題組內容

2. (15%) One of the debt models proposed by Evsey Domar, a Keynesian economist, can be described as follows. Let D and I respectively denote the national debt and national income, and assume that both are functions of time t. Furthermore, both the time rates of change of D and I are assumed to be proportional to I, so that
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Supposc /(0) = I0 and D(0) = D0.

(a) (10%) Solve both of these differential equations and express D(t) and I(t) in terms of a, r, l0, and D0.