We Modeled Populations of Aphids and Ladybugs with a Lotka-Volterra $\frac { d L } { d t } = - 0.6 L + 0.0005 \mathrm { AL }$

question 3

Multiple Choice

We modeled populations of aphids and ladybugs with a Lotka-Volterra system.Suppose we modify those equations as follows: \) \frac { d A } { d t } = 2 A ( 1 - 0.0005 A ) - 0.01 A L\) $\frac { d L } { d t } = - 0.6 L + 0.0005 \mathrm { AL }$
Find the equilibrium solution.

• A) \(A = 3200 , L = 110\)
• B) \(A = 4700 , L = 90\)
• C) \(A = 3700 , L = 120\)
• D) \(A = 1200 , L = 80\)
• E) \(A = 1500 , L = 100\)

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Definitions:

Autonomous Investment

Investment that is not influenced by the current level of income or production, often driven by technological innovations or changes in policy.

Aggregate Expenditure Line

A visual depiction in macroeconomics illustrating the overall expenditures on goods and services within an economy across different income levels.

Marginal Propensity

The tendency of a person to spend an additional unit of currency; often relates to income in the context of marginal propensity to consume or save.

Simple Multiplier

The ratio used to estimate the proportional amount of increase, or decrease, in final income that results from an injection, or withdrawal, of spending.