Problem 1 (Bertrand ). 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? = 100 - P per day (in the first half of April). Assume first that both H & R Block and Bill's have unlimited capacity to complete tax returns . Also assume both firms 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 profits ? 2. What is the Nash Equilibrium for this duopoly game ? What is profit for the two firms? 3. Show that there is no profitable deviation from the NE you found above (i.e., verify that both firms are playing a best response ). 4. Now assume that H & R Block is a bigger outfit and can complete 100 tax returns a day maximum, while Bill's has fewer employes and can complete 40