Question

a)   What is Utility ? Develop a two dimensional model of Total Utility,, and explain the purpose of this model.

b) What is Marginal Utility? Derive it from Total Utility.

c) Using utility analysis: if one is economically rational, how does he/she allocate his/her choices ?

d) What are indifference curves ? Develop and demonstrate via a two dimensional model.

e) Given indifference curves, how is a decision made as to choices ?

       Demonstrate.

Answer 1

A) Utility is a term in economics that refers to the total satisfaction received from consuming a good or service. Economic theories based on rational choice usually assume that consumers will strive to maximize their utility. The economic utility of a good or service is important to understand, because it directly influences the demand, and therefore price, of that good or service. In practice, a consumer's utility is impossible to measure and quantify. However, some economists believe that they can indirectly estimate what is the utility for an economic good or service by employing various models.  The concept of budget constraints in the field of economics revolves around the idea that a given consumer is limited in consumption relative to the amount of capital they possess. As a result, consumers analyze the optimal way in which to leverage their purchasing power to maximize their utility and minimize opportunity costs. This is achieved through using budget constraints, which represent the plausible combinations of products and/or services a buyer is capable of purchasing with their capital on hand.To expand upon this definition further, the business concept of opportunity cost via trade-offs is a central building block in understanding budget constraints. An opportunity cost is defined as the foregone value of the next best alternative in a given action. To apply this to a real-life situation, pretend you have $100 to spend on food for the month. You have a wide variety of options, but some will provide you with higher opportunity costs than others. You could purchase enough bread, rice, milk and eggs to feed yourself for the full month or you could buy premium cut steak and store-prepared dinners by the pound (which would last about one week). The opportunity cost of the former is the high quality foods which have the convenience factor of already being prepared for you while the opportunity cost of the latter is having enough food to feed yourself for the entire month. In this circumstance the decision is easy, and the trade off will be sacrificing convenience and high quality food for the ability to have enough food on the table over the course of the whole month.

B) Marginal utility quantifies the added satisfaction that a consumer garners from consuming additional units of goods or services. The concept of marginal utility is used by economists to determine how much of an item consumers are willing to purchase. Positive marginal utility occurs when the consumption of an additional item increases the total utility, while negative marginal utility occurs when the consumption of an additional item decreases the total utility. Marginal utility may be illustrated by the following example.David has four bottles of water, then decides to purchase a fifth bottle. Meanwhile, Kevin has 50 bottles of water and likewise decides to buy an additional bottle. In this case, David experiences more utility, because his extra bottle increases his total water supply by 25%, while Kevin's additional bottle augments his supply by a mere 2%.The chief takeaway from this scenario is that the marginal utility of a buyer who acquires more and more of a product steadily declines until he has zero need for any additional units of the good or service. At that point, the marginal utility of the next unit equals zero.The concept of marginal utility sprouted from the minds of 19th-century economists who were attempting to explain the economic reality of price, which they believed was driven by a product's utility. However, this led to a conundrum known as the "the paradox of water and diamonds," which is attributed to "The Wealth of Nations" author Adam Smith, which states that water has far less value than diamonds, even though water is vital to human life. Since marginal utility and marginal cost are used to determine price, this is paradoxical because the marginal cost of water is much lower than that of diamonds. The theory behind utility is simple. A certain amount of satisfaction, value, or benefit is gained when a good or service is consumed. As David consumes each slice of pizza, he experiences satisfaction. Similarly, an employee working on a project can feel a certain amount of value is added to the project based on the number of hours spent working on the project. An athlete assigns a certain amount of benefit to the amount of time spent training. The total amount of satisfaction, value, or benefit gained from the consumption of each good or service is the total utility. Let's look back at David and his pizza. As the excitement of eating pizza increases, the total utility from the consumption of one slice of pizza rises from 7 to a total utility of 12 by the consumption of the third slice. However, the total utility decreases to 5 by the time the fifth slice of pizza is consumed, as David starts to feel full. The variance in total utility as each slice of pizza is consumed is called the marginal utility.

C) We must often make decisions under conditions of uncertainty. Pursuing a degree in biology may lead to lucrative employment, or to unemployment and crushing debt. A doctor's appointment may result in the early detection and treatment of a disease, or it may be a waste of money. Expected utility theory is an account of how to choose rationally when you are not sure which outcome will result from your acts. Its basic slogan is: choose the act with the highest expected utility. This article discusses expected utility theory as a normative theory—that is, a theory of how people should make decisions. In classical economics, expected utility theory is often used as a descriptive theory—that is, a theory of how people do make decisions—or as a predictive theory—that is, a theory that, while it may not accurately model the psychological mechanisms of decision-making, correctly predicts people's choices. Expected utility theory makes faulty predictions about people's decisions in many real-life choice situations (see Kahneman & Tversky 1982); however, this does not settle whether people should make decisions on the basis of expected utility considerations. The expected utility of an act is a weighted average of the utilities of each of its possible outcomes, where the utility of an outcome measures the extent to which that outcome is preferred, or preferable, to the alternatives. The utility of each outcome is weighted according to the probability that the act will lead to that outcome. Section 1 fleshes out this basic definition of expected utility in more rigorous terms, and discusses its relationship to choice. Section 2 discusses two types of arguments for expected utility theory: representation theorems, and long-run statistical arguments. Section 3 considers objections to expected utility theory; section 4 discusses its applications in philosophy of religion, economics, ethics, and epistemology.

D) An indifference curve is a graph showing combination of two goods that give the consumer equal satisfaction and utility. Each point on an indifference curve indicates that a consumer is indifferent between the two and all points give him the same utility. An indifference curve is a curve that represents all the combinations of goods that give the same satisfaction to the consumer. Since all the combinations give the same amount of satisfaction, the consumer prefers them equally. Hence the name indifference curve.Here is an example to understand the indifference curve better. Peter has 1 unit of food and 12 units of clothing. Now, we ask Peter how many units of clothing is he willing to give up in exchange for an additional unit of food so that his level of satisfaction remains unchanged.ndifference curves like Um are steeper on the left and flatter on the right. The reason behind this shape involves diminishing marginal utility—the notion that as a person consumes more of a good, the marginal utility from each additional unit becomes lower. Compare two different choices between points that all provide Lilly an equal amount of utility along the indifference curve Um: the choice between A and B, and between C and D. In both choices, Lilly consumes one more book, but between A and B her consumption of doughnuts falls by 36 (from 120 to 84) and between C and D it falls by only five (from 40 to 35). The reason for this difference is that points A and C are different starting points, and thus have different implications for marginal utility. At point A, Lilly has few books and many doughnuts. Thus, her marginal utility from an extra book will be relatively high while the marginal utility of additional doughnuts is relatively low—so on the margin, it will take a relatively large number of doughnuts to offset the utility from the marginal book. At point C, however, Lilly has many books and few doughnuts. From this starting point, her marginal utility gained from extra books will be relatively low, while the marginal utility lost from additional doughnuts would be relatively high—so on the margin, it will take a relatively smaller number of doughnuts to offset the change of one marginal book. In short, the slope of the indifference curve changes because the marginal rate of substitution—that is, the quantity of one good that would be traded for the other good to keep utility constant—also changes, as a result of diminishing marginal utility of both goods.

E) An indifference curve is a line showing all the combinations of two goods which give a consumer equal utility. In other words, the consumer would be indifferent to these different combinations.Suppose Ms. Bain spends 2 days skiing and 3 days horseback riding per semester. She will derive some level of total utility from that combination of the two activities. There are other combinations of the two activities that would yield the same level of total utility. Combinations of two goods that yield equal levels of utility are shown on an indifference curve.Limiting the situation to two goods allows us to show the problem graphically. By stating the problem of utility maximization with equations, we could extend the analysis to any number of goods and services. Because all points along an indifference curve generate the same level of utility, economists say that a consumer is indifferent between them.