4. This question will walk you through the process of finding the long run equilibrium of the market. Until further notice, suppose fixed costs from question 3 are FC = 3. (a) Recall that in the long run, firms will enter the market when profit a is positive and exit when a is negative. How much profit will each firm earn when there are 400 firms in the market? Will more firms want to enter, or will incumbent firms want to exit? What condition characterizes a long run equilibrium? (b) Show that the long run equilibrium happens when price is po = 2V 3. (c) Using your answer to 2(f), show that this price would be attained if the number of firms were about 797.43. (d) There's no such thing as a fractional number of firms. How much profit would each firm earn if there were 797 firms in the market? What if there were 798 firms? What is the actual long run equilibrium number of firms, and why? (e) Recall in class that we found that the long run equilibrium occurs at the price where average total cost ATC is minimized: the market is producing output in the most efficient way possible. Let's check that condition here. i. How much output will each firm produce in the long run equilibrium? 3 ii. Recall that ATC is total cost divided by quantity. Find an expression for ATC as it depends on q. iii. Find the quantity of output at which ATC is minimized. To do this, take the first derivative of ATC with respect to q, set it equal to zero, and solve. iv. Does your answer to 4(e)i align with 4(e)iii? Explain briefly.2. This question will walk you through the process of solving for the short run competitive equilibrium of a. market. Throughout this question, each consumer's individual demand function for the good is given by (Mp) = 3 2;), where p is the price of the good. Moreover, each rm's supply function is given by s; (p) = gp