第7章为我们提供了测量宏观经济的工具：GDP、失业、通胀和商业周期。我们现在可以描述发生了什么——GDP下降了3%，失业率升至10%，通胀加速——但我们还无法解释为什么发生，也不知道政策制定者应该如何应对。本章构建填补这一空白的经典模型。
我们从短期产出决定的最简单故事开始：凯恩斯交叉图，其中总需求单独驱动生产。在此基础上，我们构建IS-LM模型，展示商品市场和货币市场如何共同决定产出和利率。然后我们将IS-LM作为政策分析的引擎——追踪政府支出、税收变化和央行行动的效果——随后面对IS-LM将价格固定不变这一关键局限。本章后半部分取消了这一限制。我们从IS-LM推导总需求曲线，引入短期和长期的总供给，并组装完整的AD-AS模型。到本章结束时，你将拥有诊断衰退、通胀繁荣和滞胀的完整工具包，以及评估财政和货币政策应对中内在权衡的能力。
本章的所有内容都使用代数——线性方程、代入法和图形推理。没有微积分。没有动态优化。这里的模型是刻意简化的：它们牺牲了一些现实性以换取清晰性和可处理性。第14章和第15章将用微观基础和前瞻性预期重建这些思想。但这里培养的直觉正是央行行长和财政部官员首先依赖的直觉，而且它是不可或缺的。
前置要求：第7章（GDP、国民收入恒等式、商业周期事实）。
凯恩斯交叉图是最简单的短期产出决定模型。它建立在一个强大且在20世纪30年代具有革命性的思想之上，这一思想归功于约翰·梅纳德·凯恩斯：在短期内，总需求决定产出。如果家庭和企业想要增加支出，企业就会增加生产以满足这一需求。如果支出下降，企业就会削减生产。价格被假定为固定不变——我们将在8.6至8.8节中放松这一假设。
模型从一个关于家庭如何决定支出的行为假设开始。
消费函数为：
其中$Y$是总产出（在循环流量中等于总收入），$T$是净税收，$Y - T$是可支配收入。这是一个线性关系：从自主消费基础$C_0$开始，可支配收入每增加一美元，消费增加$c$。
这个函数是凯恩斯式的，而非基于微观基础。它假设当前收入与当前支出之间存在机械联系。后面的章节将从家庭优化行为推导消费函数，纳入对未来收入和利率的预期。但简单的凯恩斯形式捕捉了基本的短期机制：当收入上升时，支出上升——而这些支出又成为其他人的收入。
在封闭经济中（没有进出口）：
目前，投资$I$和政府支出$G$是外生的——分别由动物精神和政治决策在模型之外决定。税收$T$也是外生的。只有消费对收入做出反应。
注意计划支出是收入$Y$的函数。这就是凯恩斯交叉图的引擎：支出取决于收入，而收入取决于支出。
如果产出超过计划支出（$Y > PE$），企业发现未售出的商品堆积在货架上——非计划的存货积累。它们会通过削减生产来应对。如果产出低于计划支出（$Y < PE$），企业看到存货减少并增加生产。只有当$Y = PE$时，经济才处于均衡状态。
令$Y = PE$：
$$Y = C_0 + c(Y - T) + I + G$$
$$Y = C_0 + cY - cT + I + G$$
$$Y - cY = C_0 - cT + I + G$$
$$Y(1 - c) = C_0 - cT + I + G$$
What this says: Equilibrium output equals autonomous spending (the spending that doesn't depend on income) multiplied by the multiplier. The economy settles where total spending matches total output.
Why it matters: This is the core Keynesian insight — the economy can get stuck at an output level below full employment if autonomous spending is too low. Government spending or tax cuts can raise autonomous spending and lift output by more than the initial impulse.
See Full Mode for the derivation.其中$A = C_0 - cT + I + G$是自主支出——不依赖于收入的支出部分。均衡产出等于自主支出乘以$\frac{1}{1-c}$。
拖动滑块来改变MPC、政府支出和税收。观察计划支出线的旋转和移动，看看均衡产出如何变化。
图8.1.凯恩斯交叉图。均衡出现在计划支出等于实际产出之处。PE线的斜率为MPC。
What this says: Every dollar the government spends creates more than a dollar of output. If households spend 80 cents of each extra dollar they earn, the multiplier is 5: a \$1 spending increase raises GDP by \$5.
Why it matters: The multiplier is the chain reaction of spending. My spending is your income, your spending is someone else's income. Each round is smaller, but they add up to far more than the original impulse.
See Full Mode for the derivation.当$c = 0.8$时，乘数为$\frac{1}{1 - 0.8} = \frac{1}{0.2} = 5$。政府支出每增加\$1，均衡产出增加\$5。
为什么乘数大于1？因为存在反馈回路——一个支出和收入的连锁反应：
总效应是一个无穷几何级数：
$\$1 + c + c^2 + c^3 + \ldots = \frac{1}{1 - c}$$
每一轮都比上一轮小（因为$c < 1$），所以级数收敛。但累计效应远远超过初始冲击。
What this says: Tax cuts boost output, but less than equivalent spending increases. A \$1 tax cut with MPC = 0.8 raises GDP by \$4, versus \$5 from a \$1 spending increase.
Why it matters: When the government spends \$1 directly, the full dollar enters the spending stream immediately. When it cuts taxes by \$1, households save part of the windfall, so the first-round boost is smaller.
See Full Mode for the derivation.当$c = 0.8$时，税收乘数为$\frac{-0.8}{0.2} = -4$。减税\$1使产出增加\$4——少于增加\$1政府支出带来的\$5。
为什么税收乘数的绝对值较小？当政府直接支出\$1时，在第一轮中整个美元都进入支出流。当政府减税\$1时，家庭获得\$1的额外可支配收入，但只花费其中的$c$（储蓄\$1 - c$）。第一轮较小——只有$c$而不是1——因此总的乘数效应较小。
由公式8.4和8.5：
$$\Delta Y = \frac{1}{1-c} \Delta G + \frac{-c}{1-c} \Delta T = \frac{1-c}{1-c} \Delta G = \Delta G$$
What this says: If the government raises spending by \$100 and pays for it with a \$100 tax increase, GDP still rises by exactly \$100 — regardless of the MPC.
Why it matters: Even a fully financed spending increase is stimulative. The government spends the full \$100, but the tax only removes part of households' spending (they absorb some of the tax hit by saving less). The net effect is always a one-for-one increase in output.
See Full Mode for the derivation.平衡预算乘数恰好等于1——无论$c$的值如何。政府支出增加\$100，完全由\$100的增税来融资，使产出恰好增加\$100。直觉是：支出增加直接向需求注入\$100，而增税只从需求中减去$c \times \$100$（因为家庭通过减少储蓄来吸收部分税收冲击）。净第一轮效应为$(1 - c) \times \$100$，乘以$\frac{1}{1-c}$后恰好等于\$100。
已知：$C_0 = 100$，$c = 0.8$，$I = 200$，$G = 300$，$T = 250$。
第1步——自主支出：
$$A = C_0 - cT + I + G = 100 - 0.8(250) + 200 + 300 = 100 - 200 + 200 + 300 = 400$$
第2步——均衡产出：
$$Y^* = \frac{1}{1 - 0.8} \times 400 = 5 \times 400 = 2{,}000$$
第3步——验证$Y = PE$：
$$C = 100 + 0.8(2{,}000 - 250) = 100 + 1{,}400 = 1{,}500$$
$$PE = C + I + G = 1{,}500 + 200 + 300 = 2{,}000 = Y^* \checkmark$$
第4步——乘数：$\frac{1}{1 - 0.8} = 5$。
第5步——当$G$增加50时会怎样？
$$\Delta Y = 5 \times 50 = 250$$
新均衡：$Y^* = 2{,}000 + 250 = 2{,}250$。
接例8.1：政府支出增加$\Delta G = 50$，$c = 0.8$。
| 轮次 | 本轮新增支出 | 累计总额 |
|---|---|---|
| 1 | 50.0 | 50.0 |
| 2 | 40.0 | 90.0 |
| 3 | 32.0 | 122.0 |
| 4 | 25.6 | 147.6 |
| 5 | 20.5 | 168.1 |
| 6 | 16.4 | 184.5 |
| 7 | 13.1 | 197.6 |
| 8 | 10.5 | 208.1 |
| 9 | 8.4 | 216.5 |
| 10 | 6.7 | 223.2 |
经过10轮后，累计效应为\$10 \times \frac{1 - 0.8^{10}}{1 - 0.8} = 223.2$。
理论总额（无穷级数之和）为$\frac{50}{1 - 0.8} = 250$。
经过10轮后，我们捕获了\$123.2 / 250 = 89.3\%$的总乘数效应。剩余的10.7%以越来越小的增量在后续轮次中逐渐流入。
设定MPC和初始支出冲击，然后按播放键，逐轮观察乘数效应的展开。
图8.2.逐轮乘数效应。每一轮支出都小于上一轮，但累计总额收敛至$\Delta G / (1-c)$。
凯恩斯交叉图将投资固定不变。但投资决策在很大程度上取决于借贷成本。当利率较低时，更多项目是有利可图的——一个回报率为5%的工厂在利率为3%时值得建设，但在利率为8%时则不值得。本节使投资对利率做出反应，将凯恩斯交叉图从单一产出解转变为一条曲线——将每个利率映射到其对应的均衡产出。
当$r$上升时，为新资本品融资的成本增加。企业搁置边际项目——那些预期回报刚好超过利率的项目。因此投资下降。当$r$下降时，之前无利可图的项目变得值得投资，投资上升。
将投资函数（公式8.7）代入凯恩斯交叉图均衡（公式8.3）：
What this says: The IS curve maps each interest rate to the level of output where the goods market clears. Higher interest rates discourage investment, which through the multiplier lowers equilibrium output. So the IS curve slopes downward.
Why it matters: This connects the financial side of the economy (interest rates) to the real side (output). Anything that raises autonomous spending shifts the IS curve right; anything that raises interest rates moves you along the curve to lower output.
See Full Mode for the derivation."IS"这个名称来自均衡条件：计划投资等于计划储蓄——当企业想要投资的金额与经济其他部分想要储蓄的金额相匹配时，商品市场出清。
为什么IS曲线向下倾斜：从IS曲线上的任何一点开始——商品市场处于均衡状态。现在提高$r$。较高的$r$使投资减少$b \times \Delta r$。较低的投资意味着较低的计划支出，从而触发乘数效应。产出下降$\frac{b}{1-c} \times \Delta r$。$r$越高，$Y$越低——IS曲线向下倾斜。
什么使IS曲线移动？在给定利率下任何改变自主支出的因素：
每次移动的幅度由相应的乘数决定。$G$增加$\Delta G$使IS右移$\frac{1}{1-c} \Delta G$。
IS曲线告诉我们商品市场如何对利率做出反应，但它不能告诉我们什么决定了利率。为此，我们需要货币市场。LM曲线描述了货币需求等于货币供给的产出和利率组合。
人们为什么持有货币——一种与债券不同、通常不产生利息的资产？凯恩斯指出了三种动机。
其中$e > 0$反映了货币需求的收入敏感度（交易动机），$f > 0$反映了利率敏感度（投机动机）。较高的收入增加货币需求；较高的利率减少货币需求。
中央银行控制名义货币供给$M$。短期内价格水平$P$是固定的。实际货币供给为$M/P$。
均衡要求实际货币需求等于实际货币供给：
解出$r$：
What this says: The LM curve maps each output level to the interest rate where the money market clears. When output rises, people need more money for transactions. With a fixed money supply, the interest rate must rise to convince people to hold fewer idle cash balances.
Why it matters: The LM curve slopes upward — booms push interest rates up, recessions push them down. The central bank can shift the entire curve by changing the money supply: more money means lower interest rates at every output level.
See Full Mode for the derivation.为什么LM曲线向上倾斜：从LM曲线上的一点开始。增加$Y$。较高的产出增加货币需求。在货币供给固定的情况下，利率必须上升以抑制投机性持有并恢复均衡。$Y$越高，$r$越高。
什么使LM曲线移动？
You just saw money as a quantity M in the LM curve. But what IS money? The model treats it as a given — it never asks why people accept green pieces of paper as payment.
In IS-LM, money is a stock (M) that people hold because they need it for transactions and because bonds are risky. The interest rate is the opportunity cost of holding money. Increase M, excess money supply pushes the interest rate down, investment rises, output rises. Money is a policy lever — the central bank controls M, and the model treats money's nature as irrelevant. All that matters is the quantity and its effect on interest rates.
IS-LM treats money supply as exogenous — the central bank sets M. But modern central banks target interest rates, not the money supply. The LM curve is arguably better described as a horizontal line at the target rate (the IS-MP framework). More fundamentally, IS-LM doesn't ask why people accept money at all. The model assumes money exists and works — it doesn't explain why. The commodity view says money must have intrinsic value (gold). Chartalists say money is a creature of the state — taxes create demand for government tokens. Credit theorists say all money is debt. IS-LM sidesteps all of this.
The mainstream moved from money-stock targeting (Friedman's k-percent rule) to interest-rate targeting (Taylor rule). The LM curve became a footnote in many graduate textbooks, replaced by a monetary policy rule. But the question 'what is money?' became more urgent, not less, as digital payments, cryptocurrencies, and central bank digital currencies emerged. If money is just a social convention, can a decentralized algorithm sustain one?
IS-LM gives you the macroeconomics of money — how changes in money supply or demand affect output and interest rates. It is a powerful tool for policy analysis. But it gives you no insight into what money fundamentally is. For that, you need the deeper theories: cash-in-advance, money-in-utility, the fiscal theory of the price level, and the credit theory of money. The nature of money may seem philosophical until a crisis forces the question — every hyperinflation is a failure of the social convention that money depends on.
If money's nature doesn't matter for IS-LM, does it matter at all? Come back at Chapter 16 (§16.1, §16.5–16.6), where the monetary theory gets serious — CIA, MIU, the Friedman rule, and the fiscal theory of the price level all depend on what you think money is. And the answer has real policy implications: if money is a government liability backed by future surpluses (FTPL), then fiscal policy determines the price level, not the central bank.
Peter Schiff told Joe Rogan's audience that Bitcoin fails every test of money. No intrinsic value, no government backing, wild price swings. Yet millions hold it. Does it satisfy the definition — or does it need a new one?
入门Increasing $M$ shifts LM right and raises output. So why not just keep printing? The answer depends on where the economy is relative to capacity.
入门IS曲线给出了商品市场出清的所有$(Y, r)$组合。LM曲线给出了货币市场出清的所有$(Y, r)$组合。经济必须同时处于两条曲线上。这确定了一个唯一的产出-利率组合。
我们有两个方程、两个未知数（$Y$和$r$）：
IS：$Y = \frac{1}{1-c}(C_0 - cT + I_0 + G) - \frac{b}{1-c}r$
LM：$r = \frac{e}{f}Y - \frac{1}{f}\frac{M}{P}$
将LM代入IS并求解：
What this says: IS-LM equilibrium pins down a unique output level and interest rate where both the goods market and the money market clear simultaneously. Output depends on both fiscal variables (G, T) and monetary variables (M/P).
Why it matters: This is the central result of Keynesian macroeconomics. Neither the goods market nor the money market can be analyzed in isolation — they interact. Fiscal policy shifts IS, monetary policy shifts LM, and the equilibrium adjusts in both output and interest rates.
See Full Mode for the derivation.令$D = f(1-c) + be$以简化。这个分母出现在每一个IS-LM乘数中，反映了商品市场和货币市场之间的相互作用。$D$越大，任何单一政策变化的效果越小。
已知：$C_0 = 100$，$c = 0.8$，$T = 200$，$G = 300$，$I_0 = 300$，$b = 20$，$M/P = 500$，$e = 0.5$，$f = 50$。
第1步——IS曲线：
$$Y = 5(100 - 160 + 300 + 300) - 100r = 2{,}700 - 100r$$
第2步——LM曲线：
$$r = 0.01Y - 10$$
第3步——求解：
$$Y = 2{,}700 - 100(0.01Y - 10) = 2{,}700 - Y + 1{,}000$$
$\$1Y = 3{,}700 \implies Y^* = 1{,}850$$
$$r^* = 0.01(1{,}850) - 10 = 8.5\%$$
第4步——均衡时的投资：
$$I = 300 - 20(8.5) = 130$$
第5步——验证：
$C = 100 + 0.8(1{,}850 - 200) = 1{,}420$。$PE = 1{,}420 + 130 + 300 = 1{,}850 = Y^* \checkmark$
$L = 0.5(1{,}850) - 50(8.5) = 925 - 425 = 500 = M/P \checkmark$
调整政府支出、税收、货币供给和自主投资，观察IS和LM曲线如何移动以及均衡如何变化。
图8.3.IS-LM均衡。IS曲线和LM曲线的交点决定了使商品市场和货币市场同时出清的唯一产出和利率。
IS-LM首先是一台政策分析机器。它告诉我们政府支出、税收和货币供给如何影响产出和利率——并揭示了简单凯恩斯交叉图所遗漏的一个关键复杂性：挤出效应。
假设政府增加支出$\Delta G$，税收和货币供给保持不变。在凯恩斯交叉图中，乘数将给出$\Delta Y = \frac{1}{1-c} \Delta G$。但这忽略了货币市场。
在IS-LM中：
IS-LM财政乘数：
由于$be > 0$，我们有$\frac{f}{f(1-c) + be} < \frac{1}{1-c}$。IS-LM乘数严格小于凯恩斯乘数。差额就是挤出效应。
被挤出的投资金额：
What this says: Fiscal expansion raises output, but by less than the simple Keynesian multiplier predicts. The missing output is crowding out: government spending pushes up interest rates, which discourages private investment.
Why it matters: Crowding out is the key complication IS-LM adds to the Keynesian cross. Government stimulus does work, but part of the boost is offset by reduced private investment. The more sensitive investment is to interest rates, the more crowding out occurs.
See Full Mode for the derivation.基准：$Y^* = 1{,}850$，$r^* = 8.5\%$，$I = 130$。
政策：$G$增加100（从300增加到400）。
新IS：$Y = 3{,}200 - 100r$
求解：\$1Y = 4{,}200 \implies Y^* = 2{,}100$，$r^* = 11\%$
投资：$I = 300 - 20(11) = 80$。$\Delta I = 80 - 130 = -50$。
IS-LM乘数：\$150 / 100 = 2.5$，而简单凯恩斯乘数为\$1$。
挤出缺口：凯恩斯交叉图预测$\Delta Y = 500$，IS-LM给出\$150$。挤出比率 = \$150/500 = 50\%$。
潜在刺激效果的一半被较高利率挤出私人投资所抵消。
IS-LM货币乘数：
What this says: Increasing the money supply raises output by lowering interest rates, which stimulates investment. Unlike fiscal expansion, monetary expansion reduces interest rates rather than raising them — there is no crowding out.
Why it matters: Fiscal and monetary policy work through different channels. Fiscal policy directly boosts demand but crowds out investment. Monetary policy works indirectly — through interest rates to investment to output — but actually encourages private investment rather than displacing it.
See Full Mode for the derivation.货币扩张使LM右移。利率下降。较低的利率刺激投资，通过乘数效应提高产出。与财政扩张不同，货币扩张降低利率——投资上升而非下降。不存在挤出效应。
基准：$Y^* = 1{,}850$，$r^* = 8.5\%$，$I = 130$。
政策：$M/P$增加100（从500增加到600）。
新LM：$r = 0.01Y - 12$
求解：\$1Y = 3{,}900 \implies Y^* = 1{,}950$，$r^* = 7.5\%$
投资：$I = 300 - 20(7.5) = 150$。$\Delta I = +20$。
比较：
| 财政政策（$\Delta G = 100$） | 货币政策（$\Delta(M/P) = 100$） | |
|---|---|---|
| $\Delta Y$ | +250 | +100 |
| $\Delta r$ | +2.5个百分点 | -1.0个百分点 |
| $\Delta I$ | -50 | +20 |
财政扩张对产出的效果更强但挤出了投资。货币扩张刺激投资但对产出的效果较小。
如果政府想在不挤出投资的情况下刺激经济，可以将财政扩张（IS右移）与货币扩张（LM右移）相结合。货币扩张保持利率不变，防止了原本伴随财政扩张的挤出效应。
在流动性陷阱中，LM曲线在$r = 0$处变为水平。货币扩张使LM右移但对利率或产出没有影响。相比之下，财政政策仍然完全有效：沿着平坦的LM曲线右移IS提高产出，而不产生任何挤出效应。
流动性陷阱在几十年间一直是理论上的奇异现象。在20世纪90年代的日本，它成为了政策现实，2008年金融危机后在发达世界的大部分地区也是如此，当时各国央行将利率降至接近零，发现进一步的货币扩张效果递减。
调整政策规模，并排比较同等规模的财政扩张和货币扩张的效果。
图8.4.财政扩张同时提高产出和利率（挤出投资）。货币扩张提高产出同时降低利率（刺激投资）。
查看财政刺激中有多少被挤出效应所抵消。调整财政扩张规模和投资的利率敏感度。
图8.5.挤出缺口衡量了因财政扩张推高利率并挤出私人投资而损失的产出。
You now have the multiplier and IS-LM. Here's what they say about this question — and what they can't answer yet.
The Keynesian cross gives a multiplier of $\frac{1}{1-MPC}$. A \$100 billion increase in $G$ raises GDP by $\frac{\$100B}{1-MPC}$. In IS-LM, the effect is smaller because higher $Y$ raises money demand, which raises interest rates, which crowds out private investment. The multiplier is still positive, but less than $\frac{1}{1-MPC}$. Monetary policy looks more powerful — an increase in $M$ shifts LM right without the crowding-out problem that limits fiscal policy.
The classical and Austrian critique: government spending must come from somewhere. If financed by taxes, it directly reduces private spending. If financed by borrowing, it competes with private borrowers for loanable funds, driving up interest rates. The government doesn't create resources — it reallocates them. In the extreme, the multiplier is exactly 1 (pure crowding out) or even less than 1 if government spends less efficiently than the private sector. The IS-LM model builds in the Keynesian answer by assumption — the consumption function assumes people spend a fixed fraction of income, rather than optimizing intertemporally.
The mainstream absorbed crowding out into IS-LM — that's exactly what the LM curve does. The debate shifted from "does fiscal policy work?" to "how big is the multiplier?" The answer depends on the slope of LM. A steep LM curve (the monetarist position) implies a small multiplier — most of the fiscal expansion is offset by rising interest rates. A flat LM curve implies a large multiplier. The slopes are empirical questions, not theoretical ones.
At this level, fiscal policy works but imperfectly. The multiplier is positive but less than the naive Keynesian cross suggests. Be skeptical of anyone claiming a specific multiplier number without specifying the model and conditions. And note what IS-LM hides: it assumes backward-looking consumers who spend a fixed fraction of current income. Forward-looking consumers might save a tax cut entirely, anticipating future taxes to repay the debt. That possibility — Ricardian equivalence — needs micro-foundations you don't have yet.
IS-LM is static and ad hoc — the IS and LM curves aren't derived from optimization. Forward-looking consumers might behave very differently from the MPC story. Come back in Chapter 9 (§9.1–9.2), where consumption is micro-founded via the Euler equation. And then in Chapter 15 (§15.7), the zero lower bound changes everything — when interest rates hit zero, crowding out disappears and the fiscal multiplier may exceed the textbook value.
The multiplier says a bigger stimulus would have kept unemployment below 8%. It hit 10%. Was the model wrong, or was the dose too small?
中级Increasing $M$ shifts LM right and raises output. So why not just keep printing? The answer depends on where the economy is relative to capacity.
入门IS-LM shows monetary policy shifting LM and changing output. The central bank looks powerful. But how much control does it really have?
In IS-LM, the central bank controls M. An increase in M shifts LM right, lowering the interest rate and raising output. The advantage over fiscal policy: no crowding out — the interest rate falls rather than rises, so investment is stimulated rather than displaced. At the extreme, if LM is flat (liquidity trap), monetary policy is impotent. But outside that special case, the central bank appears to be the most effective macroeconomic policymaker in the model.
The Monetarist critique (Friedman): IS-LM focuses on interest rates, but what matters is the money supply itself. The transmission mechanism is broader than the interest rate channel — money affects spending through wealth effects, portfolio balance, and credit availability. Central banks should target money supply growth, not interest rates. The Austrian critique: central banks can lower interest rates temporarily but only by distorting the price signal that coordinates saving and investment. Artificially low rates cause malinvestment — overbuilding, speculative booms, misallocation of capital — that leads to inevitable busts. The central bank doesn't control the economy; it destabilizes it.
The mainstream moved away from money supply targeting after Goodhart's Law (money demand is unstable when targeted) and toward interest rate targeting. But Friedman's deeper point — that monetary policy operates with long and variable lags — survived and influenced Taylor rule thinking. The question shifted from 'can the central bank control M?' to 'can the central bank control r effectively, and does controlling r control the economy?'
At this level, central banks can control the economy through interest rates. The IS-LM framework is clean and powerful — shift LM, change output. But note two things the model hides: expectations (people may anticipate and offset policy) and the zero lower bound (interest rates cannot go below zero, which turns a theoretical curiosity into a practical constraint). IS-LM gives you the mechanics but not the limitations.
IS-LM is static and backward-looking — agents don't anticipate policy changes. Come back at Chapter 9 (§9.5–9.6) for expectations and the Mundell-Fleming constraint (the impossible trinity), Chapter 15 (§15.5–15.7) for the Taylor rule, the NK framework, and the zero lower bound, and Chapter 16 (§16.2, §16.5) for time inconsistency and the fiscal theory's challenge to central bank power.
Ron Paul and Peter Schiff have warned for decades that the Fed is debasing the currency. The clips have millions of views. But long and variable lags, the zero lower bound, and fiscal dominance all complicate the story. How much control does the Fed really have?
高级Increasing $M$ shifts LM right and raises output. So why not just keep printing? The answer depends on where the economy is relative to capacity.
入门IS-LM将价格水平$P$视为既定。但价格确实会变化。关键洞见是价格水平通过实际货币供给$M/P$进入IS-LM。$P$的变化使LM曲线移动，从而改变均衡产出。通过追踪均衡产出随价格水平的变化，我们推导出总需求曲线。
第1步：从价格水平为$P_0$、实际货币供给为$M/P_0$、产出为$Y_0$、利率为$r_0$的IS-LM均衡开始。
第2步：将价格水平提高到$P_1 > P_0$。实际货币供给下降：$M/P_1 < M/P_0$。LM左移。
第3步：LM左移后，新的IS-LM均衡有更高的$r$和更低的$Y$。
第4步：在$(Y, P)$空间中画出$(Y_0, P_0)$和$(Y_1, P_1)$。$P$越高，$Y$越低。曲线向下倾斜。
由公式8.12，我们可以将均衡产出表示为价格水平的函数：
What this says: The AD curve slopes downward because a higher price level shrinks the real money supply, which raises interest rates, which reduces investment and output. Lower prices do the reverse.
Why it matters: AD connects IS-LM (which holds prices fixed) to the price level. Fiscal and monetary expansions shift AD right, meaning the economy demands more output at every price level. This sets up the AD-AS framework for analyzing inflation alongside output.
See Full Mode for the derivation.其中$A_0 = \frac{f(C_0 - cT + I_0 + G)}{f(1-c) + be}$，$A_1 = \frac{b}{f(1-c) + be}$。
什么使AD移动？在给定价格水平下任何使IS或LM移动的因素：
AD曲线告诉我们在每个价格水平下买方想要购买多少产出。但它不能告诉我们企业愿意生产多少。为此我们需要总供给。
为什么LRAS是垂直的？长期内，所有价格和工资都是完全灵活的。如果价格水平翻倍，工资和投入成本最终也会翻倍，使企业的实际成本保持不变。产出保持在$Y_n$。
三种理论解释了SRAS为什么向上倾斜：
What this says: In the short run, output can deviate from potential when actual prices differ from expected prices. If prices rise unexpectedly, firms produce more (their costs haven't caught up yet). If prices are lower than expected, firms cut back.
Why it matters: This is why demand stimulus works in the short run but not the long run. A demand boost raises prices above expectations, temporarily increasing output. But once workers and firms adjust their expectations, wages catch up, and output returns to potential. Only surprise inflation moves real output.
See Full Mode for the derivation.其中$\alpha > 0$是产出对意外通胀的响应程度。当$P = P^e$时，产出等于潜在水平：$Y = Y_n$。
什么使SRAS移动？
有了总需求和总供给，我们就可以分析完整的宏观经济——产出和价格水平同时决定。
经济的短期均衡是AD和SRAS的交点。产出可能高于、低于或等于潜在水平——短期内经济不必处于充分就业状态。
正向需求冲击（AD右移）：产出上升超过潜在水平，价格水平上升。经济处于繁荣期。
负向需求冲击（AD左移）：产出下降低于潜在水平，价格水平下降。经济处于衰退期。
负向供给冲击（SRAS上移/左移）：产出下降低于潜在水平，同时价格水平上升。这就是滞胀——两者兼有的最坏局面。
滞胀给政策制定者带来了残酷的两难困境。如果他们用扩张性政策对抗衰退，通胀会恶化。如果他们用紧缩性政策对抗通胀，衰退会加深。
从衰退回到潜在水平：当产出低于$Y_n$时，失业率高。随着时间推移，工人接受较低的工资。$P^e$向下调整。SRAS右移。产出在较低的价格水平下逐渐回升到$Y_n$。
从繁荣回到潜在水平：当产出高于$Y_n$时，工人要求更高的工资。$P^e$向上调整。SRAS左移。产出在较高的价格水平下回落到$Y_n$。
长期中性：长期来看，需求冲击只影响价格水平，不影响产出。只有供给侧的变化才能永久性地提高产出。
自我修正机制是真实存在的，但近一个世纪以来一直分裂经济学家的问题是：它需要多长时间？正如凯恩斯的名言："长期来看，我们都已经死了。"正确的政策取决于长期到底有多长。
设定：$Y_n = 1{,}000$，$P_0 = 100$，$P^e = 100$，$\alpha = 5$。
SRAS：$Y = 1{,}000 + 5(P - 100)$。AD：$Y = 1{,}500 - 5P$。
初始均衡：\$1{,}500 - 5P = 500 + 5P \implies P = 100$，$Y = 1{,}000 = Y_n \checkmark$
冲击：石油危机使$P^e$升至120。新SRAS：$Y = 1{,}000 + 5(P - 120) = 400 + 5P$。
新均衡：\$1{,}500 - 5P = 400 + 5P \implies P = 110$，$Y = 950$。
诊断：滞胀。产出从1,000下降到950（衰退）。价格水平从100上升到110（通胀）。经济同时陷入停滞和通胀。
产出缺口：\$150 - 1{,}000 = -50$（衰退缺口）。
自我修正：当$Y < Y_n$时，失业率高。随着时间推移，$P^e$下降，SRAS右移，产出在新的价格水平下向$Y_n$恢复。
移动总需求和总供给来探索衰退、繁荣、滞胀和通缩。
图8.6.AD-AS模型。需求和供给冲击使AD和SRAS移动，产生衰退、繁荣、滞胀或通缩。
观察经济通过自我修正机制从需求冲击中恢复。随着工资预期的调整，SRAS移动。
图8.7.自我修正机制通过工资和价格调整逐步恢复潜在产出，但这一过程可能需要数年。
You now have AD-AS — the first model that gives a causal story for recessions. But the story has conspicuous gaps.
In the Keynesian cross and AD-AS, recessions happen when aggregate demand shifts left. A fall in confidence, investment, or exports reduces planned expenditure, and the multiplier amplifies the initial shock. If prices are sticky (SRAS slopes upward), the adjustment falls on output and employment rather than prices. The economy can remain below full employment for extended periods — the self-correcting mechanism works, but slowly. Keynes's insight: demand deficiency is real, persistent, and painful.
The classical and RBC response: why would demand fall? Rational agents optimize intertemporally — they don't suddenly stop spending without reason. The Keynesian story requires either irrationality (animal spirits) or some real shock that reduces optimal spending. If it's a real shock, the recession may be an efficient response, not a market failure. Say's Law, updated: supply creates its own demand — income from production is spent or saved and invested. Persistent demand deficiency requires a coordination failure that the price system should resolve. The Keynesian model asserts sticky prices but doesn't explain why prices are sticky or how long they stay that way.
Keynes's insight that coordination failures can persist was revolutionary — the Great Depression proved that markets don't always self-correct quickly. The mainstream absorbed the idea but wanted microfoundations: why exactly are prices sticky? How do rational agents generate demand shortfalls? The answer came decades later with the New Keynesian synthesis (Chapter 15), which derives sticky prices from monopolistic competition and staggered price-setting.
Demand shortfalls are a real cause of recessions — the evidence from the Great Depression, the 2008 financial crisis, and COVID is overwhelming. Output fell, unemployment soared, and the pattern matches the AD-AS story. But the Keynesian model at this level needs two things it doesn't have: a trigger (what causes AD to shift left in the first place?) and a mechanism for persistence (why don't wages and prices adjust faster?). 'Animal spirits' and 'sticky prices' are labels for the phenomena, not explanations of them.
What are the microfoundations? Why are prices sticky? Is the demand story the whole story, or are supply shocks equally important? Come back at Chapter 14 (§14.1–14.6) for the RBC alternative — recessions as efficient responses to technology shocks — and then at Chapter 15 (§15.1–15.8) for the New Keynesian synthesis that nests both demand and supply explanations in a single framework.
Yield curve inversions, consumer confidence drops, and leading indicators flash warnings. But predicting recessions is notoriously unreliable — the models that explain them after the fact can't reliably predict them in advance.
中级The multiplier says a bigger stimulus would have kept unemployment below 8%. It hit 10%. Was the model wrong, or was the dose too small?
中级接续第7章。凯拉尼共和国的GDP已从100亿凯拉尼元（KD）下降到90亿KD。失业率从10%攀升至14%。央行的政策委员会正在开会讨论如何应对。从第7章我们知道国民账户数据：$C = 6\$1亿，$I = 2\$1亿，$G = 2.5\$1亿，$NX = -0.5\$1亿。
央行的经济学家估计了结构参数：
推导IS：
$$Y = 5(1.0 - 1.6 + 1.5 + 2.5) - 50r = 17.0 - 50r$$
推导LM：
$$r = 0.025Y - 0.2$$
求解：$Y^* = 12.0\$1亿KD，$r^* = 10\%$。
但经济实际产出为90亿，而非120亿。诊断：商业信心崩溃使自主投资从$I_0 = 1.5$降至$I_0 = 0.9$（下降6亿KD）。
新IS：$Y = 14.0 - 50r$。新均衡：$Y^* = 10.67\$1亿，$r^* = 6.7\%$。
模型正确识别了方向：投资崩溃使IS左移，同时降低了产出和利率。
方案A——财政对策：将$G$增加5亿KD。结果：$Y^* = 11.78\$1亿，$r^* = 9.4\%$。投资被大幅挤出。
方案B——货币对策：将$M/P$从4.0增加到5.5。结果：$Y^* = 12.33\$1亿，$r^* = 3.3\%$。投资部分恢复至$I = 0.57\$1亿。产出上升的同时利率下降。
方案C——政策组合：适度财政（$\Delta G = 0.5\$1亿）加上适度货币（$\Delta(M/P) = 0.75$）。结果：$Y^* = 12.61\$1亿，$r^* = 7.8\%$，$I = 0.12\$1亿。强劲的产出恢复且挤出效应有限。
在AD-AS框架下，凯拉尼衰退是一个负向需求冲击：AD左移。如果没有政策干预，自我修正机制最终会恢复$Y_n$：工资下降，SRAS右移，经济在较低的价格水平下恢复。但这可能需要数年时间。凯拉尼的工人等不了那么久。
如果央行的货币扩张过度，AD右移过多——产出暂时超过潜在水平，通胀加速。14%的失业问题变成了4%的通胀问题。
与第7章的联系：GDP缺口、14%的失业率和国民账户数据都直接来自第7章。学生现在可以通过两个视角看到同一个经济体：测量（第7章）和模型（第8章）。
1936年，大萧条进入第七个年头，约翰·梅纳德·凯恩斯出版了《就业、利息和货币通论》。古典经济学认为灵活的工资和价格会自动恢复充分就业。然而到1936年，失业率已经连续五年保持在两位数。古典经济学的预测彻底失败了。
凯恩斯的革命性主张是总需求可能持续不足。即使工资灵活，经济也可能在远低于充分就业的均衡上停滞——陷入市场力量本身无法打破的恶性循环。
凯恩斯认为，解决方案是政府干预。如果私人支出不足，政府应通过公共支出来填补缺口——必要时可以通过赤字融资。乘数效应将放大其影响。
1937年，约翰·希克斯将凯恩斯的思想提炼为IS-LM图。凯恩斯用400页厚重文字表达的内容，希克斯用两个方程和一张图就捕捉到了。IS-LM成为此后四十年宏观经济政策分析的核心工具。
AD-AS框架通过允许价格水平变化扩展了IS-LM。有了AD-AS，经济学家不仅可以分析衰退，还可以分析通胀以及两者的毁灭性组合：滞胀。
现代宏观经济学已经超越IS-LM，发展到动态的、基于微观基础的模型（第14章和第15章）。但IS-LM仍然是政策直觉的起点——你最先学到的模型，塑造政策制定者思维方式的模型，以及捕捉凯恩斯留给经济学的核心洞见的模型：需求很重要，当需求失灵时，政府必须行动。
| 标签 | 公式 | 描述 |
|---|---|---|
| 公式8.1 | $C = C_0 + c(Y - T)$, \$1 < c < 1$ | 消费函数 |
| 公式8.2 | $PE = C_0 + c(Y - T) + I + G$ | 计划支出 |
| 公式8.3 | $Y^* = \frac{1}{1-c}(C_0 - cT + I + G)$ | 凯恩斯交叉图均衡 |
| 公式8.4 | $\frac{\Delta Y}{\Delta G} = \frac{1}{1-c}$ | 支出乘数 |
| 公式8.5 | $\frac{\Delta Y}{\Delta T} = \frac{-c}{1-c}$ | 税收乘数 |
| 公式8.6 | $\frac{\Delta Y}{\Delta G}\big|_{\Delta G = \Delta T} = 1$ | 平衡预算乘数 |
| 公式8.7 | $I = I_0 - br$, $b > 0$ | 投资函数 |
| 公式8.8 | $Y = \frac{1}{1-c}(C_0 - cT + I_0 + G) - \frac{b}{1-c}r$ | IS曲线 |
| 公式8.9 | $L(r, Y) = eY - fr$ | 货币需求 |
| 公式8.10 | $\frac{M}{P} = eY - fr$ | 货币市场均衡 |
| 公式8.11 | $r = \frac{e}{f}Y - \frac{1}{f}\frac{M}{P}$ | LM曲线 |
| 公式8.12 | $Y^* = \frac{f(C_0 - cT + I_0 + G) + b(M/P)}{f(1-c) + be}$ | IS-LM均衡产出 |
| 公式8.13 | $r^* = \frac{e(C_0 - cT + I_0 + G) - (1-c)(M/P)}{f(1-c) + be}$ | IS-LM均衡利率 |
| 公式8.14 | $\frac{\Delta Y^*}{\Delta G} = \frac{f}{f(1-c) + be}$ | IS-LM财政乘数 |
| 公式8.15 | $\frac{\Delta I}{\Delta G} = \frac{-be}{f(1-c) + be}$ | 投资挤出 |
| 公式8.16 | $\frac{\Delta Y^*}{\Delta(M/P)} = \frac{b}{f(1-c) + be}$ | IS-LM货币乘数 |
| 公式8.17 | $Y = Y_n + \alpha(P - P^e)$ | 短期总供给 |
| 公式8.18 | $Y = A_0 + A_1 \cdot \frac{M}{P}$ | AD曲线（由IS-LM推导） |