Given That $d Y _ { t } = b d W _ { t }$

question 5

Multiple Choice

Given that $d Y _ { t } = b d W _ { t }$ and $X _ { t } = \ln \left( Y _ { t } \right)$ ,what is $d X _ { t }$ ?

• A) \(X _ { t } e ^ { b ^ { 2 } dt + Y _ { t } d W _ { t } }\)
• B) \(\ln \left( X _ { t } \right) \left[ \frac { 1 } { 2 } b ^ { 2 } d t + b d W _ { t } \right]\)
• C) \(- \frac { 1 } { 2 } b ^ { 2 } e ^ { 2 X _ { t } } d t + b e ^ { - x _ { t } } d W _ { t }\)
• )
• D) \(b X _ { t } \left[ \frac { 1 } { 2 } b d t + d W _ { t } \right]\)

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Definitions:

Aggregate Demand

The total demand for all goods and services within an economy at a particular time and price level, including consumption, investment, government spending, and net exports.

Say's Law

An economic theory proposing that the production of goods creates its own demand, attributed to the French economist Jean-Baptiste Say.

Recessions

Periods of economic decline lasting at least six months, characterized by decreases in GDP, employment, and consumer spending.

Monetarists

Economists who believe that changes in the money supply have major influences on national output in the short run and the price level over longer periods.