(This question will not be graded)

You are considering getting health insurance. The insurance company knows there are two types of individuals seeking this type of insurance, the healthy and the unhealthy, each group accounting for one half of the population. The insurance company offers a uniform premium and thus wants to avoid insuring the unhealthy people because they give the company an expected disutility of 15. Striking a deal with a healthy individual gives them a utility of 10. Not offering the insurance leaves them with zero utility.

A healthy individual gets a utility of 10 from insurance (no insurance gives a utility of 0). An unhealthy individual gets a utility of 20 from insurance (no insurance gives a utility of 0).

In order to signal to the insurance company that you are healthy, you can choose to provide proof of a check-up that states you are in good condition. Providing this proof implies a disutility of 5 for the healthy type and a disutility of 25 for the unhealthy type (this proof is much more difficult to achieve for the unhealthy type, who would need to find a doctor who could be bribed).

(This question will not be graded)

Natflix is a streaming platform that is

looking for new consumers. There are two types of potential consumers for

Natflix: occasional watchers (O) and binge watchers (B), which are both equally

likely. It is known that Natflix’s profits are given by

The utility of each consumer is given by a_i.m

-

The reservation utility of both consumers is 2.

Select the correct option(s):

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Goldplay have announced a world tour and Theresa bought a ticket fast enough before they all got sold out. However, Theresa won't be able to attend the concert because she will go abroad to visit her cousin and so she's trying to sell the ticket in an auction website. Theresa just wants to get the highest revenue possible from the sale of the ticket.

She knows there are two types of people who often visit that website: fans of pop music, corresponding to 30% of the website's visitors, and fans of techno music, corresponding to the remaining 70%. Pop music fans would be willing to pay 100€ to get a ticket for the concert, but techno music fans don't enjoy Goldplay that much and so would only be willing to pay 40€ for a ticket. Both types of visitors have a reservation utility of 10 and are risk neutral. 

Select the correct option(s):

(This question will not be graded)

Grace just appointed Brianna as the CEO of her company, Say Grace. Brianna can spend her time slacking off ( ), which gives her no disutility, or working hard ( ), which gives her a disutility of . Brianna's utility is given by , where is a disutility term that depends on her choice between slacking off and working hard. Assume that Brianna has a reservation utility of 0.

Moreover, Grace only cares about the profits of Say Grace, which can be 740 in case of a good quarter or 500 in case of a bad quarter. The probability of each outcome depends on Brianna's choice of how to spend her time and is given by:

Select the correct option(s):

The municipality of Lisbon wants to sell a restored building and is planning an auction.

There are two buyers and each of them may value the building at 16 (million Euros) or at 9 (million Euros). Even though each buyer is aware of her type, the municipality only knows that each buyer may have a high valuation with probability 3/4 (and a low valuation with probability 1/4). The surplus for each type of buyer will be equal to the difference between her valuation and the price she ends up paying; and zero otherwise. Each type's reservation utility is 0. The municipality cares only about maximizing expected revenue.

Imagine the following signaling game:

The productivity of a given worker is drawn by nature. It can be High or Low, with p=0.5 for each. The worker, upon observing her productivity level, can decide whether to get a college degree or not. Finally, there is a firm who does not observe the workers type, but only her level of education. This firm must decide whether to hire (or not) the worker.

If the firm does not hire the worker, both get a payoff of 0. If the firm hires the worker, its payoff is given by the difference between her productivity and the wage that is paid. Regarding the employee, her payoff is given by the difference between the wage she receives and the education costs.

Assume that, for a high productivity worker, the productivity is 4 and the cost of a college degree is 2. For a low productivity worker, the productivity is 2, and the cost of a college degree is 4 (bear in mind that both types have an educational cost of 0 when they decide to not pursue a degree). Finally, assume that the firm pays a wage of 1 to non-educated workers, and a wage of w to educated ones.

Which of the following statements is/are TRUE:

The principal is risk-neutral and the agent is risk-averse. The two have the following utility functions:

B(x,w)=x - w    U(w,e)=w^1/4 - e

Where x represents the outcome, w the salary paid to the agent, and e is effort. The reservation utility of the agent is 1.

Pablo

is a legitimate and hardworking entrepreneur from Medellín, Colombia.

He produces and sells fluor for a living. Unfortunately, a producer from

Cali decided to expand into Pablo's city. As a consequence, he is considering hiring someone to get rid of the competition (in a totally friendly way, of course, since Pablo is an upstanding citizen).

Let the (non-negative) variables q and p

represent the quality of the service

(which is linked to the likelihood of eliminating the competition) and the respective payment, while

Which of the following statements is/are TRUE: