Consider the Market Model $\begin{array} { l } Q _ { S } = 4 P - 3 \\Q _ { D } = - 2 P + 13 \\\frac { d P } { d t } = 0.4 \left( Q _ { D } - Q _ { S } \right)\end{array}$

question 7

Multiple Choice

Consider the market model
$\begin{array} { l } Q _ { S } = 4 P - 3 \\Q _ { D } = - 2 P + 13 \\\frac { d P } { d t } = 0.4 \left( Q _ { D } - Q _ { S } \right) \end{array}$
Find an expression for $Q _ { D } ( t )$ when $P ( 0 ) = 2$ .

• A) \(\frac { 2 } { 3 } \left( 4 - e ^ { - 2.4 t } \right)\)
• B) \(\frac { 1 } { 3 } \left( 23 + 4 e ^ { - 2.4 t } \right)\)
• C) \(\frac { 1 } { 3 } \left( 4 + e ^ { - 2.4 t } \right)\)
• D) \(\frac { 2 } { 3 } \left( 4 + e ^ { - 2.4 t } \right)\)
• E) \(\frac { 1 } { 3 } \left( 23 - 8 e ^ { - 2.4 t } \right)\)

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Definitions:

Government Bonds

Debt securities issued by a government to finance its expenditure, promising to pay a specified interest rate and to return the principal at maturity.

Groceries

Items of food and other goods sold by a grocer or supermarket, typically for household consumption.

Gasoline

A flammable liquid derived from petroleum, predominantly used as fuel in internal combustion engines.

Flow Variable

A quantity that is measured over a specified period of time, contrasting with stock variables which are measured at one specific time.