Qs = 15,000 + 350P, Qd = 35,000 - 150P, TC = 40 + 2Q.
a) Marginal Revenue of this firm is MR = P. In equilibrium Qd = Qs, so:
15,000 + 350P = 35,000 - 150P,
500P = 20,000,
Pe = $40,
So, MR = P = $40.
b) The Marginal Cost of this firm is MC = TC' = 2.
c) The optimal output for this firm is Qe = 15,000 + 350*40 = 29,000 units.
d) The optimal total revenue and profit for this firm are:
TR = P*Q = 40*29,000 = $1,170,000,
TP = TR - TC = 1,170,000 - (40 + 2*29,000) = $1,111,960.
e) As in a perfectly competitive market firms earn zero profit in the long run, the firms continue to stay in business if profit is zero.