Concern a simple model of the national economy described by the difference equation

Here Y_k is the total national income during year k, a is a constant less than 1, called the marginal propensity to consume, and b is a positive constant of adjustment that describes how changes in consumer spending affect the annual rate of private investment.

Find the general solution of equation (14) when a = .9 and b = 4/9. What happens to Y_k as k increases?

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D [ = Aq» + + Aq + DD - z+ ¥K