Ten competitive sawmills currently supply lumber to a market whose demand q,  depends on lumber price, p, as follows:                              q = 3550 - 350p

Ten competitive sawmills currently supply lumber to a market whose demand q, 

depends on lumber price, p, as follows: 

                            q = 3550 - 350p. 

The cost function of each mill is identical: 

                   C_i  = 5q_i  + 0.05q_i²  + 80                                  i = 1........10 

(a) Determine the market supply curve. 

(b) Determine the short run equilibrium market price and output. 

(c) Is the equilibrium in (b) also a long run equilibrium? Why or why not? 

(d) Technical development changes the cost function of new mills to: 

                         C_j  = 5q_j  + 0.1q_j²  + 22.5 

Ninety new competitive mills enter the market. What becomes the new short-run equilibrium market price and output? Assume the old mills still operate and that the entry and exit of mills do not affect individual mill cost functions. 

(e) What will be the long run market equilibrium price and output? How many mills of what type - new or old - will survive?