成本 = 总固定成本 ÷ 产量 |
| AVC = TVC ÷ Q | 平均可变成本 = 总可变成本 ÷ 产量 |
| ATC = TC ÷ Q = AFC + AVC | 平均总成本 = 总成本 ÷ 产量 = 平均固定成本 + 平均可变成本 |
| MC = ΔTC ÷ ΔQ | 边际成本 = 总成本变化 ÷ 产量变化 |
Marginal cost intersects both AVC and ATC at their minimum points. When MC is below average cost, the average falls; when MC is above, the average rises.
边际成本在平均可变成本和平均总成本的最低点与它们相交。当边际成本低于平均成本时，平均成本下降；当边际成本更高时，平均成本上升。
7. Revenue and Profit Formulas | 收益与利润公式
A firm’s revenue and profit calculations are crucial for analyzing market decisions. The fundamental relationships are:
企业的收益与利润计算对分析市场决策至关重要。基本关系为：
TR = P × Q
AR = TR ÷ Q = P
MR = ΔTR ÷ ΔQ
Profit = TR – TC
总收入 = 价格 × 销量；平均收益 = 总收入 ÷ 销量 = 价格；边际收益 = 总收入变化 ÷ 销量变化；利润 = 总收入 – 总成本
In all market structures, the demand curve faced by the firm is also its average revenue curve. In perfect competition, since the firm is a price taker, MR equals AR and price.
在所有市场结构中，企业面对的需求曲线也是其平均收益曲线。在完全竞争中，由于企业是价格接受者，边际收益等于平均收益和价格。
8. Profit Maximization: MR = MC | 利润最大化：边际收益等于边际成本
The profit-maximizing rule for any firm is to produce the output level where marginal revenue equals marginal cost.
任何企业利润最大化的法则是在边际收益等于边际成本的产量水平上进行生产。
MR = MC
If MR > MC, the additional revenue from selling one more unit exceeds the additional cost, so the firm increases output. If MR < MC, the firm should reduce output. This rule applies regardless of market structure, but in perfect competition it simplifies to P = MC.
如果 MR > MC，多销售一单位带来的额外收益超过额外成本，企业增加产出；如果 MR < MC，企业应减少产出。该法则适用于所有市场结构，但在完全竞争中简化为 P = MC。
9. Perfect Competition Key Equations | 完全竞争关键等式
A perfectly competitive firm faces a perfectly elastic demand curve at the market price. This leads to a critical set of identities:
完全竞争企业面对的是在市场均衡价格处的一条完全有弹性的需求曲线。这引出一组关键的恒等式：
P = MR = AR = Dfirm
价格 = 边际收益 = 平均收益 = 企业需求曲线
Because the firm cannot influence price, its marginal revenue from selling one more unit equals the constant market price. The firm produces where P = MC, and its short-run supply curve is the MC curve above AVC.
由于企业无法影响价格，多卖一单位的边际收益就等于不变的市场价格。企业在 P = MC 处生产，其短期供给曲线是位于平均可变成本之上的边际成本曲线。
10. Tax Incidence and Elasticity | 税收归宿与弹性
When a per-unit tax is imposed, the burden shared between consumers and producers depends on the relative elasticities of demand and supply. The consumer share of the tax is given by:
当征收从量税时，消费者和生产者之间分担的税负取决于需求和供给的相对弹性。消费者承担的税负份额为：
Consumer Share = PES ÷ (PED + PES)
消费者份额 = 供给弹性 ÷ (需求弹性 + 供给弹性)
Likewise, the producer share is PED ÷ (PED + PES). The more inelastic the demand relative to supply, the greater the proportion of the tax paid by consumers. These formulas assume absolute values for PED and PES.
同样，生产者份额为需求弹性 ÷ (需求弹性 + 供给弹性)。需求相对于供给越缺乏弹性，消费者承担的税收比例就越大。这些公式使用PED和PES的绝对值。
11. Marginal Product and Average Product | 边际产量与平均产量
In the short run, at least one input is fixed. The marginal product of labor (MPL) and average product of labor (APL) are defined as:
在短期内，至少有一种投入是固定的。劳动的边际产量和平均产量定义为：
MPL = ΔTP ÷ ΔL
APL = TP ÷ L
边际产量 = 总产量变化 ÷ 劳动投入变化；平均产量 = 总产量 ÷ 劳动投入
The law of diminishing marginal returns states that as more units of a variable input are added to a fixed input, the marginal product eventually declines. MP equals AP at the maximum point of the AP curve.
边际收益递减规律指出，随着越来越多的可变投入添加到固定投入上，边际产量最终会下降。MP在AP曲线的最高点与AP相等。
12. Consumer Surplus and Producer Surplus | 消费者剩余与生产者剩余
Consumer surplus is the difference between what consumers are willing to pay and what they actually pay. Producer surplus is the difference between the market price and the minimum price producers are willing to accept. In a linear demand-supply model, these can be calculated as triangular areas:
消费者剩余是消费者愿意支付的金额和他们实际支付的金额之间的差额。生产者剩余是市场价格与生产者愿意接受的最低价格之间的差额。在线性供需模型中，它们可以计算为三角形面积：
CS = ½ × Qe × (Max Willingness to Pay – Pe)
PS = ½ × Qe × (Pe – Min Acceptable Price)
消费者剩余 = ½ × 均衡数量 × (最大支付意愿 – 均衡价格)；生产者剩余 = ½ × 均衡数量 × (均衡价格 – 最低接受价格)
Total surplus, the sum of consumer and producer surplus, is maximized at competitive equilibrium. Deadweight loss arises when output deviates from this efficient level, often modeled as a triangle between the demand and supply curves.
总剩余即消费者剩余与生产者剩余之和，在竞争均衡时达到最大。当产量偏离这一有效水平时便产生无谓损失，通常表示为供需曲线
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