Problem 2 'Using the revealed preference t... [FREE SOLUTION]

Chapter 7: Problem 2

'Using the revealed preference theory, Samuelson derived the law of demand.

Short Answer

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Answer: Samuelson used the revealed preference theory to derive the law of demand by observing consumer behavior through their choices in the market and considering the effects of changes in price on their optimal choices. When the price of a good decreases, the budget constraint line pivots outward, allowing the consumer to consume more of both goods. The consumer will then choose a new bundle of goods that offers the highest level of utility within the new budget constraint. As the consumer moves to a point where the new marginal rate of substitution matches the new price ratio, the quantity demanded of the good increases, demonstrating the inverse relationship between price and quantity demanded, which is the law of demand.

Step by step solution

1. Introduction to Revealed Preference Theory

Revealed preference theory was developed by economist Paul Samuelson in 1938. The theory is used to analyze consumer behavior by observing the choices that they make. According to this theory, if a consumer chooses one bundle of goods over another, it is inferred that the chosen bundle is more preferable or offers more utility than the unchosen one. The underlying assumption is that consumers act rationally, always trying to maximize their utility based on their preferences and budget constraints.

2. Understanding the concept of preference and choice

In the revealed preference theory, consumer behavior is observed through their choices in the market. Samuelson proposed the Weak Axiom of Revealed Preferences (WARP), which states that if a consumer chooses a bundle of goods A over another bundle of goods B when both are affordable, then the consumer would never choose B if A remains affordable.

3. Budget constraints and optimal choice

Along with preferences, the budget constraint plays a crucial role in a consumer's decision-making process. A consumer's budget constraint represents the feasible combinations of goods that can be afforded given the income and prices of the goods. The optimal choice for a consumer lies on the budget constraint line and offers the highest level of utility within the constraint.

4. Indifference curves and the concept of marginal rate of substitution

An indifference curve represents all the combinations of goods that provide the same level of utility or satisfaction for a consumer. The slope of the indifference curve determines the marginal rate of substitution (MRS) 鈥� the rate at which a consumer is willing to trade one good for another while maintaining the same level of utility. In general, the MRS decreases as a consumer consumes more of one good and less of another, reflecting the diminishing marginal utility of goods.

5. Deriving the law of demand using revealed preference theory

Now, we can show how Samuelson derived the law of demand using the concepts from revealed preference theory. The law of demand states that there is an inverse relationship between the price of a good and its quantity demanded, holding all other factors constant. Consider a consumer who faces a change in the price of one good while holding the price of another good and the consumer's income constant. When the price of the good decreases, the budget constraint line pivots outward, allowing the consumer to consume more of both goods. According to the revealed preference theory, the consumer will choose the new bundle of goods that offers the highest level of utility within the new budget constraint. At this new optimal point, a new indifference curve will be tangent to the budget constraint line at a higher level of utility. Since the MRS is equal to the ratio of the prices of the goods, the decrease in the price of the good will lead to an increase in the quantity demanded of the good (as the consumer moves to a point where the new MRS matches the new price ratio). This demonstrates the inverse relationship between price and quantity demanded, which is the law of demand.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

The Law of Demand

The law of demand is a fundamental principle in economics that explains how price influences consumer purchasing behavior. In simple terms, it states that, all else being equal, when the price of a good or service decreases, the quantity demanded for that good or service tends to increase. Conversely, if the price goes up, demand usually decreases.

The reason behind this inverse relationship can be illustrated through revealed preference theory. As price decreases, consumers have greater purchasing power, allowing them to buy more even with the same budget. It can also lead to substituting more expensive goods with the cheaper one, hence increasing its demand. This key concept helps businesses and governments understand and predict how changes in prices can affect market demand patterns.

Consumer Behavior

Consumer behavior involves the study of how individuals make decisions to spend their available resources on various goods and services. This includes what they buy, why they buy it, how much they buy, and the frequency of their purchases. Revealed preference theory contributes significantly to understanding consumer behavior, as it relies on actual choices rather than stated preferences or intentions.

For instance, observed decisions in purchasing patterns can indicate a consumer's preference for certain goods over others, highlighting their priorities and economic rationale. Businesses use this understanding to tailor their products and make them more appealing to consumers. Economists, on the other hand, interpret these behaviors to assess how well markets are functioning and to make economic predictions.

Budget Constraints

A budget constraint represents the various combinations of goods and services a consumer can purchase given their current income and the prices of those goods and services. This constraint is symbolized by a line on a graph, where each point indicates a potential bundle of goods that the consumer can afford.

When a consumer's income or the prices of goods change, so does the budget constraint line. For example, a price drop in a good shifts this line outwards, providing the consumer with more options. The concept also implies that there's a trade-off involved; to purchase more of one item requires purchasing less of another, unless there's a change in income or prices that alters the constraint itself. Understanding budget constraints is essential for both consumers planning their expenditures and for businesses setting prices.

Marginal Rate of Substitution

The marginal rate of substitution (MRS) is an economic concept representing the rate at which a consumer is willing to give up one good in exchange for an incremental amount of another good, while maintaining the same level of overall satisfaction or utility. Mathematically, it is depicted as the slope of the indifference curve at any given point.

The diminishing MRS illustrates that as a consumer has more of one good, the less they are willing to give up of another good for more of the first one. This concept marries the ideas of personal preference and scarcity, reflecting the basic economic problem faced by consumers. In the context of revealed preference, the MRS adjusts to reflect consumers' choices in response to changing economic circumstances, such as price shifts, which can be linked to shifts in demand per the law of demand.

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