3. (POINTS: 40) Consider an economy there are 4 consumers and they each have the following demand function q"(p) =82.5-p There are many identical firms that produce this good according to the cost function C(q) = 11q- -6q+99 to maximize profits. (a) (Points: 4) What is the aggregate demand function Q"(p) for this economy? Answer: (b) (Points: 8) Suppose in the short run, there are / = 89 firms. Solve for the short run partial equilibrium. Be sure to setup the firms profit maximization problem over quantity and also check if the firms will shutdown in the short run. Answer:(c) (Points: 8) Now let firms freely enter and exit. Solve for the long run partial equilibrium. Answer:(d) (Points: 10) Graph the aggregate demand curve, short run aggregate supply curve, and the long run aggregate supply curve on a qp -diagram. Be sure to label the graph clearly. Hint: Draw the aggregate supply and demand as price as a function of quantity. Answer:(e) (Points: 10) Compare the total, consumer, and producer surplus in the short run vs in the long run. Hint: Because demand and supply are linear in this setup, surplus will be calculated as areas of triangles. Answer: Short Run Long Run CS PS TS