这是一份manchester曼切斯特大学ECON10252T/ECON10262T/ECON20022T/ECON20032T/ECON20262T/ECON20532T/ECON30032T/ECON30532T作业代写的成功案例

$$
\pi_{u t}=u_{u t} Y_{u t}-g r_{i t} K_{u}=\left(u_{i t} \phi-g r_{u t}\right) K_{u t}
$$
and expected profit is $E\left(\pi_{i t}\right)=\left(\phi-g r_{i t}\right) K_{i t}$.
In this economy, firms may go bankrupt as soon as their net worth becomes negative, that is $A_{i t}<0$. The law of motion of $A_{i t}$ is:
$$
A_{u}=A_{u t-1}+\pi_{u \prime}
$$
that is, net worth in previous period plus (minus) profits (losses). Making use of (4.16) and (4.17), it follows that the bankruptcy state occurs whenever:
$$
u_{i t}<\frac{1}{\phi}\left(g r_{i t}-\frac{A_{t-1}}{K_{i t}}\right) \equiv \bar{u}_{i t} .
$$

ECON10252T/ECON10262T/ECON20022T/ECON20032T/ECON20262T/ECON20532T/ECON30032T/ECON30532T COURSE NOTES ：

$$
\frac{A_{i j}}{x_{i} x_{j}}=\frac{\tau_{i}}{x_{i}} \text { for any } i, j \in J_{x^{*}}
$$
Similarly,
$$
\frac{A_{r s}}{X_{r} \cdot X_{s}}=\frac{t_{s}}{X_{s}} \text { for any } r, s \in J_{\boldsymbol{x}} .
$$
Since the indices $i$ and $s$ are in $J_{x}$,
$$
A_{\text {is }}=t_{s} x_{i}=\tau_{i} x_{s} \text {, }
$$
which in turn implies that
$$
\frac{\tau_{i}}{x_{i}}=\frac{t_{s}}{x_{s}} .
$$