For problems 2, 3, and 4, assume demand for electricity in Alberta is p = 100 q and the marginal cost of production is c = 20. Assume that there are n = 10 identical rms producing electricity, and m = 1000 identical consumers. 2. First, consider the simple models of regulation. (a) Solve algebraically for the competitive and monopoly equilibria and show these on a graph, with labels qc and p,2 for the competitive equilibrium and labels gm and pm for the monopoly equilib rium. Calculate Consumer's surplus and prots for each case. (b) Under the Stigler theory of regulation, if the regulator chooses the quantity, what quantity, (13, and price p3 would you expect the regulator to choose? Explain. (c) How would your answer differ if the quantity produced were determined by a regulator under the capture theory? What di'erentiates the two theories? 3. Now suppose the government cares about votes, and that the number of votes it receives is V = H 6p, where p is the industry price, H is industry prots, and where [3 > 0. (a) Given that industry prots are H(p) = (p 20)(100 p) (why?), show the relationship between H and p on a graph. Identify the competitive and monopoly prices and prots, HC and jpC for competitive and Hm and pm for monopoly. (b) Draw a graph showing an iso-vote curve when [3 = 40. Show the regulated price p3 for this case. Hint: at what price, 103, is the slope of the prot curve equal to ? Plot the isovote curve and show H R, and 193 on your graph. (c) Now, suppose that ,6 varies. For what values of 6 will the government choose the competitive price? Hint: You need to calculate the slope of H' (p) at p = 20. Hint: if y = [5'0 + ,8193 + [32332, then (y/dz: = l + 262:1). (d) For what values of [3 would you expect the government to allow monopolization of the electricity market? Explain with reference to a graph. Hint: for what ,8 is 113 = pm