Problem 1. There are two companies who offer tax return services in College Springs: H & R Block and Bill's Financial Service. Marginal cost for doing a tax return is c = $10 and demand in College Springs for tax returns is Q = 100 P per day (in the rst half of April). Assume rst that both H 85 R Block and Bill's have unlimited capacity to complete tax returns. Also assume both rms are choosing price simultaneously. (In other words, this a Bertrand game with homogeneous goods.) 1. Suppose (for this part only) Bill was a monopolist, what price would he set? What would be Bill's prots? (Hint: It is identical to solve this problem by maximizing price or maximizing quantity) 2. What is the Nash Equilibrium for this duopoly game? What is prot for the two rms? 3. Show that there is no protable deviation from the NE you found above (i.e., verify that both rms are playing a best response). (Hint: Consider a rm's possible deviations and show that they are not protable). 4. Now assume that H & R Block is a bigger outt and can complete 100 tax returns a day maximum, while Bill's has fewer employes and can complete 40 tax returns per day maximum. Is the Nash equilibrium you found in 1 still a Nash Equilibrium? If not, show a protable deviation. If so, show there is no protable deviation. 5. Now suppose there is a shortage of trained tax accountants because of the advent of Turbo tax. This has caused H 85 R to only be able to complete 30 tax returns per day maximum and Bill's to only be able to complete 20 tax returns per day maximum. Is the Nash equilibrium you found in 1 still a Nash Equilibrium? If not, show a protable deviation. If so, show there is no protable deviation. . Now suppose that the capacity constraints are as in the previous part and each rm sets a. price of $50. Is this a. Nash Equilibrium? If not, show a protable deviation. If so, show there is no protable deviation