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# 经济代写|宏观经济学代考Macroeconomics代写|Model Assumptions

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## 经济代写|宏观经济学代考Macroeconomics代写|Model Assumptions

To make this model work, we will have to specify a rule for output, population growth, how the price level is determined and what limits there are on borrowing. I list all of the model’s assumptions here for convenience:

1. Output per capita $y_t$ is constant and $y_t=1$, but population $N_t$ grows at the constant rate $n$, so $N_t=(1+n) N_{t-1}$, where $N_0>0$ is given. So total GDP each period $Y_t=y_t N_t$ is just equal to population.
2. The real interest rate on government debt is constant at $r_t=r$, and the government never defaults on its debt. This includes default by unexpected inflation when bonds are denominated in dollars. Thus we are dealing with inflation-indexed bonds. We also make the very important assumption that $r>n$. Without this assumption, most of the “arithmetic” is not so “unpleasant”.
3. A stark monetarist Quantity Theory of Money relation with a constant velocity, $v=1$ :
$(18.2)$
$$P_t Y_t=v M_t$$
Combine this with the definition of $Y_t$ in Assumption (1) above to find the price level in period $t, P_t$, is:
$$P_t=\frac{M_t}{N_t}$$
4. There is an upper bound on per-capita bond holdings by the public of $\bar{b}$. That is, $B_t^g / N_t \leq \bar{b}$

In addition, to make life easier, we will specify that the government’s fiscal policy, which is a sequence of deficits $\left{D_t\right}_{t=0}^{\infty}$, is simply a constant per-capita deficit of $d$. Thus:
$$\frac{D_t}{N_t}=d, \text { for all } t=0,1, \ldots, \infty \text {. }$$

## 经济代写|宏观经济学代考Macroeconomics代写|Monetary Polic

The monetary authority (in the U.S., the Fed) produces a sequence of money stocks $\left{M_t\right}_{t=0}^{\infty}$. These then feed through the quantity theory of money relation (18.2) to produce a sequence of inflation rates. A monetary policy will be a choice for the growth rate of money. If the stock of debt is growing, eventually the bond ceiling will be reached and the Fed will no longer be able to pick an inflation rate, it will be forced to provide enough seigniorage revenue to cover the government’s reported deficit. We call this the catastrophe. The catastrophe happens at date $T$. The catastrophe date $T$ is itself as a function of choice made by the government.
Given money supply growth, the gross inflation rate in period $t$ is:
$$\frac{P_t}{P_{t-1}}=\frac{M_t}{N_t} \frac{N_{t-1}}{M_{t-1}}=\frac{1}{1+n} \frac{M_t}{M_{t-1}} .$$
The net inflation rate is defined as $P_t / P_{t-1}-1$. For simplicity, assume (with Sargent and Wallace) that the Fed picks a constant growth rate for money, $\theta$, in the periods before the catastrophe. Thus:
$$\frac{M_t}{M_{t-1}}=1+\theta, \text { for all } t=0,1, \ldots, T \text {. }$$
This implies that inflation is:
$$\frac{P_t}{P_{t-1}}=\frac{1+\theta}{1+n} \text {, for all } t=0,1, \ldots, T$$

# 宏观经济学代写

## 经济代写|宏观经济学代考MACROECONOMICS代写|MODEL ASSUMPTIONS

1. 人均产出 $y_t$ 是常数并且 $y_t=1$, 但人口 $N_t$ 以恒定的速度增长 $n$ ，所以 $N_t=(1+n) N_{t-1}$ ，在哪里 $N_0>0$ 给出。所以每个时期 的总GDP $Y_t=y_t N_t$ 正好等于人口。
2. 政府债务的实际利率不变 $r_t=r$ ，而且政府从不拖欠债务。这包括以美元计价的债券因意外通华憉胀而违约。因此，我们正在 处理与通胀挂钧的债券。我们还做出了一个非常重要的假设 $r>n$. 没有这个假设，大部分的“算术”都没有那么“难听”。
3.一个鲜明的货币主义货币数量理论，速度恒定， $v=1$ :
$(18.2)$
$$P_t Y_t=v M_t$$
结合这个与定义 $Y_t$ 在假设 1 上面找到期间的价格水平 $t, P_t$ ，是:
$$P_t=\frac{M_t}{N_t}$$
3. 公众人均债券持有量有上限. . 那是, $B_t^g / N_t \leq \bar{b}$
$$\frac{D_t}{N_t}=d, \text { for all } t=0,1, \ldots, \infty$$

## 经济代写|宏观经济学代考MACROECONOMICS代写|MONETARY POLIC

$$\frac{P_t}{P_{t-1}}=\frac{M_t}{N_t} \frac{N_{t-1}}{M_{t-1}}=\frac{1}{1+n} \frac{M_t}{M_{t-1}} .$$

$$\frac{M_t}{M_{t-1}}=1+\theta \text {, for all } t=0,1, \ldots, T \text {. }$$

$$\frac{P_t}{P_{t-1}}=\frac{1+\theta}{1+n}, \text { for all } t=0,1, \ldots, T$$

## Matlab代写

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