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The Theory of Ownership Price and Fear of Loss.

Behavioral science is a discipline that applies the understanding of human behavior to explain decision-making. Since Gary Beck's winning of the 1992's Nobel Prize (in economics) for his contributions to the understanding of human behavior through micro-analysis, behavioral science has emerged as a prominent field with its ability to explain intriguing phenomena. Recent years have seen important new explorations along the boundaries between economics and psychology (e.g.,Simon, 1959). In 2017, Richard Thaler won the Nobel Prize for incorporating new insights from human psychology into economic analysis. (1) Thaler has provided economists with a richer set of analytical and experimental tools for understanding human behavior. This paper results from our attempt to resolve the following paradox mentioned by Dan Ariely (2010).
   Suppose that a person wants to buy a new pen, which costs $10 at
   store A, right next to the person's house and costs $5 at store B
   (15-minute walk from the person's house). The person is very likely
   to buy at store B. Now, suppose that the same person wants to buy a
   new shirt, which costs $200 at store A, right next to the person's
   house and costs $195 at store B (15-minute walk from the person's
   house). The person is much less likely to buy at store B. (2)

A superficial attempt to solve the paradox may explain that because a gain of $5 is trivial to a loss of $200, the person simply does not care about a saving of $5 anymore. This explanation is not persuasive because if we place store B right next to store A, the person is very likely to buy at store B. Therefore, we cannot say that the person does not care about a saving of $5 anymore. There seems to be an effect of the amount of money spent on the time spent before the purchase. In particular, for the pen, the person is willing to spend 15 minutes before the purchase, but for the shirt, the person is not. This thought motivates us to create a model explaining how the amount of money spent influences the amount of time spent and support the U-curve relationship between these two variables.

We develop theoretical models of the human price of ownership and the human fear of loss that have been briefly mentioned in books written by famous economists (e.g., Ariely, 2010; Levitt, 2005; Thaler & Sunstein, 2008), but there is hardly deeper research in the literature. Our paper is novel in the sense that much of the literature focuses on the psychological consequences of income inequality while not on how psychological effects lead to income inequality.

We choose the price of ownership and the fear of loss because the two effects give new reasons for efficiency wages and income inequality and thus, new insights into the labor market. Though the price of ownership and fear of loss are different in nature, we need the price of ownership to explain the wide income gap while we need the fear of loss to explain the growing income gap. Therefore, if we want to see how psychological effects shape the income distribution, we need to look at both the price of ownership and the fear of loss simultaneously.

We contribute to the literature in the following ways. First, we offer and argue for two theories through a combination of psychological effects and mathematical modeling. The two theories are

Theory 1: As people over-evaluate their properties, the price of ownership (in percentage term) grows with the price range,

Theory 2: The fear of loss is composed of two opposing components, which are the fear-avoiding effect and the fear-facing effect. The time people spend between planning to buy something and buying it has a Ucurve relationship with the amount of money spent. As a result, more money spent does not associate with more time to decide before a purchase.

Next, we show how these two theories, representing psychological effects, shape the income distribution among a population with many examples and evidence.

The price of ownership and a wide income gap Theory

People tend to value their own property higher than what others, who are not owners, do. To give a formal definition, the price of ownership is the difference between the prices of a property given by the property owner and others who do not own the property. For example, Thaler and Sustein (2008) conducted an experiment in which half of the students were given free cups, while the other half were given none. Then the students were allowed to trade with one another; however, the sellers often demanded a higher price than what the buyers offered. The experiment shows that the students who had the cups valued them higher than those who did not; what we are calling the price of ownership.

The theory of the price of ownership poses a paradox; that is, no transactions can be achieved. Indeed, in a given market, sellers are property owners while buyers are not, and so, sellers often demand a higher price than what buyers offer. If buyers and sellers cannot agree on the same price, then the market is frozen. We can explain this paradox by looking at the role of negotiations and brokers. Before any purchase, the buyer and seller expect a price for the goods in transaction. We call these the initial buyer's price and seller's price. By negotiations and by realizing that the buyer (seller) demands a lower (higher) price, the seller (buyer) may lower (raise) his/her previous price. If the two initial prices converge to a common price, the transaction is achieved, and the common price is the market price. To emphasize, the market price of a property is the common price agreed upon by buyers and sellers after a finite number of negotiations.

There are some markets that buyers and sellers themselves cannot negotiate to reach a common price [P.sub.o]. A notable example is the housing market, where most buyers and sellers rely on brokers to conduct a transaction. The brokers, with their negotiation skill, persuade buyers and sellers to agree on a practical market price and make transactions possible. What is the characteristic that determines whether a market needs brokers or not? In other words, what makes negotiations harder in some markets than others? The key determinant is the price range of the property, which is bounded by the prices given by buyers and sellers. Formally defined, a price range is a spectrum of prices bounded by two prices. Given the two price ranges and [[P.sub.b]1, [P.sub.s] 1] we say the first price range is lower (higher) than the second price range if [P.sub.s]1 << [P.sub.b] 2 ([P.sub.b] 1 >> [P.sub.s]2). It is often true that the higher the price range is, the rarer and the more customized is the property. This causes the property owner to be affected more by the price of ownership. Hence, [P.sub.0]b and [P.sub.0]s differ by a lot, resulting in the two sides being unable to reach [P.sub.0]. On the other hand, if the price range is generally low, the property is often common, which acts as a string to pull the price of ownership down. These facts explain why there is a broker in the housing market but none in the cup market! From now on, by the price of ownership, we mean the percentage of the difference between initial seller's and buyer's price over the initial buyer's price. In particular, the initial seller's price is [P.sub.0]s and the initial buyer's price is [P.sub.0]b as in Table l.In notation, the price of ownership is ([P.sub.0]s - [P.sub.0]b)/[P.sub.0]b x 100%. This way, we standardize the price of ownership and allow ourselves to compare the price of ownership of one property to another. As explained above, a person may ask for a price of ownership of 10% for his cup but may ask for 25% for his house. We call this feature of the price of ownership the growing law of ownership price (GLOP).

A wide income gap and the prevalence of efficiency wages

Income gap, or income inequality, refers to the extent to which income is unevenly distributed within a population. Literature has shown that the current wide income gap in many countries cannot be explained solely by differences in skills and the number of skilled workers. The literature points to different reasons, such as corruption (e.g., Gupta & Alonso-Terme, 2002), the decline of the union, market determination of wage setting rather than institutional determination, low minimum wage, and globalization (e.g., Freeman, 2007). Also, many reasons have been offered for why firms pay workers higher than the market-clearing wage. Markin (2012) listed four theories: 1) higher wages bring about better nutrition and healthier workers; 2) high wages reduce labor turnover; 3) higher wages reduce adverse selection; 4) high wages improve workers' effort. On the other hand, efficiency wage points to the incentive for firms to pay their employees higher than the market-clearing rate to increase their productivity or efficiency while reducing turnovers considerably. In this section, we make a link between GLOP, income gap, and efficiency wage. Our theory offers a new explanation for the wide income gap and efficiency wages. We will return to GLOP in a moment. Consider now three people: person A with a doctorate degree, person B with a college degree, and person C with a high school degree. For simplicity, we assume three firms: firm 1 only employs persons with doctorates, firm 2 only employs persons with bachelor degrees, and firm 3 only employs high school graduates. In the long run, the supplies of these three types of labor are constant.

Figure 2 shows the wage rates when there is no GLOP. Specifically, [W.sub.1], [W.sub.2], and [W.sub.3] are the wage rates the market (without GLOP) would pay to workers with a high school degree, a college degree, and a doctorate, respectively. We now add GLOP to the picture. Labor is the workers' assets that are sold to firms. The value of labor is closely and positively associated with educational levels, which are again intangible assets of workers. (4) Therefore, we can use educational levels as a proxy for the value of labor. Because each educational level is at a totally different level of the price range, people with higher education add a higher price of ownership to their degrees than people with lower education. Because the educational level is a proxy for labor value, people with higher education add a higher price of ownership to the value of their labor than people with lower education. They would, therefore, ask firms to pay them higher than the market-determined wages. (5) Table 2 provides an example of GLOP's effect on wage gaps.

We have seen that the wage gap between high school and doctorate degrees is widened from 20 (30-10) baskets of goods to 24 (34.5-10.5) baskets of goods. We have shown that GLOP contributes to a wide income gap but not a growing income gap, which we will address in the next section.

Fear of loss and the U-curve between money spent and time spent

People are risk-averse and are often obsessed more with losing a property than with gaining it. The fear of loss is sometimes so large that people may forgo opportunities to make money. Rabin and Thaler (2011) claimed that the hesitation over risky monetary prospects even when they involve an expected gain will not strike most economists as surprising.

For example, suppose that a person is given two choices:

1) receive $50 for sure,

2) with 60% chance, receive $160 and with 40% chance, lose $100.

The expected value of the latter choice is $56, which is larger than the former. However, many people would make the first choice since they do not want to face the risk of losing $100 (e.g., Rabin and Richard, 2011).

We can understand how the fear of loss influences people's purchasing decision by looking at the time people spend between planning to buy something and actually making the purchase. (Our assumption is that if people decide to buy something, they will surely buy it later.) We split the fear of loss' influence on time spent into two opposing components: people's fear of loss makes people act relentlessly (fear-avoiding effect) and people's fear of loss makes people act slowly (fear-facing effect). We offer this equation:

Time spent before a purchase = Fear-avoiding effect + Fear-facing effect.

The fear-avoiding effect is negative by convention because it decreases the time spent before a purchase. The fear-facing effect is positive because it increases the time spent before a purchase. The only requirement is that the interaction between the two produces a nonnegative number. We define and study the two effects below.

Fear-avoiding effect. When people plan to spend, the fear of loss urges them to act quickly so that they do not have to face the fear for long. They want to get the property quickly and have the feeling of gaining instead of losing. When the amount of money spent is small, the effect is small in magnitude. As the amount grows, the urge increases, and the effect grows larger in magnitude. We let f (M) denote the fear-avoiding effect as a function of M, money spent. We list properties of f(M): for all M, f(M) < 0 because the fear-avoiding effect decreases the time spent. Also, f'(M) < 0 because the effect is stronger as M increases. The fear-avoiding effect describes human irrationality rather than rationality. This is important in understanding the shape of the function. The fear-avoiding effect is stronger when we increase the amount of money spent from $0 to $50 than when we increase from $500 to $550, for example. Hence, f'(M) > 0. We see that f(M) <0, f'(M) < 0 f" (M) >0.

Fear-facing effect. When people plan to spend, the fear of loss urges them to act slowly so that the money is well-spent. The more alternatives they have with the money spent, the more they must consider and the larger the fear-facing effect. Hence, we can use the number of alternatives as a proxy to the fear-facing effect. We let g(M) denote the fear-facing effect as a function of M, money spent. We list properties of g(M): for all M, g(M) > 0 because the fear-facing effect increases the time spent. Also, g'(M) > 0 because as the amount of money spent increases, the fear-facing effect gets larger. Note that the fear-facing effect describes people's rationality rather than irrationality; that is, people consider alternatives to money spent. We claim that as the amount of money spent increases, the time spent grows at least linearly. To see this, we compare the increase in the fear-facing effect when the amount of money spent increases from $0 to $1,000 and when the amount increases from $10,000 to $11,000. Recall that we use the number of alternatives as a proxy to the strength of the effect. The increase of $1,000 in the latter case gives an increase in alternatives at least equal to what given by the increase of $1,000 in the former case. Hence, the slope of g(M), g'(M) at least increases as M increases; therefore, we conclude that g"(M) [greater than or equal to] 0.

We see that g(M) >, 0 g'(M) > 0, g" (M)[greater than or equal to] 0. The two effects combined. Let T(M) denote the time spent before a purchase with money spent M. We have T(M) = f(M) + g(M). Let C be a critical point of T (M). Then T'(C) = f'(C) + g' = 0, or equivalently, at C, the marginal influences of the two effects are equal in magnitude. Because for all M, f" (M) > 0 and g" (M) [greater than or equal to] 0, f"(C) + g"(C) > 0. By the second derivative test, C is the minimum point. Therefore, T (M) has a critical point that is a minimum. We graph T(M) in Figure 5.

We have shown the U-curve relationship between money spent and time spent. One weakness of our model is that we do not account for the dependence of time spent on what to buy. For example, it may take less time for a student to buy a required textbook than to buy a set of video games at the same price. However, the effect of "what to buy" on time spent depends on individuals' preferences, which are different across people and so, are hard to incorporate into our model.

Evidence for the U-curve

The paradox. The U-curve explains the paradox mentioned in the Introduction. Based on Figure 6, the person spends less time before buying the shirt than before buying the pen. In particular, the price of the shirt is either $195 or $200, and both prices correspond to about 10 minutes before the purchase. So, the person does not spend 15 minutes to buy at store B. However, with a price of either $5 or $10, the person spends about 17 minutes before the purchase and thus, is willing to spend 15 minutes to buy at store B. Two changes that may make the person buy at store B: 1) the shirt price at store B is low enough so that the time spent increases to more than 15 minutes; 2) store B is 9 minutes away from store A.

Auction. Another piece of evidence of the U-curve is seen during an auction, where people keep raising the price until no one wants to raise. At the beginning of the auction, it takes a relatively long time to find a call. This is because, at a low price, people spend more time to decide. As the price increases and we go down the first branch of the U-curve, it takes less time to find a call because people decide faster. However, as we go up the second branch of the U-curve, it is harder to find a call. This explains why at some point in the middle of an auction, people fight relentlessly for a higher price.

Growing income gap If high income inequality is bad for the economy, rising income inequality is worse because a few rich people will exert tremendous power on the whole economy, resulting in inherent financial instability (e.g., Freeman, 2007). As expected, the possible sources of the rising income inequality result from the increasing magnitude of the forces that cause income inequality. We give a new reason for the expanding income gap by using GLOP and the U-curve relationship between money spent and time spent.

First, due to GLOP, wage raises (in the percentage of the base wage) that are used to attract workers and award for efforts and dedication that workers put into their work are at a higher rate for skilled workers than for unskilled workers. In evaluating their raises, the skilled add a higher price of ownership to their dedication to the company and thus, demand a higher raise. Therefore, the wage gap keeps expanding as shown in Table 3. We see that the wage gap is initially at 24% and is at 31% after three years.

Our theory of the U-curve also implies that the skilled get raises more frequently and more generously than the unskilled. For the unskilled, firms may take more time before a raise because such a small raise lies on a high point of the first branch of the U-curve; in contrast, for the skilled, it takes firms less time because a larger raise lies on a lower point on the curve.


We have acquired a better understanding of the price of ownership and human fear of loss and showed how the human fear of loss influences people's spending behavior. In particular, the price of ownership (in percentage terms) is positively associated with the price range. Furthermore, the relationship between the amount of money spent and time spent before a purchase forms a U-curve, meaning that more money spent does not associate with more time spent. This is an unexpected conclusion; however, this conclusion is supported by our examples of a paradox and auctions. Along the way, we break down the fear of loss into its two components, which are the fear-avoiding effect and fear-facing effect. Our analysis gives more insights into notable phenomena in the labor market, including efficiency wage, wide income gap, and rising income inequality.


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Author Note: Hung V. Chu: Mathematics and Economics Department, Washington and Lee University, Lexington, VA 24450, USA. Email: Lan K. Chu: Research and Consultancy Department, Banking Academy of Vietnam, Hanoi 10000, Vietnam. Email:

Hung V. Chu

Washington and Lee University

Lan K. Chu

Banking Academy of Vietnam

(1) Advanced information. Nobel Media AB 2019. Thu. 18 Jul 2019. <> Author info: Correspondence should be sent to: Dr. Hung V. Chu, Department of Math & Economics, Washington & Lee University, Lexington, VA 24450

(2) We assume that the shirts and pens offered at the two stores are identical. The only two differences are prices and distances to the stores.

(3) This theory is not new, but we offer an explanation using both economics and psychology.

(4) The value of labor to an economy is defined by how much the labor contributes to the growth of GDP. For example, a CEO may create millions of jobs to workers, which boosts GDP quickly though the CEO is not directly doing the workers' job. Similarly, countries often boost their GDP through subsidizing education because more educated citizens have higher value of labor.

(5) We create a model with the main goal is to show that more education often results in higher price of ownership, which results in income inequality. The example we provide shows how the price of ownership contributes to income inequality. We do not argue that all PhDs, for example, expect to be paid at higher than average wages. In building a model, we cannot take into account other factors such as vacation days, types of industry, levels of stress, etc.

Caption: FIGURE 1. The price of Ownership with Respect to the Price Range

Caption: FIGURE 2. Note that MPL is the marginal product of labor. Job markets for the three types of labor: because S1 > S2 > S3 and MPL is shifted to the right for people with a higher degree, W1 < WK < W3.

Caption: FIGURE 3. The Fear-avoiding Effect Corresponding to Amount of Money Spent

Caption: FIGURE 4. The Fear-facing Effect Corresponding to Amount of Money Spent

Caption: FIGURE 5. The relationship between the amount of money spent and the time it takes before making a purchase

Caption: FIGURE 6. The relationship between the amount of money spent and the time it takes before making the purchase
TABLE 1. Negotiation to reach a common price.
For all [l.sub.i] [P.sub.l] b < [P.sub.l]S.

            Initial     Negotiation 1   Negotiation 2     ...

Buyer     [P.sub.0]b     [P.sub.1]b      [P.sub.2]b       ...
Seller    [P.sub.0]s     [P.sub.1]s      [P.sub.2]s       ...

          Negotiation n

Buyer       [P.sub.0]
Seller      [P.sub.0]

TABLE 2. GLOP Causes a Wider Income Gap Than What the
Labor Market Determines.

                  MPL        GLOP    Real wage
               (real wage)           (with GLOP)

High school        10         5%        10.5
College            20         10%        22
Doctorate          30         15%       34.5

TABLE 3. GLOP causes differences in wage raises and thus,
widen the income gap as time passes.
(S = skilled, U = unskilled)

                    Year 1          Year 2          Year 3
                      U       S       U       S       U       S

Base wage            100     120     102     126     104     132
Bonus wage           2%      5%      2%      5%      2%      5%
Total wage           102     126     104     132     106     139

[DELTA] total        24%             27%             31%
total wage x

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Author:Chu, Hung V.; Chu, Lan K.
Publication:North American Journal of Psychology
Date:Dec 1, 2019
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