# Mathematical Influence Models

A simplified model of the national economy can be described as follows. The national income is the sum of consumption, investment, and government spending. Consumption is related to the total income of all individuals and the taxes they pay on income. Taxes are related to income by the tax rate. Investment is also related to the size of income.

- Draw in influence diagram recognizing that the phrase "A is related to B" implies that A influences B in the Model

- Assuming that "A is related to B" can be translated into mathematical terms as A= kB, where is k is some constant. Come up with a mathematical model for the information provided.

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#### Solution Preview

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Given information:

A simplified model of the national economy can be described as follows. The national income is the sum of consumption, investment and government spending. Consumption is related to the total income of all individuals and the taxes they pay on income. Taxes are related to income by the tax rate. Investment is also related to the size of income.

MODEL REPRESENTATION:

NY = C + I + G

Where:

NY = national income

C = consumption expenditure

I = Investment

G = government enxpenditure

C = b (Y - aY)

Where:

b = constant ( consumption rate)

a = tax rate

T = ...

#### Solution Summary

The expert draws an influence diagram recognizing phrase.