Consider the following information (note that Q represents the market quantity and q represents the firm quantity): Demand for pizza: Q = 750 - 25P TC = q2/2 + 50 MC = q a. Find the long run equilibrium P & q for this firm (Hint: find the min of ATC by setting MC = ATC) b. Find the market equilibrium Q. c. How many firms are in this industry? d. Now suppose that demand doubles to Q = 1500 - 50P. Calculate the short run equilibrium. i. Find the equation for the firm's short run supply curve (set P=MC for all P>AVC) (use the format q=f(P).) ii. Find the market S by taking the number of firms found in c and multiply this by the firm's SR supply curve. iii. Set the market S equal to the market D and solve for the SR market equilibrium. iv. Set P=MC to find how much each firm produces (q). v. Calculate the profit for each firm. e. In the long run, price falls back to the level found in part a (assuming costs have not changed). What is the new market equilibrium Q? How many firms are in the industry?