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# 经济代写|宏观经济学代考Macroeconomics代写|Monetary Policy and the Phillips Curve

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## 经济代写|宏观经济学代考Macroeconomics代写|Monetary Policy and the Phillips Curve

For the rest of this chapter we will be using a modified version of equation (19.5). Assume that:
$$u=u^{\star}+\gamma\left(\pi^e-\pi\right) .$$

Here $u$ is the unemployment rate, $u^{\star}$ is the “natural rate” of unemployment, $\pi^e$ is the $e x$ pected inflation rate and $\pi$ is the actual inflation rate. The natural rate of unemployment is the level of unemployment when inflation is perfectly anticipated, so no industries are fooled into thinking that relative demand is unusually high or low. The slope of this Phillips curve is $-\gamma$ where we assume $\gamma>0$ (monetary expansions reduce unemployment). If we think that there is uncertainty about the state of the real economy, we can add a mean zero shock term, $\varepsilon$, to produce:
$$u=u^{\star}+\gamma\left(\pi^e-\pi\right)+\varepsilon$$
For the most part we will assume that the monetary authority knows the state of the real economy with certainty.

In Figure (19.1) we plot Phillips curves with two different values of expected inflation $\pi^e$, a low value in which the expected inflation rate is zero, and a high value, in which the expected inflation rate is $8.3 \%$. The dotted line gives the natural rate of unemployment (here $u^{\star}=5 \%$ ), and $\gamma=0.3$. Notice that when inflationary expectations are high, to achieve any given unemployment rate requires a higher inflation rate, and to achieve zero inflation requires an unemployment rate well above the natural rate.

## 经济代写|宏观经济学代考Macroeconomics代写|Monetary Policy with Fixed Expectations

Assume that the government (or which ever arm of the government controls monetary policy) has a utility function over unemployment and inflation of $V^g(u, \pi)$ given by:
$$V^g(u, \pi)=-u^2-\pi^2$$
That is, the government dislikes unemployment and inflation equally. We will assume this form for $V$ for the rest of the chapter, so it’s worth mentioning that the Federal Reserve Board is, by law, supposed to balance the twin goals of full employment and price stability. Thus this utility function seems to be written in law.

If we assume that $\pi^e$ is given exogenously and fixed, we can substitute the Phillips curve in equation (19.6) into the government’s utility function above to produce a maximization problem. Thus if the private sector has fixed expectations about the inflation rate given by $\pi^e$, then the government’s optimal choice of inflation $\pi$ is given by:
$$\max _\pi\left{-\left[u^{\star}+\gamma\left(\pi^e-\pi\right)\right]^2-\pi^2\right} \text {. }$$
The first-order condition with respect to inflation $\pi$ is:
$$2 \gamma\left[u^{\star}+\gamma\left(\pi^e-\pi\right)\right]-2 \pi=0 .$$

# 宏观经济学代写

## 经济代写|宏观经济学代考MACROECONOMICS代写|MONETARY POLICY AND THE PHILLIPS CURVE

$$u=u^*+\gamma\left(\pi^e-\pi\right) .$$

$$u=u^{\star}+\gamma\left(\pi^e-\pi\right)+\varepsilon$$

V^g(u, \pi)=-u^2-\pi^2
$$也就是说，政府同样不喜欢失业和通货膨胀。我们将采用这种形式 V 对于本章的其余部分，值得一提的是，根据法律，联邦储备委员会应该平衡 充分就业和价格稳定的双重目标。因此，这个效用函数似乎是写在法律上的。 如果我们假设 \pi^e 是外生固定的，我们可以用菲利普斯曲线代入等式19.6上面的政府效用函数产生一个最大化问题。因此，如果私营部门对通货膨 胀率有固定的预期 \pi^e, 那么政府对通货膨胀的最优选择 \pi 是 (谁) 给的: 关于通货膨胀的一阶条件 \pi 是:$$
2 \gamma\left[u^{\star}+\gamma\left(\pi^e-\pi\right)\right]-2 \pi=0 .


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