In a perfectly competitive market, a firm has the following short run total cost function:

STC=30,000 + 450q^2 + 100q^3

The firm's long run total cost function is given by:

LTC=1350q - 20q^2+ 0.2q^3

The market demand is given by:

P=10,000-Q

a) In short run, there are 10 identical firms in the market producing. derive the short-run equilibrium Q (market equilibrium quantity), q (a firm's equilibrium quantity), and p (market price).Does a typical firm earn a short-run profit?If yes, compute the short-run profit for each firm; if no, show your calculation and explain.

b) How many identical firms will there be when the market is in long-run equilibrium? Draw the graph of the market in long run equilibrium and show your calculation step by step.