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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 经济代写|宏观经济学代写Macroeconomics代考|The steady-state marginal product of capital

In any event, as in the Solow model, there is something we can say about efficiency here. Notice that, at the steady state, the marginal product of capital is
$$f^{\prime}\left(k^\right)=\alpha\left(k^\right)^{\alpha-1}=r^*=\left(\frac{\alpha}{1-\alpha}\right)(2+\rho)(1+n) .$$
Notice that this interest rate depends on more parameters than in the NGM. The relationship between the discount factor and the interest rate is still there. A higher discount factor implies less savings today and a higher interest rate in equilibrium. But notice that now that the population growth affects the interest rate. Why is this the case? The intuition is simple. A higher growth rate of population decreases the steady-state stock of capital thus increasing the marginal product of capital. How does this compare with the golden rule of $f^{\prime}\left(k_G\right)=n$ ? From the above it is clear that $k^>k_G$ if $$r^<n,$$
which in turn implies
$$\alpha<\frac{n}{n+(1+n)(2+\rho)} .$$
That is, if $\alpha$ is sufficiently low (or, alternatively, if $n$ is sufficiently high), the steady-state capital stock in the decentralised equilibrium can exceed that of the golden rule.

## 经济代写|宏观经济学代写Macroeconomics代考|Dynamic inefficiency

Suppose a benevolent planner found that the economy was at the steady state with $k^$ and $y^$. Suppose further that $k^*>k_G$. Is there anything the planner could do to redistribute consumption across generations that would make at least one generation better off without making any generation worse off? Put differently, is this steady state Pareto efficient?

Let resources available for per-capita consumption (of the young and old), in any period $t$, be given by $x_t$. Note next that in any steady state,
$$x_{S S}=k_{S S}^\alpha-n k_{S S}$$
Note that, by construction, $k_G$ is the $k_{S S}$ that maximises $x_{S S}$, since $\frac{\partial x_{S S}}{\partial k_{S S}}=0$.
The initial situation is one $k_{\mathrm{SS}}=k^$, so that $x_{\mathrm{SS}}=c^$. Suppose next that, at some point $t=0$, the planner decides to allocate more to consumption and less to savings in that period, so that next period the capital stock is $k_G$. Then, in period 0 , resources available for consumption will be $$x_0=\left(k^\right)^a-n k_G+\left(k^-k_G\right) .$$ In every subsequent period $t>0$, resources available for consumption will be $$x_t=k_G^a-n k_G, t>0 .$$ Clearly, in $t>0$ available resources for consumption will be higher than in the status quo, since $k_G$ maximises $x_{S S}$. Note next that $x_0>x_t$ (this should be obvious, since at time 0 those alive can consume the difference between $k^$ and $k_G$ ). Therefore, in $t=0$ resources available will also be higher than in the status quo. We conclude that the change increases available resources at all times. The planner can then split them between the two generations alive at any point in time, ensuring that everyone is at least as well off as in the original status quo, with at least one generation being better off. Put differently, the conclusion is that the decentralised solution leading to a steady state with a capital stock of $k^$ is not Pareto efficient. Generally, an economy with $k^>k_G$ (alternatively, one with $r^*<n$ ) is known as a dynamically inefficient economy.

# 宏观经济学代考

## 经济代写|宏观经济学代写宏观经济学代考|资本的稳态边际产量

. >

$$f^{\prime}\left(k^\right)=\alpha\left(k^\right)^{\alpha-1}=r^*=\left(\frac{\alpha}{1-\alpha}\right)(2+\rho)(1+n) .$$

，这反过来意味着
$$\alpha<\frac{n}{n+(1+n)(2+\rho)} .$$

## 经济代写|宏观经济学代写宏观经济代考|动态低效率

.

$$x_{S S}=k_{S S}^\alpha-n k_{S S}$$

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## MATLAB代写

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