Jack and Annie are the only sellers of otters in a three-state area. The inverse market demand for otters is given by P = 100 - 0.5Q, where Q = the total quantity offered for sale in the marketplace. Specifically,
Q = qJ + qA, where qJ is the amount of otters offered for sale by Jack and q A is the amount offered for sale by Annie. Both Jack and Annie can produce otters at a constant marginal and average total cost of $20.
a. Graph the market demand curve. What would be the prevailing price and quantity if this industry were controlled by a monopolist?
b. Suppose that Jack, an excellent mathematician (but perhaps not quite as brilliant an economist), solves part (a). Being a very egalitarian sort, Jack announces that he will bring half of the monopoly quantity to market each day.
i. The market inverse demand for otters is given by P = 100 - 0.5(qJ + qA). Plug in Jack's announced output for q A to solve for the residual demand curve faced by Annie.
ii. Solve for, and graph, the residual marginal revenue curve faced by Annie.
iii. Given Annie's otter production cost of $20, how many units should Annie bring to market to maximize her profit?
c. Given your answers to (b), what will the industry quantity and final price of otters be? How much profit will Annie earn? Jack?
d. Suppose that Jack observes Annie's output from part (b), and decides to change his own.
i. Solve for, and graph, the residual demand curve faced by Jack.
ii. Solve for, and graph, the residual marginal revenue curve faced by Jack.
iii. Given Jack's otter production cost of $20, how many units should he bring to market to maximize his profit? iv. What will the industry quantity and final price of otters be? How much profit will Annie earn? Jack?
e. Is the outcome you found in part (d) an equilibrium outcome? How do you know?