Exercise 136

1 How many factors of production are explicitly considered in the Domar model? What does this fact imply with regard to the capital-labor ratio in production?

2 We learned in Sec. 10.2 that the constant r in the exponential function Ac" represents the rate of growth of the function. Apply this to (13.16), and deduce (13.18) without going through integration.

3 Show that even if we let investment be negative in the equation |/| = Ae''x', upon definitizing the arbitrary constant A we will still end up with the solution (13.18).

4 Show that the result in (13.18) can be obtained alternatively by finding—and equating — the definite integrals of both sides of (13.16),

1 dl m = ps with respect to the variable t, with limits of integration t = 0 and t = t. Remember that when we change the variable of integration from t to /, the limits of integration will change from t = 0 and t = t, respectively, to / = 1(0) and I = I(t).

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