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# MEC-001/101: Microeconomics Analysis Assignment Solution

## 7. Write short notes on the following:

(A.) Moral Hazard.
(B.) Homogeneous and Homothetic production function.
(C.) Arrow prat measure of risk averseness.
(D.) Bergson-Samuelson Social welfare function.

#### Moral Hazard.

Moral hazard is a term used in economics and finance to describe a situation where one party in a contract takes on more risk than they would otherwise due to the actions of another party. This can occur when one party is insured against a certain risk, and their behaviour changes as a result.

For example, consider a situation where a person buys insurance to protect their car against theft. If the person knows that their car is insured, they may be less careful about locking it or keeping it in a secure location, leading to an increased risk of theft. In this case, the insurance company bears some of the risks of theft, and the insured person has the incentive to take on more risk than they would otherwise. This is known as a moral hazard.

Moral hazard can lead to inefficiencies in resource allocation and can have negative consequences for both the insured party and the insurer. To mitigate the effects of moral hazard, insurance companies may use various methods, such as deductibles, copays, and exclusions, to encourage insured parties to take on more of the risk themselves.

Overall, moral hazard is a phenomenon that can arise in situations where one party is insured against a certain risk and their behaviour changes as a result. It can lead to inefficiencies and negative consequences for both the insured party and the insurer and is an important factor to consider in the design and operation of insurance contracts.

#### Homogeneous and Homothetic production function.

A production function describes the relationship between the inputs used in the production process (such as labour and capital) and the output produced. A production function is homogeneous if a change in the inputs is proportional to a change in the output. In other words, if the inputs are increased by a certain percentage, the output will also increase by that same percentage.

A production function is homothetic if it satisfies the following properties:

1. It is homogeneous of degree 1, which means that a change in the inputs is proportional to a change in the output.
2. It is scale-invariant, which means that the production function does not depend on the scale of the inputs.
3. It is separable, which means that the production function can be written as the product of two functions, one representing the inputs and the other representing the output.

Homogeneous production functions are useful for analyzing the behaviour of firms and economies under various conditions, as they allow for easy comparison of different production scenarios. Homothetic production functions are useful for analyzing economies with constant returns to scale, as they allow for easy analysis of the effects of changes in the scale of production on output.

Overall, homogeneous and homothetic production functions are important tools in economics for understanding the relationship between inputs and output in the production process.

#### Arrow prat measure of risk averseness.

The Arrow-Pratt measure of risk aversion is a mathematical model used to quantify an individual’s level of risk aversion. It was developed by economists Kenneth Arrow and John Pratt in the 1960s and has since become a widely used tool in economics and finance.

The Arrow-Pratt measure is based on the concept of utility, which represents an individual’s preferences over different outcomes of a decision-making problem. An individual’s level of risk aversion can be quantified by measuring the curvature of their utility function, which represents the rate at which their utility changes as a function of the outcomes of a decision.

In general, an individual with a higher level of risk aversion will have a more concave utility function, which means that their utility decreases at an increasing rate as the outcomes of a decision become more uncertain. An individual with a lower level of risk aversion will have a more convex utility function, which means that their utility decreases at a decreasing rate as the outcomes of a decision become more uncertain.

The Arrow-Pratt measure is defined as the negative of the second derivative of the utility function, which represents the rate at which the curvature of the utility function changes as a function of the outcomes of a decision. A higher Arrow-Pratt measure indicates a higher level of risk aversion, while a lower Arrow-Pratt measure indicates a lower level of risk aversion.

Overall, the Arrow-Pratt measure is a useful tool for quantifying an individual’s level of risk aversion and understanding their preferences over different outcomes of a decision-making problem. It is widely used in economics and finance to study the behaviour of individuals and firms in risky situations.

#### Bergson-Samuelson Social welfare function.

The Bergson-Samuelson social welfare function is a mathematical model used in economics to represent the overall well-being or utility of society. It was developed by economists Abram Bergson and Paul Samuelson in the 1950s as a way to measure and compare the welfare of different societies.

The Bergson-Samuelson social welfare function is based on the idea that a society’s welfare can be represented as a function of the utility levels of its individual members. It is typically defined as a weighted sum of the utility levels of all members of the society, where the weights represent the relative importance of each member’s utility.

One key feature of the Bergson-Samuelson social welfare function is that it allows for the comparison of societies with different populations or utility distributions. It does this by expressing the welfare of each society in terms of a common unit of measurements, such as utility points or dollars.

The Bergson-Samuelson social welfare function has been widely used in economics and policy analysis as a way to measure and compare the welfare of different societies. It has also been the subject of much debate and criticism, as it relies on subjective assumptions about the utility levels of different individuals and the relative importance of their welfare.

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