3. Problem (10 points) The market for tomato sauce in SouthCounty during the fall season is represented by the demand function Q(P) = 90 - P. The market is served by two identical firms, A and B, which compete a la Bertrand and share the same production technology, requiring 10 pounds of raw tomatoes for each liter of sauce: C(qi) = 10qi for i = A, B. 1. Show that in equilibrium each firm produces 40 liters of sauce. Find the equilibrium price and profits. (1 point) 2. Is the outcome efficient? (1 point) During summer, tourists from NorthCounty move to SouthCounty and demand for the summer months increases to Q(P) = 250 - P. However, each firm has a capacity of 80 liters of sauce only. 3. Show that the equilibrium price is now 90. Find quantities and profits for the summer months. (1 point) 4. Should firms invest in extra capacity to cover all demand? Discuss. (1 point) 5. How would results at question 3 change if firms were instead competing a la Cournot? Discuss. (2 points) During winter, firm B experiences a parasite infestation at its fields, which makes tomatoes smaller. As a result, firm B now needs 30 pounds of raw tomatoes to produce one liter of sauce. Demand is back to its "normal" level: Q(P) = 90 - P