Question

1. The sunflower oil industry is perfectly competitive. Every producer has a following long-run total cost function given by TC(Q) = 2Q³− 15Q² + 40Q where Q is measured in tons of sunflower oil.
   1. What is the marginal cost for an individual firm?
   2. Calculate and graph the long-run average total cost of producing oil that each firms faces for values of Q from 1 to 10.
   3. What will the long run equilibrium price of sunflower oil be?
   4. How many units of sunflower oil will each firm produce in the long run?
   5. Suppose that the market demand for canola oil is given by Q = 999 − .25P. At the long-run equilibrium price, how many tons of sunflower oil will consumers demand?
   6. Given your answer to part e, how many firms will exist when the industry is in the long-run equilibrium?

Answer 1

TC(Q) = 2Q³− 15Q² + 40Q (total cost function)

MC = dTC/dQ (the first order derivative of the total cost function) = 6Q^2-30Q+40

AC = TC/Q = 2Q^2-15Q+40

long run equilibrium occurs at a point where price equals the minimum of average total cost P=min ATC.

to find min ATC we take first order derivative of average cost function.

dAC/dq = 4Q - 15 = 0 or Q = 15/4 = 3.75 (Quantity for each firm)

at Q = 3.75, ATC = 2*(3.75)^(2)-15*3.75+40 = 11.875

So the long run equilibrium price will be $11.875

If the demand function is given by  Q = 999 − 0.25P, then at long run Price P =11.875, Quantity sold will be Q= 999-0.25*11.875 = 996.03

Number of firms = 996.03/3.75 = 265.608