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Show Your Work for Quantitative Questions

Show your work for quantitative questions. You can create diagrams with any means you like (with Excel, by hand, etc.), as long as they are clear and contain the required material.

Show your work for quantitative questions. You can create diagrams with any means you like (with Excel, by hand, etc.), as long as they are clear and contain the required material. Full credit is given for answers that use correct economic terminology, where appropriate.

Full credit is given for answers that use correct economic terminology, where appropriate. For the following questions, show your work for all answers.

1

You work for a graphics design company and have the opportunity to submit a design proposal for a news outlet’s logo re-design effort. You have a competitive advantage in designing logos using serif fonts, which are trending right now. The incumbent design company, who is your major competitor for this contract, has a competitive advantage in designing logos with sans serif fonts. The news outlet is accepting proposals and may decide the winner based on those submissions. You and your competitor know the following facts:

• If you submit a logo using a serif font and they also use a serif font, you will be offered the design contract and expect a profit of $10k from redesigning the logo (and submitting the bid). Your competitor will receive a net benefit from its team gaining more design experience, worth $1k.
• If you submit a logo using sans serif font and they also use a sans serif font, they will win the contract and expect a profit of $15k. You will take home a net benefit of $1k from the design experience.
  
  
• If you submit a logo using sans serif font and your competitor uses a serif font, your equally poor designs will result in neither firm being offered a contract. You both will experience a net cost from reputational impacts. Your cost will be $3k, and your competitor’s will be $5k.
  
  
• If you submit a logo using a serif font and your competitor uses a sans serif font, your equally good submissions will result in a tie. You both come out of the competition empty-handed with a net benefit of participating of $0, waiting for how the news outlet will proceed with any future evaluation of your work.

1. Represent this competition visually using the correct tool(s) from economic game theory.
2. What is the Nash Equilibrium/Equilibria set(s) of best responses in this “game”? Show how you arrived at this answer by highlighting or circling each firm’s payouts from its best responses and providing a brief explanation.
3. Will a Nash Equilibrium be realized if you and your competitor do not communicate before submitting your proposals? Why or why not?
4. Will a Nash Equilibrium be realized if you and your competitor communicate before submitting your proposals? Why or why not?

2

You work for a biotech company that is considering new R&D for a substance that would simultaneously consume ocean plastic, absorb greenhouse gases, and increase ocean albedo. You’re confident in your ability to develop a reasonably successful product, but you are not sure how well you can safeguard your intellectual property (IP) from rival biotech firms. You are risk-neutral. You face three alternative choices:

• Invest in the R&D and apply for a patent. In this case, you expect to spend $10m on R&D and $5m on patent expenses but obtain $60m in revenue. (Note that you will have to commit to patent application when deciding on R&D.)
  
  
• Invest in R&D and not apply for a patent. In this case, you expect to spend $10m on R&D and receive $60m in revenue. However, there is a 70% chance that some aspects of your IP will “spill over” to rival biotech companies, and you will not be able to maintain a monopoly position as the sole producer of this wonder substance. Other firms may enter, and you will lose market share resulting in a revenue loss given by L.
• Don’t invest in R&D. Incur no research costs and receive no revenue from such an endeavor.

1. Represent the key aspects of the decision you face with an appropriate decision tree.
2. If L = $5m, what alternative will you chose?
3. If L = $10m, what alternative will you chose?
4. Under what values of L would you prefer to patent your technology than operate without a patent? (Round to two decimal places.)
5. Now assume that conducting R&D reveals whether your IP will spill over to other firms. Your R&D cost is still $10m. Your understanding of the probability of an IP spill-over as of now is the same (there is a 70% chance of spill-over occurring), but R&D will reveal whether or not it will occur with certainty.

• If, after R&D, your IP is safe, you can expect the same $60m in revenue as before.
• If, after R&D, you expect your IP to spill over to other firms and you do not patent your technology, you expect to lose $10m in revenue compared to the case of your IP being safe. If you patent your tech, your patent cost will be $5m and your revenue will be $60m.

1. Represent the key aspects of the decision you face with an appropriate decision tree.
2. Will you invest in R&D and patent right away, invest in R&D and consider patenting after conducting research, or chose not to invest in R&D? What calculations led you to this decision?

• Discuss how this scenario relates to the “Real Options” framework for investing under uncertainty by identifying (1) the option in this scenario and (2) how your choice of whether and when to exercise that option allows you to make the best decision.

3

You produce children’s toys and are shopping for product liability insurance. You have conducted very thorough engineering and lab tests of your toys and have calculated hazard rates from toy breakage, incidents from how children interact with them, etc. You have determined that there is a 0.02% chance of a “major” incident occurring with one of your toys in the next year, defined as an incident resulting in $1m in damages.

1. Based on these facts, what is the premium you expect to pay for actuarily fair insurance?
2. After shopping around, you are offered a few premiums that are higher than you expect. Insurers define “major” events the same way but disagree on the probability of one of your toys causing a major event in the next year. (They claim this probability is higher.)

1. Why might prospective insurers assume a higher probability of a major event?
2. What can you do to try to resolve the difference in understanding of this
   probability? List and describe two.
3. If instead prospective insurers cite the same definition of a “major” event and the
   probability of it occurring in the next year, why might they be asking for premiums higher than the actuarily fair rate (aside from market power)? What is a solution to this issue?

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