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

question 14

Multiple Choice

Given that $d Y _ { t } = b d W _ { t }$ and $X _ { t } = Y _ { t } ^ { 3 }$ ,what is $d X _ { t }$ ?

• A) \(3 b X _ { t } ^ { 1 / 3 } \left[ 2 b d t + X _ { t } ^ { 1 / 3 } d W _ { t } \right]\)
• B) \(3 b Y _ { t } \left[ Y _ { t } d t + b d W _ { t } \right]\)
• C) \(b ^ { 3 } d W _ { t } ^ { 3 }\)
• D) \(b ^ { 3 } d W d t\)

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Definitions:

Potential Output

The maximum level of economic productivity that can be maintained in the long run without causing inflation to rise.

Governmental Intervention

Actions taken by a government to affect the economy, which can include regulations, subsidies, and taxes.

Discretionary Policy

Economic policies based on judgment decisions by policymakers, as opposed to rules-based policies, to manage the economy.

Policy Tools

Policy tools are mechanisms used by government or monetary authorities to influence the economy, such as interest rates, taxation, and government spending.