Question

An agent chooses high or low effort on a project. If the agent exert's high effort, the project will succeed with prob. 0.96, but under low effort the prob. of success is only 0.74. The ex ante cost of high effort is $500 and the cost of low effort is $0. The agent will be paid $Z only if the project succeeds. What is the minimum Z necessary to persuade the agent to choose high effort?

Group of answer choices

$2,133

$2,273

$2,445

$2,544

An investor has wealth of $500 and a project that requires a $500 investment. If the investor choose Safe, the project yields revenue $580, but if the investor chooses Risky, the project yields revenue $660 with prob. 0.75 and revenue $0 otherwise. If the investor uses her own wealth, her final (expected) payoff from choosing Safe is ____ and from Risky it is ____.

Group of answer choices

$565; $522

$565; $495

$580; $522

$580; $495

Answer 1

1. Given,

Probability of high effort = 0.96

Probability of low effort = 0.74

Cost of high effort = $500

Cost of low effort = $0

Amount to paid when project succeeds = $Z

Now,

Expected amount you get with high effort = Probability of high effort * Amount received on success

So, Expected amount under high effort = 0.96 * Z = $ 0.96Z

Similarly, Expected amount under low effort = 0.74 * Z = $ 0.74Z

Extra amount received under high effort compared to low effort = $ (0.96Z - 0.74Z) = $ 0.22Z

We know extra cost of high effort compared to low effort = $500 - $0 = $500

For Minimum Z to choose high effort :- The extra amount received under high effort must equal the extra cost associated with it.

So, $ 0.22*Z = $500

Z = $ 500/0.22 = $2272.72 = $2273

Hence, Minimum Z necessary to persuade the agent to choose high effort is $2273

So, Option B) $2273 is correct

2. Under Safe option the project yields = $580

Under Risky option the project yields = $660 with probability 0.75 and $0 otherwise

As, Safe option is a associated with a definite probability = 1

Now Formula of expected payoff :-

So, Expected payoff of safe option = (1 * $580 ) + (0 * 0) = $580

Expected payoff of risky option = ( 0.75 * $660 ) + ( 0.25 * $0) = 0.75 * $660 = $495

So, Option D) $580 ; $495 is correct