Question: The price a firm obtains for a commodity varies with demand Q according to the formula P (Q) = 18 - 0.006Q. Total cost is C(Q) = 0.004Q2 + 4Q + 4500.
(a) Find the firm's profit π(Q) and the value of Q that maximizes profit.
(b) Find a formula for the elasticity of P (Q) w.r.t. Q, and find the particular value Q∗ of Q at which the elasticity is equal to -1.
(c) Show that the marginal revenue is 0 at Q∗.