Total national economy during time period n is

t(n) = c(n) + p(n) + g(n)

where c(n) is the amount consumers spend, p(n) is the amount of additional investment made, and g(n) is the amount the government spends, all during the nth time period.

c(n) = a*t(n-1) , The constant a is known as the marginal propensity to consume(MPC)

p(n) = b*{c(n)-c(n-1)} , The constant b is known as the marginal propensity to investment(MPI)

g(n) = 1 , Assume that government expenditures are constant. represent one unit of money

This dynamical system is a variation of the accelerator-multiplier model, which was first developed in 1939.

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