The demand for cigarettes is given by P = 450450 - 0.20.2Q. Cigarettes are manufactured at a constant marginal cost of 5050 and sold in a competitive market. What is the quantity of cigarettes sold in equilibrium? Upper Q Subscript PrivateQPrivate = nothing

Q = 1,000

Explanation:

The firms will product until marginal revenue matches marginal cost

being marginal cost $50

then the revenue per additional unit of cigarettes sold should be $50

Revenue = P x Q

Revenue = (450 - 0.20Q) x Q = - 0.20Q^2 + 450Q

Marginal revenue: slope of the revenue function:

dRq/dQ = - 0.4Q + 450

Now we equalize and solve for Q

Marignal Revenue = Marginal Cost

-0.4Q + 450 = 50

(450 - 50) = 0.4Q

400 / 0.4 = Q

Q = 1,000