## SECTION B

Answer the following questions in about 400 words each. Each question carries 12 marks.

**6. (A.) Given the Von Neumann-Morgenstern utility function of an individual, U (W) =W Â½, where W stands for the amount of money. Comment upon the attitude towards the risk of such an individual with the help of a diagram.**

The Von Neumann-Morgenstern utility function is a mathematical model used to represent an individual’s preferences over different outcomes of a decision-making problem. In this case, the utility function is given as U(W) = W^(1/2), where W stands for the amount of money.

The shape of the utility function can help us understand an individual’s attitude towards risk. In general, an individual with a risk-averse attitude will prefer a sure outcome with a lower expected value to a risky outcome with a higher expected value. An individual with a risk-seeking attitude will prefer a risky outcome with a higher expected value to a sure outcome with a lower expected value.

In this case, the utility function is a concave function, which means that it decreases at an increasing rate as W increases. This indicates that the individual is risk-averse, as they prefer a lower level of wealth with a higher level of certainty to a higher level of wealth with a lower level of certainty.

[Make a Diagram here, If you wanna make otherwise leave it]

As the diagram shows, the individual is willing to trade off some potential wealth in exchange for a higher level of certainty. For example, they might prefer a sure outcome of W = 100 to a risky outcome with an expected value of W = 150 but a chance of earning nothing.

Overall, the shape of the Von Neumann-Morgenstern utility function can help us understand an individual’s attitude towards risk and their preferences over different outcomes. In this case, the concave shape of the utility function indicates that the individual is risk-averse.

**6. (B.) Now suppose this individual possesses a building worth â‚¹1600. If the building catches fire, its value falls to â‚¹ 400. Let the probability of the building catching fire be Â¼. On the basis of the given information, find out whether the individual would be willing to pay a risk premium of â‚¹ 76 to the insurance company in order to eliminate the risk associated with the factory building.**

To determine whether the individual, in this case, would be willing to pay a risk premium of 76 to the insurance company to eliminate the risk associated with the building, you can use the following steps:

- Calculate the expected value of the building: The expected value of the building is the sum of the value of the building in each possible outcome, multiplied by the probability of that outcome occurring. In this case, the expected value of the building is:

Expected value = (1600 * Â¾) + (400 * Â¼) = 1200 + 100 = 1300

- Calculate the expected value of the insured building: If the individual buys insurance to eliminate the risk of the building catching fire, the expected value of the building is equal to its value in the best possible outcome (1600).

The expected value of the insured building = 1600

- Calculate the risk premium: The risk premium is the difference between the expected value of the insured building and the expected value of the uninsured building. In this case, the risk premium is:

Risk premium = 1600 – 1300 = 300

- Compare the risk premium to the cost of insurance: If the risk premium is greater than or equal to the cost of insurance, the individual would be willing to pay the insurance premium to eliminate the risk. In this case, the risk premium is 300, which is greater than the cost of insurance (76), so the individual would be willing to pay the insurance premium to eliminate the risk.

The individual, in this case, would be willing to pay a risk premium of 76 to the insurance company to eliminate the risk associated with the building, as the expected value of the insured building is greater than the expected value of the uninsured building.

#MEC : Microeconomic Analysis Solved assignment 2022

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