Problem 1. Suppose a firm has go units of a non-renewable resource. Let the firm's inverse instantaneous demand curve be p(x(t)). That is, at instant t if the firm sells x(t), then the price will be p(x(t)). The firm's problem is max s.t. dq x,9 JO e-at x (t )p(x(t))dt dt = -x(t) q(0) = 40 q (T) 20 (1) Write the first order condition for the firm's problem. (2) Suppose p(x) = 1 - 4 for 0 2. (a) Show that A(t) = A is constant. (b) Solve for A using the boundary constraint(s). (c) Solve for x(t). (d) Solve for a(t )