SM) 9. Let N = N() denote the size of a certain population, X = X() the total product, and x (t) = X(1)/N(t) the product per capita at time f. T. Haavelmo (1954) studied the model: () N/N = Q - BN/X (ii) X = AN where a, B, and a are positive constants, with a # 1. Show that this leads to a differential equation of the form (3) for x = x(). Solve this equation and then find expressions for N = N (t) and X = X (t). Examine the limits for x (t), N(t), and X (t) as t -> co in the case 0