An economic agent has the following utility function over income. U(I) = √I/100. (square root of...

An economic agent has the following utility function over income.

U(I) = √I/100. (square root of I over 100)

Suppose the agent has $3600 in income. The agent faces the following choice. The agent can keep his current level of income or accept the following gamble. With some probability, P, the agent either wins $1300, or with some probability, 1-P, the agent loses $1100. Determine if the following statement is either True or False. For the agent to take the gamble, the probability of winning has to be greater than 11/24 because when the probability exceeds this value the expected value of the gamble is greater than 0.

Solutions

Expert Solution

Let's note down some numbers systematically

1. Income

Current 3600

If win the bet 3600+1300 = 4900

If lose the bet 3600-1100 = 2500

Probabiliyt of win = p

Probability of losing = 1-p

2. Utiliity

Current = square root of (3600/100) = 6

If win the bet = square root of (4900/100) = 7

If lose the bet = square root of (2500/100) = 5

3. For this person to be indifferent

current utility = expected value of utility with bet

6 = p*7 + (1-p)*5

6 = 2p +5

p = 1/2 or 12/24

The statement is false. The probability has to be greater than 12/24 (not 11/24) for the agent to take teh bet.

Rahul Sunny answered 1 year ago

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