There are two movie theaters in the town of Harkinsville: Modern Multiplex, which shows first-run movies, and Sticky Shoe, which shows movies that have been out for a while at a cheaper price. The demand for movies at Modern Multiplex is given by QMM 5 14 2 PMM 1 PSS, while the demand for movies at Sticky Shoe is QSS 5 8 2 2PSS PMM, where prices are in dollars and quantities are measured in hundreds of moviegoers. Modern Multiplex has a per-customer cost of $4, while Sticky Shoe has a percustomer cost of only $2. (a) From the demand equations alone, what indicates whether Mod- ern Multiplex and Sticky Shoe offer services that are substitutes or complements?
(b) Write the profit function for each theater in terms of Pss and PMM Find each theater's best-response rule.
(c) Find the Nash equilibrium price, quantity, and profit for each theater.
(d) What would each theater's price, quantity, and profit be if the two decided to collude to maximize joint profits in this market? Why isn't the collusive outcome a Nash equilibrium?

Imagine us is a startup that offers high definition 3d prenatal ultrasounds for high-end customers. the service process includes four activities that are conducted in the sequence described below. (the time required for each activity is shown in parentheses): activity 1: welcome a patient and explain the procedure. (20 minutes)activity 2: prep the patient (e.g., show them to the room, apply ultrasound gel). (17 minutes) (*your id number represents the amount of time needed to complete this task)activity 3: take images. (5 minutes)activity 4: discuss diagnostic with patient. (20 minutes)at each location there are employees (servers) s1, s2, and s3. the assignment of tasks to servers is the following: s1 does activities 1 and 2.s2 does activity 3.s3 does activity 4.a. what is the capacity of this process (in customers per hour)? b. suppose 3 patients arrive every hour on average. ignoring any “start of day” or “end of day” effects, what are the utilizations of all three servers (%)? c. suppose each activity can be done by any server and any server can do any set of activities. however, each activity is done by only one server. for example, a possible assignment includes: s1 does activity 1, s2 does activity 2, and s3 does activities 3 and 4. of course, the original assignment of servers to activities is also feasible. what is the maximum capacity of the process (in customers per hour)? d. now consider the capacity measures in (c) and (a), what is the percentage change? why can you improve capacity without using additional resources? (there is no free lunch, right? )note: for all hw assignments, show your process of getting the results. only providing the final answers is not acceptable and will get 0%. if necessary, use a separate sheet of paper to show your work.