Question

1 True/false + explanations

1.8 An event is risky if you do not know the possible outcomes of the event.

1.9 Subjective probability is estimated with frequency.

1.10 Lottery A: you flip a coin and receive $10 if it’s heads and $0 if it’s tails. Lottery B: you flip a coin and receive $9 if it’s heads and $1 if it’s tails. Lottery A is more risky than lottery B.

1.11 When an individual has utility function U(W) =W, the expected value and expected utility of a risky event are the same.

1.12 Risk averse individuals never prefer a lottery over a sure bet.

1.13 In a lemons market with adverse selection, the equilibrium always involves only the lemons being bought and sold.

1.14 If a firm achieves efficiency in production when hiring they also necessarily achieve efficiency in risk bearing.

1.15 Only the total compensation paid to a worker determines the amount of moral hazard they may engage in.

1.16 A fixed-fee rental contract always acheives production efficiency.

Answer 1

1.8) False. Risky event is defined as the event in which probable outcomes are known.

1.9) False. Subjective probabilities are computed on the basis of personal biases of the individual. There is no formal method of computing.

1.10) True

The expected return of lottery A = 0.5 x 10 + 0.5 x 0 = 5

The expected return of lottery B = 0.5 x 9 + 0.5 x 1 = 5

As it is clearly seen that the expected return is same in both the cases. Risk-averse would prefer to minimise the losses. Thus, in the event getting a tail on flipping a coin, the payoff of 0 and payoff of 1 in lottery A and B respectively. Therefore, can conclude that the loss is minimum in the case of lottery B.

Hence, lottery B is less risky than lottery A.

1.11) U(W) = W is the utility function of the risk-neutral individual. And it is a linear function. For such an individual the utility of expected value of events of a gamble is equal to the expectation of the utilities of events of a gamble.

False, because of the expected value of a gamble is not equal to the utility of risky event.

1.12) True. Risk-averse individuals are the ones who prefer sure event over a fair gamble.

1.13) True. Adverse selection is explained as, a scenario in which the buyer has no idea whether he is buying lemons or peaches. Thus, he willing to pay an average of willingness to pay of peaches and lemons. And if such average turns out lower than the cost to provide peaches (as peaches good quality product and thus cost more than the lemons (bad quality)) to sellers. Therefore, the seller doesn't sell peaches. Thus, only lemons being exchanged in the economy as the average price willing to pay is more than the cost of providing lemons.

1.14) True. The efficiency is achieved in production by properly hiring via screening of employees. As the employer is unaware of what kind of employee he is hiring, whether low productive or high productive. So, if an employer is able to distinguish between the two or somehow manage to hire highly productive employees. Then in such a scenario, the employee will able to maximise its production and this is possible only if efficiency is risk bearing is achieved.

1.15) False. The moral hazard on the part of an employee depends not only the total remuneration. But also mode of remuneration. As in the case of the fixed rental contract, the moral hazard is lower than the sharecropping contract. As in the fixed rent risk is solely born by the employee. Thus, it lowers the chances of undersupplying effort to maximise the return. Whereas, in the sharecropping, the return and losses are shared between the employee and employer. Thus, comparatively higher chance of moral hazard.

1.16) False. The case of limited liability where tiller does not have enough wealth and his yield is quite uncertain. Then in such a scenario, there is no certainty that fixed rent will be paid. Thus, in such a scenario possible that employee does something else than what is desired, that is, investing in risky ventures. And will not necessarily maximise production and efficiency.