FIN 321: Managerial Economics
Practice Final
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I.
Problems (Please show all work and remember to label all graphs!)
1) Competition: Pure; Monopolistic, Monopoly
You are the manager of San Diego Computers, a manufacturer of computers that meet
the specifications required by the city. Over 90% of your clientele consists of college
students. San Diego computers is not the only firm that builds computers to meet this
city’s specifications; indeed, it competes with many manufacturers. As each firm
produces a homogenous product, each firm has no ability to impact price. The weekly
cost of producing computers is TC= C(Q)=2+(1/2)*Q2 and the demand for your
product is given by Q(P)=5-0.5*P. Other firms in the industry sell at market price
which is $1.00.
a) What price and quantity should you produce to maximize your firm’s profits?
b) What profits do you expect to earn ? (Please use graphs to support your answer.)
2) Oligopoly and Game Theory, Pricing Topics
Assume that two companies (A and B) are duopolists who produce identical products.
Demand for the products is given by the following linear demand function:
p = 200 − QA − QB
where QA and QB are the quantities sold by the respective firms and p is the selling
price. The total cost functions for the two companies are:
TCA = 1500 + 55QA + QA2
TCB = 1200 + 20QB + QB2
Assume that the firms act independently as in the Cournot model (i.e., each firm
assumes that the other firm’s output will not change). Based upon this information,
a. Determine the long-run equilibrium output and selling price for each firm.
b. Determine Firm A, Firm B, and total industry profits at the equilibrium
solution found in (a).
3) Please use the given normal form matrix below to answer the following
questions.
a. If they exist, please find the dominant strategy for player 1 and player 2.
b. Please find any Nash equilibria that exists.
II.
Essays
4) Please read the article titled “Meet the generation of robots for
manufacturing” and answer the following questions.
a. The article mentions, “Greater use of robots means fewer people are
needed on factory floors”. Assuming that the implication of this statement
is a reduction in cost, please use graphs to demonstrate the validity of this
statement.
b. According to the article, how have robots changed the face of
manufacturing? Please explain (Please cite facts/information/figures from
the article in your answer.)
Meet the New Generation of Robots for Manufacturing
They are nimbler, lighter and work better with humans. They might
even help bring manufacturing back to the U.S.
ABB and others have introduced robots designed to assemble small parts and detect whether products
are being put together properly.PHOTO: ABB ROBOTICS
By
JAMES R. HAGERTY
June 2, 2015 11:08 p.m. ET
A new generation of robots is on the way—smarter, more mobile, more collaborative and more
adaptable. They promise to bring major changes to the factory floor, as well as potentially to the
global competitive landscape.
Robots deployed in manufacturing today tend to be large, dangerous to anyone who strays too
close to their whirling arms, and limited to one task, like welding, painting or hoisting heavy
parts.
The latest models entering factories and being developed in labs are a different breed. They can
work alongside humans without endangering them and help assemble all sorts of objects, as large
as aircraft engines and as small and delicate as smartphones. Soon, some should be easy enough
to program and deploy that they no longer will need expert overseers.
That will change not only the way an increasing number of products are made. It could also
mean an upheaval in the competition between companies and nations. As robots become less
costly and more accessible, they should help smaller manufacturers go toe to toe with giants. By
reducing labor costs, they also may allow the U.S. and other high-wage countries to get back into
some of the processes that have been ceded to China, Mexico and other countries with vast
armies of lower-paid workers.
Some of the latest robots are designed specifically for the tricky job of assembling consumerelectronics items, now mostly done by hand in Asia. At least one company promises its robots
eventually will be sewing garments in the U.S., taking over one of the ultimate sweatshop tasks.
ENLARGE
“Robots are going to change the economic calculus for manufacturing,” says Hal Sirkin, a
Chicago-based senior partner of Boston Consulting Group. “People will spend less time chasing
low-cost labor.”
The changing face
Today, industrial robots are most common in auto plants—which have long been the biggest
users of robot technology—and they do jobs that don’t take much delicacy: heavy lifting,
welding, applying glue and painting. People still do most of the final assembly of cars, especially
when it involves small parts or wiring that needs to be guided into place.
Now robots are taking on some jobs that require more agility. At a Renault SA plant in Cleon,
France, robots made by Universal Robots AS of Denmark drive screws into engines, especially
those that go into places people find hard to get at. The robots employ a reach of more than 50
inches and six rotating joints to do the work. They also verify that parts are properly fastened and
check to make sure the correct part is being used.
The Renault effort demonstrates a couple of trends that are drastically changing how robots are
made. For one, they’re getting much lighter. The Renault units weigh only about 64 pounds, so
“we can easily remove them and reinstall them in another place,” says Dominique Graille, a
manager at Renault, which is using 15 robots from Universal now and plans to double that by
year-end.
Researchers hope robots will become so easy to set up and move around that they can reduce the
need for companies to make heavy investments in tools and structures that are bolted to the floor.
That would allow manufacturers to make shorter runs of niche or custom products without
having to spend lots of time and money reconfiguring factories. “We’re getting away from the
[structures and machinery] that can only be used for one thing on the factory floor and [instead]
using robots that can be easily repurposed,” saysHenrik Christensen, director of robotics at
Georgia Institute of Technology.
Built to collaborate
Another big trend at work: The Renault robots are “collaborative,” designed to work in proximity
to people. Older types of factory robots swing their steel arms with such force that they can
bludgeon anyone who strays too close. Using sonar, cameras or other technologies, collaborative
robots can sense where people are and slow down or stop to avoid hurting them.
At a Renault car plant, robots drive screws into engines—a sign of their progress in handling small
parts. PHOTO:RENAULT
These types of innovations aren’t limited to the auto industry. ABB Ltd of Switzerland, Bostonbased Rethink Robotics Inc. and others have recently introduced robots designed to help
assemble consumer-electronics items, among other products. These new robots are designed to
work close to people and handle small parts, rather than doing heavy lifting or welding or
painting.
Another aspect of doing more delicate work is the robots’ ability to sense whether parts are being
assembled correctly, something that wasn’t possible with previous generations of clumsier
robots. At a trade show in Germany in April, Kuka Roboter GmbH showed one of its robots
installing a tube inside a dishwasher. Kuka’s robot uses “force torque” sensors to judge whether a
part is in the right place. “The robot is able to wiggle it into place like a human would,” says
Dominik Bösl, Kuka’s innovation manager.
This delicacy is allowing robotics to spread into a wider variety of industries. At a plant in
Wichita, Kan., due to open in November, JCB Laboratories will use robots to pick up syringes,
fill them with medications and snap on caps, among other tasks. The production line, designed
by ESS Technologies Inc. of Blacksburg, Va., involves three robots from
Japan’s Fanuc Corp. The robots will be five to six times faster than the people who now do the
work, says Brian Williamson, president of JCB, owned by Fagron NV of Rotterdam.
Using robots also will reduce the risk of human error or contamination, he says: “They’re very
precise, they don’t get tired, and they only do things they’re told to do.” The robots will
eliminate two jobs, Mr. Williamson says, but the workers can be redeployed to other tasks.
Fender Musical Instruments Corp. uses Fanuc robots to apply polyester and urethane coatings to
guitars at a plant in Corona, Calif. A spokeswoman says the robots apply coatings faster and
more consistently than people could and allow people at the plant to “focus on areas that are
more crucial to the overall look, feel and sound” of the instruments. Those tasks include
designing, buffing and assembly.
Some in the robotics industry see machines moving into even more industries. Per Vegard
Nerseth, ABB’s global robotics chief, expects increasing demand for robots from makers of
watches, razors, toothbrushes and toys. He also thinks robots could help make muffins in local
bakeries, slice vegetables and meat, and wash windows.
An Atlanta startup, SoftWear Automation Inc., which last year attracted $3 million of venture
capital, has developed robots that the firm says can sew garments. The company hopes the robots
will allow some clothing production to move back to the U.S. from low-wage nations.
Robots everywhere?
But some caveats are in order for this rosy picture.
Though the U.S., Europe and other high-wage areas should benefit from these trends, they won’t
have the field to themselves. China also is investing heavily in robots as its wages soar and its
population ages. For now, China has just 30 robots per 10,000 manufacturing employees, trailing
South Korea (437), Japan (323), Germany (282) and the U.S. (152), according to the
International Federation of Robotics, a trade group. But the federation projects that the total
number of industrial robots being used in China will exceed that of North America next year.
IHS Technology, a research firm, projects that robot sales in China will surge to about 211,000
units in 2019 from 55,000 last year.
Competition among manufacturing nations isn’t only about robots, of course. Other factors that
determine where things are made include taxes, regulation, availability of skilled workers and
suppliers, energy costs and willingness to make long-term investments. At a minimum, though,
investing in robots and using them effectively will be a price of staying in the global
manufacturing game, says Mr. Sirkin of Boston Consulting Group. So even nations that rely on
low-cost labor today will be forced to explore robotics or risk losing even more jobs.
Even if robots allow manufacturing to relocate, the impact on the workforce itself will be mixed.
Greater use of robots means fewer people are needed on factory floors; those doing routine tasks
requiring little education are most vulnerable. Yet even highly automated factories create or
sustain jobs in design, engineering, machine maintenance and repair, marketing, logistics and
other services.
What’s more, robots will have to make further strides in the years ahead to allow a major shift of
electronics and other assembly work to migrate from Asia to the U.S. and Europe.
Speed restrictions
One problem is that today’s collaborative robots frequently have to slow down or stop whenever
people veer into their paths, disrupting production. Take the case of Baxter, a friendly looking
two-armed collaborative robot from Rethink.
The company introduced Baxter with huge fanfare three years ago. Yet Rethink has sold fewer
than 1,000 of the robot, which is mainly used for such simple tasks as moving materials, picking
up parts, and packing or unpacking boxes. In part, that’s because the robot’s speed is restricted
by safety considerations.
Rodney Brooks, chairman of Rethink and a renowned robot developer, says Baxter has been a
“tremendous learning experience” and has helped manufacturers and others see the potential of
collaborative robots. In March, Rethink unveiled a new robot, Sawyer, which the company says
will be up to twice as fast as Baxter, depending on the application.
Another hurdle is creating robots that can come closer to matching people’s fine motor skills in
manipulating materials and small parts. For all the advances in recent years, robots have trouble
dealing with soft or floppy things, such as cloth or bundles of electrical wire.
“Anywhere you manipulate flexible materials, that’s a very challenging task for robots,” says
Julie Shah, an assistant professor at the Massachusetts Institute of Technology. People use
“tactile feedback,” Dr. Shah says. If something doesn’t feel quite right, they adjust. Robotic
science is only starting to deal with that challenge.
Mr. Hagerty is a news editor in The Wall Street Journal’s Pi sburgh bureau.
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