Suppose a monopoly can produce any level of output it wishes at a constant marginal (and average) cost of $5 per unit. Assume the monopoly sells its goods in two different markets separated by some distance. The demand curve in the rst market (market 1) is given by: Q1 =55-P1 and the demand curve in the second market (market 2) is given by Q2 = 70 2P2 Suppose the monopolist can maintain the separation between the two markets. Enter the prot maximizing price and quantity for each market in the table. Market Price Quantity Market 1 Q = 25 PI = $30 Market 2 Q; = 30 P; = $20 The total prots across both markets are 3* = $1,075 V . Suppose it costs demanders only $5 to transport goods between the two markets. In order to prevent arbitrage, the monopolist sets the constraint that P1 = P2 + 5. In this case, the monopolist will choose to charge P; = $21.66 V and P: = $26.66 V . This would yield a total profit of V across the two markets. (Hint: Use the Lagrangian method, where the monopolist must choose P1 and P2 to maximize prots subject to the constraint that P1 = P2 + 5.) Suppose transportation costs are now zero and that the rm was forced to follow a single-price policy P1 = P2 = P. In this case, the monopolist will choose to charge a price P* = V . The monopolist will choose to produce Q: = V in market 1, and Q: = V in market 2. This would yield a total profit of V across the two markets. Now assume the two different markets, 1 and 2, are just two individual consumers. Suppose the firm could adopt a linear two-part tariff under which marginal prices charged to the two consumers must be equal but their lump-sum entry fees might vary. That is, the monopolist can adopt the two- part tariff: T(Q1) = a1 + le T(Q2) = 012 + sz The monopolist can maximize prots by setting the marginal price (m) equal to m = s , setting the entry fee for market 1 as on = $ , and setting the entry fee for market 2 as $