1.) Please consider the following market demand curve: P=20-Q Let's suppose that all firms in the market have the cost function c(q) = 4+4q. Furthermore, all firms in the market engage in Cournot quantity competition. (a) What is the slope of the market demand curve (12)? (b) Write down the average cost function for firms in this market and make a plot of it. (c) Differentiate the average cost function so as to find an expression for the slope of average cost. (d) At what quantity level is the slope of average cost equal to the slope of the demand curve? Let's call this quantity R. What is level of average cost at this quantity? Let's call this ACER (e) How large would the market quantity (Q) need to be in order to generate a market price equal to ACER? (f) If each firm in the market produced QR, then how many firms would there be in the market? Let's call this number, niR. (g) Suppose you were one of these nR firms in the market. What would your residual demand curve be? Carefully plot this residual demand curve along with your average cost and marginal cost functions. Label the intercepts of the residual demand curve and your optimal supply level. (h) What is the socially optimal number of firms in the market? How much does the level of social surplus drop when the socially optimal number of firms rises to the number of firms under monopolistic competition?