Slutsky Equation and Negative Elasticity of Labor Supply: Behavioral Bias or Optimal Consumption-Leisure Choice?

One of the applications of the prospect theory is the behavioral phenomenon of the negative elasticity of the individual labor supply. This paper argues that the negative elasticity of labor supply can be understood better with the help of the interpretation of the Slutsky equation with regard to the common consumption-leisure choice. The interpretation of the Slutsky equation corresponds to the empirical evidence that leisure is a net complement for an important part of consumption

Law of nature or invisible hand: when the satisficing purchase becomes optimal

The transformation of the classical labor-leisure choice into the labor-search-leisure choice enables the analysis of the individual behavior under price dispersion. The consumer maximizes his consumption-leisure utility with respect to the equality of marginal loss on the search with its marginal benefit. The satisficing approach challenges this equality but the analysis of the moment of the intention to buy, when real balances and supplies as well as the knowledge about the price distribution are close to zero, discovers the unit elasticity of total consumer’s efforts on purchase with respect to any level of consumption for the given time horizon. If at the beginning the consumer evaluates correctly his purchasing power with respect to the market trade-off of leisure for consumption and if he is realistic about what he can buy with his efforts, he avoids the computational complexity of marginal values because the unit elasticity rule mechanically reproduces his optimal psychic consumption-leisure trade-off. The reproduction of the optimal choice by the unit elasticity rule looks like the law of nature but the optimal allocation of time between the labor and the search at any level of consumption, which. maximizes the consumption-leisure utility, appears like the work of the invisible hand. The satisficing decision with the inequality of the marginal values of search comes to the corner solution, when the consumer doesn’t make efforts on labor and search because the quantity demanded is not worth these efforts. If the consumer challenges the corner solution and start to work and to search, the unit elasticity rule reproduces high prior expectations and the outcome results in the disappointment on purchase. The unit elasticity rule provides the exit for the satisficing decision-making from the corner. If the consumer gradually changes his aspiration level and his optimistic prior expectations during the search, once he finds the satisficing price for the quantity demanded and the disappointment is gone. But the first satisficing offer, which doesn’t generate the disappointment, is the optimal one. The satisficing suboptimal purchase of the item of the immediate consumption occurs, when real balances, supplies, and knowledge are positive. These positive values produce the noise, which weakens the unit elasticity rule and make it useless. Under the unworkable unit elasticity rule the optimal choice really needs cumbersome calculations, and the consumer prefers to choose the first satisficing offer. The satisficing purchase of the durable item becomes necessary because the consumer substitutes the uncertainty of the search by the certainty of the use of the item and optimizes his consumption-leisure choice during its lifecycle with the help of his willingness to take care of the big-ticket purchase. The consumer stops to care for the durable item, when the efforts on its following use are expected greater than on average. This simple commonsense rule produces the equality of the marginal costs with the average after-purchase costs and becomes the sufficient condition to optimize the prior purchase. While the following negative willingness to take care exponentially raises the maintenance costs, the equality of the marginal and average after-purchase costs results in the optimal consumption-leisure choice of the purchase and exhibits the right moment to replace or to sell the item

Proof of the invisible hand: the optimal consumer allocation of time under price dispersion

The analysis of the labor-search-leisure model discovers some special optimality properties of the consumer choice under price dispersion. If the consumer is realistic about what he can buy with his efforts, the unit elasticity of his labor and search efforts with respect to consumption reproduces his initial consumption-leisure trade-off; it results in the equality of the marginal loss on search with its marginal benefit and the optimal consumption-leisure choice for any quantity purchased. The inequality of the marginal values of search, described by the satisficing approach, doesn’t take place, because this inequality represents the reproduction of the corner prior expectations by the same unit elasticity rule. If the consumer challenges the initial corner solution and start to work and to search, the unit elasticity rule reproduces high prior expectations and the following outcome produces the disappointment. As a result, the consumer either buys satisfactorily as well as optimally under the equality of the marginal values of search, or he quits the market without purchase. In this way the unit elasticity rule provides a powerful illustration of the consistency of consumer’s preferences. The consumer avoids the computational complexity of the marginal analysis because the unit elasticity rule automatically reproduces his realistic prior expectations how much leisure should be given up for consumption. However, the unit elasticity rule provides the optimality of the total efforts and tells nothing about their distribution between labor and search. But this distribution also is optimal, because it equalizes the marginal values of search with respect to the individual propensity to search. While the propensity to search gets the strong mathematical description ex-post with regard to the given price dispersion, it doesn’t exist ex-ante, on the level of prior expectations, when the consumer decides to give up some leisure time and starts to work and to search, but he hasn’t the reliable information on the price dispersion. It looks like the consumer makes the intuitive decision, or there is some hidden market mechanism, which provides the optimal allocation of his time between labor, search, and leisure, and confirms in this way the hypothesis of the invisible hand

Law of nature or invisible hand: when the satisficing purchase becomes optimal

The transformation of the classical labor-leisure choice into the labor-search-leisure choice enables the analysis of the individual behavior under price dispersion. The consumer maximizes his consumption-leisure utility with respect to the equality of marginal loss on the search with its marginal benefit. The satisficing approach challenges this equality but the analysis of the moment of the intention to buy, when real balances and supplies as well as the knowledge about the price distribution are close to zero, discovers the unit elasticity of total consumer’s efforts on purchase with respect to any level of consumption for the given time horizon. If at the beginning the consumer evaluates correctly his purchasing power with respect to the market trade-off of leisure for consumption and if he is realistic about what he can buy with his efforts, he avoids the computational complexity of marginal values because the unit elasticity rule mechanically reproduces his optimal psychic consumption-leisure trade-off. The reproduction of the optimal choice by the unit elasticity rule looks like the law of nature but the optimal allocation of time between the labor and the search at any level of consumption, which. maximizes the consumption-leisure utility, appears like the work of the invisible hand. The satisficing decision with the inequality of the marginal values of search comes to the corner solution, when the consumer doesn’t make efforts on labor and search because the quantity demanded is not worth these efforts. If the consumer challenges the corner solution and start to work and to search, the unit elasticity rule reproduces high prior expectations and the outcome results in the disappointment on purchase. The unit elasticity rule provides the exit for the satisficing decision-making from the corner. If the consumer gradually changes his aspiration level and his optimistic prior expectations during the search, once he finds the satisficing price for the quantity demanded and the disappointment is gone. But the first satisficing offer, which doesn’t generate the disappointment, is the optimal one. The satisficing suboptimal purchase of the item of the immediate consumption occurs, when real balances, supplies, and knowledge are positive. These positive values produce the noise, which weakens the unit elasticity rule and make it useless. Under the unworkable unit elasticity rule the optimal choice really needs cumbersome calculations, and the consumer prefers to choose the first satisficing offer. The satisficing purchase of the durable item becomes necessary because the consumer substitutes the uncertainty of the search by the certainty of the use of the item and optimizes his consumption-leisure choice during its lifecycle with the help of his willingness to take care of the big-ticket purchase. The consumer stops to care for the durable item, when the efforts on its following use are expected greater than on average. This simple commonsense rule produces the equality of the marginal costs with the average after-purchase costs and becomes the sufficient condition to optimize the prior purchase. While the following negative willingness to take care exponentially raises the maintenance costs, the equality of the marginal and average after-purchase costs results in the optimal consumption-leisure choice of the purchase and exhibits the right moment to replace or to sell the item

Proof of the invisible hand: the optimal consumer allocation of time under price dispersion

The analysis of the static labor-search-leisure model discovers some special optimality properties of the consumer choice under price dispersion. If the consumer is realistic about what he can buy with his efforts, the unit elasticity of his labor and search efforts with respect to consumption reproduces his initial consumption-leisure trade-off; it results in the equality of the marginal loss on search with its marginal benefit and the optimal consumption-leisure choice for any quantity purchased. The inequality of the marginal values of search, described by the satisficing approach, doesn’t take place, because this inequality represents the reproduction of the corner prior expectations by the same unit elasticity rule. If the consumer challenges the initial corner solution and start to work and to search, the unit elasticity rule reproduces high prior expectations and the following outcome produces the disappointment. As a result, the consumer either buys satisfactorily as well as optimally under the equality of the marginal values of search, or he quits the market without purchase. In this way the unit elasticity rule provides a powerful illustration of the consistency of consumer’s preferences. The consumer avoids the computational complexity of the marginal analysis because the unit elasticity rule automatically reproduces his realistic prior expectations of how much leisure should be given up for consumption. However, the unit elasticity rule provides the optimality of the total efforts and tells nothing about their distribution between labor and search. But this rule cannot work without the optimal consumer labor-search trade-off. It means that there is some inner market mechanism, which leads the producer along the production possibility frontier to make an offer with respect to the consumer optimal allocation of time. So to the consumer it feels under the unit elasticity rule like the producer is more about being at the right place and the right time with a price, which optimizes the consumer labor-search trade-off and in this way maximizes his consumption-leisure utility function

Willingness to take care of good cars: from the theorem of lemons to the Coase theorem

The study of the marginal scenario of the theorem of lemons under the total failure of the market of used cars – nobody buys, but everybody gets taxi – shifts the analysis of the equilibrium down from the level of cars to the level of mileage, because the market of used cars stays under the pressure of options whether to buy or to lease and whether to rent a car or to get taxi. The buying of a car with regard to the demand for mileage represents the purchase of input for home production where driving like gardening and pets’ care can provide a direct utility but is also something one can purchase on the market. The equilibrium price of a mile equalizes the willingness to pay of shoppers, consumers with zero search&maintenance costs, and the willingness to accept or to sell of searchers, consumers with positive search&maintenance costs. The practice to sell rights for queue jumping and illegal taxicab operations illustrate the arbitrage between shoppers’ willingness to pay and searchers’ willingness to accept. The analysis of choice between a good high-mileage car and a bad aged low-mileage car goes beyond the traditional considerations on status purchases and describes the phenomenon of the consumers’ willingness to take care of good cars. The willingness to take care increases after-the-purchase costs of ownership above the level of standard technological maintenance costs. As a result, after-the-purchase costs of ownership per mile for high-mileage cars become greater than for aged low-mileage cars. The willingness to take care of big-ticket items supports the demand and sellers of good cars do not quit the market. The willingness to take care redistributes used cars, i.e., assets for the home production of miles, for its more efficient use and cleans up the way to the Coase theorem

Deriving utility: consumers’ diligence under externalities and technical progress

If we present sales items or trade units, cars and apartments, in the units of consumption, miles and nights, like it takes place in the sharing&rental economy, we can get the model of the optimal consumption-leisure choice, where the efforts on pre-purchase search and after-purchase care produce non-monetary costs before the use of a trade unit. The paper argues that the productivity of these efforts differs from the efficiency of consumers’ efforts on the workplace. The consumer searches diligently the quantity to be purchased, he spends money earned by his labor or high-productive industry on the purchase and, following his willingness to take care of the purchased item, he takes low-productive diligent efforts in order to finally enjoy it. While the purchase price of the trade unit is equal to consumer’s willingness to pay, the total costs of his industry and diligence become equal to his willingness to accept or to sell the trade unit, the car and the apartment, where his marginal and average costs become equal to the equilibrium price of the unit of consumption, a mile or a night, and total costs become equal to the equilibrium price of the trade unit. The consumers’ productivity function really gets the S-shape, which slows the growth of monetary costs and accelerates the growth of non-monetary costs. While the consumers’ diligence derives the utility from the trade item at the equilibrium level, it enlarges also the spectrum of solutions for the Coase theorem, because the consumers’ diligence copies also with externalities. The trade-off between quantity of consumption units to be purchased and non-monetary efforts for its’ efficient use appears. The assets are redistributed for its more efficient use, from slight to great diligence, or from low to high willingness to take care of the trade unit just in accordance with the Black’s Law Encyclopedia where the great or high diligence is defined as the diligence that a very prudent person exercises in handling his or her own property like that at issue. The model demonstrates that the labor augmenting technical progress decreases the marginal monetary costs of consumers’ industry and increases non-monetary costs of consumers’ diligence at the equilibrium level that can be explained by the loss in the quality of trade units, cars and apartments. The outcome of the service augmenting technical progress is ambiguous. While it raises the equilibrium price, the consumption falls. But the fall in consumption reduces consumers’ diligence and results in the development of the sharing&rental economy. However, if the production and services are gross complements, the consumption growths and Veblen effect is to be expected where consumption becomes “bad” with respect to leisure and the consumers’ diligence becomes excessive

Money flexibility and optimal consumption-leisure choice under price dispersion

The synthesis of G.Sigler’s rule of the optimal search with the classical individual labor supply model can incorporate the satisficing decision procedure in the neoclassical framework. Many psychological anomalies and puzzles like the paradox of little pre-purchase search for big-ticket items and the effect of sunk costs sensitivity get the purely economic rationale. This synthesis also enlarges the understanding of the phenomenon of money flexibility under price dispersion. The specific constraints of the search model establish the correspondence between elasticity of the marginal utility of labor income with regard to price dispersion, wage rates, and the propensity to search. The money flexibility under price dispersion discovers specific features of Veblen effect. When the smart shopping of luxuries results in price reductions, which are greater than the wage rate, the marginal utility of labor income becomes negative. The marginal utility of luxuries also becomes negative. And the total consumption-leisure utility is increasing only due to the increase in leisure time. The paper argues that the same mechanism underlies the phenomenon of money illusion due to the relatively excess money balances

Consumer search behavior and willingness to pay for insurance under price dispersion

When the increase in income reduces the time of search and increases prices of purchases, the increase in price can be presented as the increase in the willingness to pay for insurance. The optimal consumer decision represents the trade-off between the propensity to search for proficient insurance and marginal savings on insurance policy. Under price dispersion the indirect utility function takes the form of cubic parabola, where the saddle point represents the comprehensive insurance. The comparative static analysis of the saddle point of the utility function discovers the ambiguity of the departure from risk-neutrality. This ambiguity can produce the ordinary risk seeking behavior as well as mathematical catastrophes of Veblen-effect’s imprudence and over prudence of family altruism. The comeback to risk aversion is also ambiguous and it results either in increasing or in decreasing relative risk aversion. The paper argues that the decreasing risk aversion results in the optimum quantity of money

A paradox of little pre-purchase search for durables: the trade-off between prices, product lifecycle, and savings on purchases.

The paper describes the microeconomic trade-off between prices, savings on purchases, and the time horizon of the consumption-leisure choice during the search for different products. When marginal costs of the search are equal to its marginal benefit, the time of search is proportional to products’ lifecycles and it is inversely proportional to starting prices