Answer:  答案：
a) The Keynesian cross illustrates an economy’s planned expenditure function, $PE=C(Y-$$PE=C(Y-$PE=C(Y-P E=C(Y- $T)+I+G$$T)+I+G$T)+I+GT)+I+G, and the equilibrium condition that actual expenditure equals planned expenditure, $Y=PE$$Y=PE$Y=PEY=P E, as shown in Figure 12-6.
a) 凯恩斯交叉图阐释了经济体的计划支出函数 $PE=C(Y-$$PE=C(Y-$PE=C(Y-P E=C(Y- $T)+I+G$$T)+I+G$T)+I+GT)+I+G ，以及实际支出等于计划支出的均衡条件 $Y=PE$$Y=PE$Y=PEY=P E ，如图 12-6 所示。

Figure 12-6  图 12-6

An increase in government purchases of $\mathrm{\Delta }G$$\mathrm{\Delta }G$Delta G\Delta G shifts the planned expenditure function upward. The new equilibrium is at point B . The change in equilibrium GDP $Y$$Y$YY equals the product of the government-purchases multiplier and the change in government spending: $\mathrm{\Delta }Y=[1/(1-MPC)]\mathrm{\Delta }G$$\mathrm{\Delta }Y=[1/(1-MPC)]\mathrm{\Delta }G$Delta Y=[1//(1-MPC)]Delta G\Delta Y=[1 /(1-M P C)] \Delta G. Since the marginal propensity to consume $MPC$$MPC$MPCM P C is less than one, this expression tells us that a one-unit increase in $G$$G$GG leads to an increase in $Y$$Y$YY that is greater than one unit.
政府购买增加 $\mathrm{\Delta }G$$\mathrm{\Delta }G$Delta G\Delta G 会使计划支出函数向上移动。新均衡点位于 B 点。均衡 GDP 的变化 $Y$$Y$YY 等于政府购买乘数与政府支出变化的乘积： $\mathrm{\Delta }Y=[1/(1-MPC)]\mathrm{\Delta }G$$\mathrm{\Delta }Y=[1/(1-MPC)]\mathrm{\Delta }G$Delta Y=[1//(1-MPC)]Delta G\Delta Y=[1 /(1-M P C)] \Delta G 。由于边际消费倾向 $MPC$$MPC$MPCM P C 小于 1，该表达式表明 $G$$G$GG 每增加一单位将导致 $Y$$Y$YY 出现大于一单位的增长。
b) An increase in taxes of $\mathrm{\Delta }T$$\mathrm{\Delta }T$Delta T\Delta T reduces disposable income by $\mathrm{\Delta }T$$\mathrm{\Delta }T$Delta T\Delta T and, therefore, reduces consumption by $MPC\times \mathrm{△}T$$MPC\times \mathrm{△}T$MPC xx/_\TM P C \times \triangle T. For any given level of income $Y$$Y$YY, planned expenditure falls. In the Keynesian cross, the tax increase shifts the planned-expenditure function down by $MPC\times \mathrm{△}T$$MPC\times \mathrm{△}T$MPC xx/_\TM P C \times \triangle T, as in Figure 12-7.
b) 税收增加 $\mathrm{\Delta }T$$\mathrm{\Delta }T$Delta T\Delta T 导致可支配收入减少 $\mathrm{\Delta }T$$\mathrm{\Delta }T$Delta T\Delta T ，从而使得消费减少 $MPC\times \mathrm{△}T$$MPC\times \mathrm{△}T$MPC xx/_\TM P C \times \triangle T 。对于任意给定的收入水平 $Y$$Y$YY ，计划支出随之下降。在凯恩斯交叉图中，增税使计划支出函数向下移动 $MPC\times \mathrm{△}T$$MPC\times \mathrm{△}T$MPC xx/_\TM P C \times \triangle T ，如图 12-7 所示。

Figure 12-7  图 12-7

The amount by which equilibrium GDP changes is given by the product of the tax multiplier and the change in taxes:
均衡 GDP 的变化量由税收乘数与税收变动的乘积决定：

c) We can calculate the effect of an increase in both government expenditure and taxes by adding the multiplier effects from parts (a) and (b):
c) 通过综合(a)部分的政府支出乘数效应与(b)部分的税收乘数效应，我们可以计算政府支出与税收同时增加的影响：

Government purchases and taxes increase by the same amount, $\mathrm{\Delta }G=\mathrm{\Delta }T$$\mathrm{\Delta }G=\mathrm{\Delta }T$Delta G=Delta T\Delta G=\Delta T. Therefore, we can rewrite the above equation as
政府购买和税收同时增加相同金额 $\mathrm{\Delta }G=\mathrm{\Delta }T$$\mathrm{\Delta }G=\mathrm{\Delta }T$Delta G=Delta T\Delta G=\Delta T 。因此，我们可以将上述等式改写为

This expression tells us that an equal increase in government purchases and taxes increases $Y$$Y$YY by the same amount as $G$$G$GG. That is, the balanced-budget multiplier is exactly 1 .
该表达式表明，政府购买与税收的等额增加会使 $Y$$Y$YY 的增量与 $G$$G$GG 相同。也就是说，平衡预算乘数恰好为 1。
2) The following equations describe a small open economy:
2) 以下方程组描述了一个小型开放经济体：

a) Derive and graph the IS* and LM* curves.
a) 推导并绘制 IS*曲线与 LM*曲线。
b) Calculate the equilibrium exchange rate, income, and net exports.
b) 计算均衡汇率、收入水平和净出口额。
c) Assume a floating exchange rate. Calculate what happens to the exchange rate, income, net exports, and the money supply if the government increases its spending by 50 . Use a graph to show your findings.
c) 假设实行浮动汇率制。若政府支出增加 50 单位，请计算汇率、收入水平、净出口和货币供应量的变化情况，并用图表展示分析结果。
d) Now, assume a fixed exchange rate. Calculate what happens to the exchange rate, income, net exports, and the money supply if the government increases its spending by $50\mathrm{\%}$$50\mathrm{\%}$50%50 \%. Use a graph to show your findings.
d) 现假设实行固定汇率制。若政府支出增加 $50\mathrm{\%}$$50\mathrm{\%}$50%50 \% 单位，请计算汇率、收入水平、净出口和货币供应量的变化情况，并用图表展示分析结果。

Answer:  答案：
a) To obtain the $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} curve, we start with the goods-market-clearing condition, substitute in the given information, and simplify as follows:
a) 为推导 $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} 曲线，我们从商品市场出清条件出发，代入给定信息并按如下步骤简化：

To obtain the $L{M}^{\ast }$$L{M}^{\ast }$LM^(**)L M^{*} curve, we start with the money-market-clearing condition, substitute in the given information, and simplify as follows:
要得到 $L{M}^{\ast }$$L{M}^{\ast }$LM^(**)L M^{*} 曲线，我们从货币市场出清条件出发，代入给定信息并按如下步骤简化：

b) Equating output from the $L{M}^{\ast }$$L{M}^{\ast }$LM^(**)L M^{*} curve with output from the $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} curve, we have
b) 令 $L{M}^{\ast }$$L{M}^{\ast }$LM^(**)L M^{*} 曲线与 $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} 曲线的产出相等，可得

Thus, the equilibrium exchange rate is 2 , income is 1,200 , and net exports are 100 .
因此，均衡汇率为 2，收入为 1,200，净出口为 100。
c) With government spending increased by 50 , we proceed as in part (a) to derive a new $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} equation of
c) 当政府支出增加 50 时，我们按照(a)部分的步骤推导出新的 $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} 方程

With a floating exchange rate, the $L{M}^{\ast }$$L{M}^{\ast }$LM^(**)L M^{*} curve is unchanged because there is no change in the money supply, price level, or world interest rate. Therefore, equilibrium income remains at 1,200 . Then, with the new $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} equation, we have an equilibrium exchange rate of 3. The exchange rate appreciates such that the increase in government spending is matched by a decrease in net exports, so net exports fall to 50 . Graphically, the $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} curve shifts to the right, as illustrated in Figure 14-1
在浮动汇率制下， $L{M}^{\ast }$$L{M}^{\ast }$LM^(**)L M^{*} 曲线保持不变，因为货币供应量、物价水平或世界利率均未发生变化。因此均衡收入仍维持在 1,200。根据新的 $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} 方程，我们得出均衡汇率为 3。汇率升值使得政府支出增加被净出口减少所抵消，因此净出口下降至 50。如图 14-1 所示， $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} 曲线会向右移动
d) If government spending increases by 50 , the new $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} equation is $Y=1,800-200\epsilon$$Y=1,800-200\epsilon$Y=1,800-200 epsiY=1,800-200 \varepsilon as derived in part ©. If the exchange rate is fixed at $\epsilon =2$$\epsilon =2$epsi=2\varepsilon=2, then income must increase to $Y=$$Y=$Y=Y= 1,400. From part (a), we know that the $L{M}^{\ast }$$L{M}^{\ast }$LM^(**)L M^{*} equation is given by $M/3=Y-200$$M/3=Y-200$M//3=Y-200M / 3=Y-200, so the money supply must increase to $M=3,600$$M=3,600$M=3,600M=3,600. That is, to prevent the currency from appreciating, the central bank must sell domestic currency and buy foreign currency. This shifts the $L{M}^{\ast }$$L{M}^{\ast }$LM^(**)L M^{*} curve to the right, as illustrated in Figure 14-16. Since the exchange rate is unchanged, so are net exports.
d) 若政府支出增加 50，根据©部分推导，新的 $I{S}^{\ast }$$I{S}^{\ast }$IS^(**)I S^{*} 方程为 $Y=1,800-200\epsilon$$Y=1,800-200\epsilon$Y=1,800-200 epsiY=1,800-200 \varepsilon 。当汇率固定在 $\epsilon =2$$\epsilon =2$epsi=2\varepsilon=2 时，收入必须增至 $Y=$$Y=$Y=Y= 1,400。根据(a)部分可知， $L{M}^{\ast }$$L{M}^{\ast }$LM^(**)L M^{*} 方程由 $M/3=Y-200$$M/3=Y-200$M//3=Y-200M / 3=Y-200 给出，因此货币供应量必须增加至 $M=3,600$$M=3,600$M=3,600M=3,600 。也就是说，为防止本币升值，央行必须卖出本币并买入外币。如图 14-16 所示，这将使 $L{M}^{\ast }$$L{M}^{\ast }$LM^(**)L M^{*} 曲线右移。由于汇率未变，净出口也保持不变。

Figure 14-15  图 14-15

Figure 14-16  图 14-16
3) The Fed is considering two alternative monetary policies:
3) 美联储正在考虑两种替代性货币政策方案：

In the IS-LM model, which policy will better stabilize output under the following conditions? Explain your answer.
在 IS-LM 模型中，以下哪种情况下的政策能更好地稳定产出？请解释你的答案。
a) All shocks to the economy arise from exogenous changes in the demand for goods and services.
a) 所有经济冲击均源于商品和服务需求的外生性变化。
b) All shocks to the economy arise from exogenous changes in the demand for money.
b) 所有经济冲击均源于货币需求的外生性变化。

Answer:  答案：
a) Figure 13-27(A) depicts the $IS-LM$$IS-LM$IS-LMI S-L M model for the case in which the Fed holds the money supply constant. Figure 13-27(B) depicts the model for the case in which the Fed adjusts the money supply to hold the interest rate constant; this policy makes the effective $LM$$LM$LML M curve horizontal.
a) 图 13-27(A)展示了美联储保持货币供应量不变情形下的 $IS-LM$$IS-LM$IS-LMI S-L M 模型。图 13-27(B)则描绘了美联储通过调节货币供应量以维持利率不变的政策情景；该政策使得有效的 $LM$$LM$LML M 曲线呈现水平状态。

Figure 13-27  图 13-27

If all shocks to the economy arise from exogenous changes in the demand for goods and services, then all shocks shift the $IS$$IS$ISI S curve. Suppose a shock causes the $IS$$IS$ISI S curve to shift from $I{S}_1$$I{S}_1$IS_(1)I S_{1} to $I{S}_2$$I{S}_2$IS_(2)I S_{2}. Figure 13-28 shows the effect of this under the two policies. With a constant money supply (panel A), the change in the interest rate partially offsets the change in output. With a constant interest rate (panel B), this offsetting effect is absent, so output fluctuates more. Thus, if all shocks are to the $IS$$IS$ISI S curve, then the Fed should follow a policy of keeping the money supply constant.
如果所有经济冲击都源于商品和服务需求的外生变化，那么所有冲击都会使 $IS$$IS$ISI S 曲线发生位移。假设某次冲击导致 $IS$$IS$ISI S 曲线从 $I{S}_1$$I{S}_1$IS_(1)I S_{1} 移动到 $I{S}_2$$I{S}_2$IS_(2)I S_{2} 。图 13-28 展示了两种政策下这种冲击的影响效果。在货币供应量保持不变的情况下（图 A），利率变化会部分抵消产出的变化。而在利率保持不变的情况下（图 B），这种抵消效应不存在，因此产出波动更大。由此可见，如果所有冲击都作用于 $IS$$IS$ISI S 曲线，那么美联储应当采取保持货币供应量恒定的政策。

Figure 13-28  图 13-28

b) If all shocks in the economy arise from exogenous changes in the demand for money, then all shocks shift the $LM$$LM$LML M curve. Figure 13-29 shows the effects under the two policies. With the money supply held constant (panel A), shifts in the $LM$$LM$LML M curve lead to changes in output. With the interest rate held constant (panel B), the $LM$$LM$LML M curve does not shift in response to money demand shocks because the Fed immediately adjusts the money supply to satisfy demand at the given interest rate. There is no effect on output. Thus, if all shocks are to the $LM$$LM$LML M curve, the Fed should adjust the money supply to hold the interest rate constant, thereby stabilizing output.
b) 如果经济中的所有冲击都源于货币需求的外生变化，那么所有冲击都会使 $LM$$LM$LML M 曲线发生移动。图 13-29 展示了两种政策下的效应。在保持货币供应量不变的情况下（图 A）， $LM$$LM$LML M 曲线的移动会导致产出变化。而在保持利率不变的情况下（图 B），由于美联储会立即调整货币供应量以满足给定利率下的需求， $LM$$LM$LML M 曲线不会因货币需求冲击而发生移动，因此对产出没有影响。由此可见，如果所有冲击都作用于 $LM$$LM$LML M 曲线，美联储应通过调整货币供应量来维持利率稳定，从而实现产出稳定。

Figure 13-29  图 13-29

4) Suppose an economy has the Phillips curve:
4) 假设某经济体的菲利普斯曲线为：

a) What is the natural rate of unemployment?
a) 自然失业率是多少？
b) Graph the short-run and long-run relationships between inflation and unemployment.
b) 绘制通货膨胀与失业率之间的短期和长期关系曲线图。
c) How much cyclical unemployment is necessary to reduce inflation by 4 percentage points? Using Okun’s law, compute the sacrifice ratio.
c) 需要多少周期性失业才能将通货膨胀降低 4 个百分点？运用奥肯定律计算牺牲率。
d) Inflation is running at 6 percent. The central bank wants to reduce it to 2 percent. Give two scenarios that will achieve that goal.
d) 当前通货膨胀率为 6%。中央银行希望将其降至 2%。给出两种能够实现该目标的方案。

The economy has the Phillips curve
经济中存在菲利普斯曲线

a) The natural rate of unemployment is the unemployment rate at which the inflation rate does not deviate from the expected inflation rate. Here the expected inflation rate is last period’s inflation rate. Setting the inflation rate equal to last period’s inflation rate (that is, setting $\pi =\pi -1$$\pi =\pi -1$pi=pi-1\pi=\pi-1 ), we find that the natural rate of unemployment is $u=5$$u=5$u=5u=5 percent.
a) 自然失业率是指通货膨胀率与预期通货膨胀率无偏离时的失业率。此处的预期通货膨胀率为上一期的实际通胀率。令当期通胀率等于上一期通胀率（即设定 $\pi =\pi -1$$\pi =\pi -1$pi=pi-1\pi=\pi-1 ），可得出自然失业率为@1%。
b) In the short run (that is, in a single period), the expected inflation rate is the inflation rate in the previous period ${\pi }_{-1}$${\pi }_{-1}$pi_(-1)\pi_{-1}. The short-run relationship between inflation and unemployment is given by the graph of the Phillips curve: it has a slope of -0.5 and passes through the point where $\pi ={\pi }_{-1}$$\pi ={\pi }_{-1}$pi=pi_(-1)\pi=\pi_{-1} and $u=5$$u=5$u=5u=5 percent, as shown in Figure 15-1. In the long run, expected inflation equals actual inflation, so $\pi ={\pi }_{-1}$$\pi ={\pi }_{-1}$pi=pi_(-1)\pi=\pi_{-1}, unemployment is at its natural rate of 5 percent, and output is at its natural level. The long-run Phillips curve is thus vertical at an unemployment rate of 5 percent.
b) 短期内（即单期内），预期通货膨胀率等于上一期的实际通胀率 ${\pi }_{-1}$${\pi }_{-1}$pi_(-1)\pi_{-1} 。通胀与失业的短期关系由菲利普斯曲线图示呈现：该曲线斜率为-0.5，且经过@1%失业率与@2%通胀率的交点（如图 15-1 所示）。长期中，预期通胀等于实际通胀，故 $\pi ={\pi }_{-1}$$\pi ={\pi }_{-1}$pi=pi_(-1)\pi=\pi_{-1} ，失业率处于 5%的自然水平，产出也处于自然水平。因此长期菲利普斯曲线在 5%失业率处呈垂直状态。

c) To reduce inflation, the Phillips curve tells us that unemployment must be above its natural rate of 5 percent. We can write the Phillips curve in the form
c) 根据菲利普斯曲线，要降低通胀就必须使失业率高于 5%的自然水平。我们可以将菲利普斯曲线表述为

A fall in the inflation rate of 4 percentage points gives us $\pi -{\pi }_{-1}=-4$$\pi -{\pi }_{-1}=-4$pi-pi_(-1)=-4\pi-\pi_{-1}=-4. Plugging this into the left side of the above equation, we find the needed unemployment rate as follows:
通货膨胀率下降 4 个百分点，得到 $\pi -{\pi }_{-1}=-4$$\pi -{\pi }_{-1}=-4$pi-pi_(-1)=-4\pi-\pi_{-1}=-4 。将其代入上述等式左侧，我们计算出所需的失业率如下：

Hence, a fall in inflation of 4 percentage points requires 8 percentage points of cyclical unemployment above the natural rate of 5 percent.
因此，要使通货膨胀率下降 4 个百分点，需要使周期性失业率比 5%的自然失业率高出 8 个百分点。

Okun’s law says that a change of 1 percentage point in unemployment translates into a change of 2 percentage points in GDP. Hence, an increase in unemployment of 8 percentage points corresponds to a fall in GDP of 16 percentage points. The sacrifice ratio is the percentage of a year’s GDP that must be forgone to reduce inflation by 1 percentage point. Dividing the 16-percentage-point decrease in GDP by the 4-percentage-point decrease in inflation, we find that the sacrifice ratio is $16/4=4$$16/4=4$16//4=416 / 4=4.
奥肯定律指出，失业率每变动 1 个百分点，GDP 将相应变动 2 个百分点。因此，失业率上升 8 个百分点意味着 GDP 下降 16 个百分点。牺牲比率是指为使通货膨胀率降低 1 个百分点而必须放弃的年度 GDP 百分比。用 GDP 下降的 16 个百分点除以通货膨胀率下降的 4 个百分点，可得出牺牲比率为 $16/4=4$$16/4=4$16//4=416 / 4=4 。
d) To reduce the inflation rate by 4 percentage points, one option is to have very high unemployment for a short period of time (for example, 13 percent unemployment for a single year). An alternative is to have a lower rate of unemployment for a longer period of time (for example, 7 percent unemployment for four years). Both plans bring the inflation rate down by 4 percentage points but at different speeds.
d) 要将通胀率降低 4 个百分点，一种方案是在短期内维持极高的失业率（例如单年失业率达到 13%）；另一种方案则是以较低失业率维持更长时间（例如连续四年保持 7%失业率）。两种方案都能实现通胀率下降 4 个百分点的目标，但调整速度存在差异。