Tag Archives: Advanced Macroeconomics代写

高级宏观经济学 Advanced Macroeconomics ECON343

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这是一份liverpool利物浦大学ECON343的成功案例

高级宏观经济学 Advanced Macroeconomics ECON343


Suppose the individual has labor income of $Y_{1}$ in the first period of life and zero in the second period. Second-period consumption is thus $(1+r)\left(Y_{1}-C_{1}\right) ; r$, the rate of return, is potentially random.
(i) Find the first-order condition for the individual’s choice of $C_{1}$.
(ii) Suppose $r$ changes from being certain to being uncertain, without any change in $E[r]$. How, if at all, does $C_{1}$ respond to this change?
Suppose the individual has labor income of zero in the first period and $Y_{2}$ in the second. Second-period consumption is thus $Y_{2}-(1+r) C_{1} \cdot Y_{2}$ is certain; again, $r$ may be random.

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ECON343 COURSE NOTES ：

(i) Show that $\partial \ln K_{\mathrm{t}+1} / \partial \ln K_{\mathrm{t}}$ (holding $A_{t}, L_{t}, C_{t}$, and $G_{t}$ fixed) is (1+ $\left.r_{t+1}\right)\left(K_{\mathrm{t}} / K_{t+1}\right)$.
(ii) Show that this implies that $\partial \ln K_{t+1} / \partial \ln K_{t}$ evaluated at the balanced growth path is $\left(1+r^{}\right) / e^{n+g} \cdot 4^{47}$ Show that $$ \tilde{K}{t+1} \simeq \lambda{1} \tilde{K}{t}+\lambda{2}\left(\tilde{A}{t}+\tilde{L}{t}\right)+\lambda_{3} \tilde{G}{t}+\left(1-\lambda{1}-\lambda_{2}-\lambda_{3}\right) \tilde{C}{l} \text {. } $$ where $\lambda{1} \equiv\left(1+r^{}\right) / e^{n+g}, \lambda_{2} \equiv(1-\alpha)\left(r^{}+\delta\right) / \alpha e^{n+g}$, and $\lambda_{3}=-\left(r^{}+\delta\right)$ $(G / Y)^{} / \alpha e^{n+g}$; and where $(G / Y)^{}$ denotes the ratio of $G$ to $Y$ on the balanced growth path without shocks. (Hints: 1 . Since the production function is Cobb-Douglas, $Y^{}=\left(r^{}+\delta\right) K^{} / \alpha^{} 2$. On the balanced growth path, $K_{t+1}=e^{n+g} K_{t}$, which implies that $\left.C^{}=Y^{}-G^{}-\delta K^{}-\left(e^{n+g}-1\right) K^{*} .\right)$
Use the result in (b) and equations (4.43)-(4.44) to derive (4.52), where $b_{\mathrm{KK}}=\lambda_{1}+\lambda_{2} a_{\mathrm{LK}}+\left(1-\lambda_{1}-\lambda_{2}-\lambda_{3}\right) a_{\mathrm{CK}} b_{\mathrm{KA}}=\lambda_{2}\left(1+a_{\mathrm{LA}}\right)+\left(1-\lambda_{1}-\lambda_{2}-\lambda_{3}\right) a_{\mathrm{CA}}$, and $b_{\mathrm{KG}}=\lambda_{2} a_{\mathrm{LG}}+\lambda_{3}+\left(1-\lambda_{1}-\lambda_{2}-\lambda_{3}\right) a_{\mathrm{CG}}$.










高级宏观经济学 Advanced Macroeconomics ECON30002T

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这是一份manchester曼切斯特大学ECON30002T作业代写的成功案例

高级宏观经济学 Advanced Macroeconomics ECON30002T

Averaging the $p_{i}$ ‘s and using the fact that the average of the $z_{i}$ ‘s is zero, we obtain
$$
p=\frac{\gamma-1}{1+\eta \gamma-\eta} y+p
$$
implies that the equilibrium value of $y$ is simply ${ }^{3}$
$$
y=0
$$
Finally, imply
$$
m=p
$$
Not surprisingly, money is neutral in this version of the model: an increase in $m$ leads to an equal increase in all $p_{i}$ ‘s, and hence in the overall price index, $p$. No real variables are affected.

英国论文代写Viking Essay为您提供作业代写代考服务

ECON30002T COURSE NOTES ：

Although we have already examined aspects of individuals’ consumption decisions in our investigations of the Ramsey and Diamond models in Chapter 2 and of real-business-cycle theory in Chapter 4 , here we start with a simple case. Consider an individual who lives for $T$ periods whose lifetime utility is
$$
U=\sum_{t=1}^{T} u\left(C_{t}\right), \quad u^{\prime}(\bullet)>0, \quad u^{\prime \prime}(\bullet)<0
$$
where $u(\cdot)$ is the instantaneous utility function and $C_{t}$ is consumption in period $t$. The individual has initial wealth of $A_{0}$ and labor incomes of $Y_{1}, Y_{2}, \ldots, Y_{T}$ in the $T$ periods of his or her life; the individual takes these as given. The individual can save or borrow at an exogenous interest rate, subject only to the constraint that any outstanding debt must be repaid at the end of his or her life. For simplicity, this interest rate is set to zero. ${ }^{1}$ Thus the individual’s budget constraint is
$$
\sum_{t=1}^{T} C_{t} \leq A_{0}+\sum_{t=1}^{T} Y_{t}
$$