Assignment-daixieTM为您提供利物浦大学University of Liverpool NUMERICAL METHODS FOR APPLIED MATHEMATICS MATH266应用数学的数值方法代写代考和辅导服务！
Instructions:
Macroeconomics is the study of the behavior of the economy as a whole. It is concerned with the analysis of large-scale economic systems and the factors that influence them, such as inflation, unemployment, national income, economic growth, and monetary and fiscal policies.
Macroeconomics is concerned with understanding the aggregate behavior of individuals, firms, and households in the economy. It seeks to explain the fluctuations in the overall level of economic activity and to develop policies that can be used to stabilize the economy and promote growth.
Some of the key concepts in macroeconomics include Gross Domestic Product (GDP), which measures the total output of goods and services produced in a country over a specific period, the Consumer Price Index (CPI), which measures the cost of a basket of goods and services consumed by households, and the unemployment rate, which measures the percentage of the labor force that is currently without work.
Macroeconomics also explores the role of government policies in influencing economic performance, such as monetary policy (which involves managing the money supply and interest rates to stabilize the economy) and fiscal policy (which involves managing government spending and taxation to promote economic growth and stability).
Consider the balance sheet of an American bank before the crisis. On the liabilities side, the bank has a total capital of 10 billion dollars and deposits worth of 150 billion dollars. On the assets side, $10 \%$ of the assets are subprime mortgages. The rest of assets are considered safe and will not go through changes in value.
- What is the leverage of this bank?
$\lambda=\frac{10+150}{10}=16$
Suppose that after the outbreak of the crisis, the value of the subprime loans falls by a half. Is the bank still solvent? What is its new leverage?
The total amount of subprime mortgages that the bank has is $160 \times 10 \%=16$ billion dollars before the crisis. After the crisis, the value of them fell in half and become 8 billion dollars. The bank takes a hit of 8 million in its capital, but it remains solvent. Its remaining capital is $10-8=2$ billion dollars.
$$
\lambda^{\prime}=\frac{2+150}{2}=76
$$
According to the Basel III rule (the international rule that determines banks’ minimum required capital, try to google it out if you haven’t heard about it before), banks are supposed to have a leverage ratio of at most $\frac{100}{3}$. Does this bank need to recapitalize? If so, by how much?
Since $76>\frac{100}{3}$, the bank needs to recapitalize. Let $x$ be the amount of recapitalization. The bank’s leverage after recapitalization would be
$$
\lambda^{\prime \prime}=\frac{2+x+150}{2+x}
$$
$\lambda^{\prime \prime} \leq \frac{100}{3}$ if and only if $\frac{2+x+150}{2+x} \leq \frac{100}{3}$, or $x \geq \frac{256}{97}$.
