Information Asymmetry, Consumer behavior and Market Equilibrium

Euro-Asian Journal of Economics and Finance ISSN: 2310-0184 Volume: 1, Issue: 1 (October 2013), Pages: 33-40 © 2013 Academy of Business & Scientific Research http://www.absronline.org/eajef Information Asymmetry, Consumer behavior and Market Equilibrium Dr. Bairagya Ramsundar1* & Sarkar Shubhabrata2 1. Department of Economics, SambhuNath College, Labpur, Birbhum, West Bengal, India. 2. Department of Commerce, Sundarban Mahavidyalaya, Kakdwip, South-24 Pargana, West Bengal, India. In a perfectly competitive market we simply assume that full knowledgeable sellers and buyers have full information about the market condition and the information is free and costless. The firm is a price taker and has an infinitely elastic demand curve. But this is not generally happened in information asymmetry ad adverse section may occur. Equilibrium does not necessarily depict a single price rather it is characterized by a distribution set of price. Here the potential buyers and sellers are not price takers rather price setters. Multiple price equilibrium are quite similar to it but they differ only due to asymmetric information. Thus, in a buyers’ equilibrium no seller will be benefited for announcing his own price. But in a seller’s equilibrium (when all sellers have distinct price) some buyers may be benefitted by announcing their price. This is because the presence of adverse selection may induce a bias towards the market adopting a convention in which the buyers act as price setters. Keywords: Adverse selection; information asymmetry; multiple equilibrium; price distribution; utility index INTRODUCTION In his classic paper on adverse selection G Akerlof‟s (1970) “The Market for Lemons” brought a new dimension in economic theory. In a market sellers wishes to sell their cars to some potential buyers and they differ in the quality of the cars they are going to sell. Whereas buyers differ in the values they attach to the cars of same quality. Thus sellers know the quality of the used cars and the buyers can only observe the average quality of the used cars sold at each price. In this conditions market equilibrium is at single price, but with certain signals on the quality of the cars (J Levin 2001)) there exist a distribution of price. So far as equilibrium is concerned two things are important; who is the price taker? Either a buyer or a seller. The next is that, equilibrium does not necessarily depict a single price. Rather it is characterized by a distribution of price. The price mechanism of market with adverse selection needs to be understood (Wilson C 1977, 78). In the next sections we will discuss on market equilibrium when buyers and sellers are price setters. It is commonly belief that the owner of a car knows more than any potential buyer. The various car manufactories industries establish various showrooms in various parts of a country to cover the entire market. Generally the buyer thinks the quality of a product depends upon its own price. They employ many agents, advertising agencies, media, and news papers to show their superiority of high quality and facility at a low price than other companies and earn more profit through asymmetric information. As a result of asymmetric information‟s the potential buyers due to relative *Corresponding author: Dr. Bairagya Ramsundar, Department of Economics, SambhuNath College, Labpur, Birbhum, West Bengal, India E-Mail: [email protected] 33 Consumer behavior and Market Equilibrium ignorance assumed that any used car have a low quality (after all the seller of the car may secretly have a good reasons to get rid of). Finally, a high quality car even after one day of buying if the owner wants to sell it, the buyer bid down the price of one day used car judging either the car is of a low quality or any defect. This due to adverse selection, a high quality car does not get actual price in case of repeated sale. Information Asymmetry Another classic example of the asymmetric information is the O‟ Henry “Gift of the Magi”. This is also a problem of Battle of Sexes. The precise story is that Jim and Della lived in a poor family but they loved each other very much. Della has a beautiful long brown hair like a cascade but she has no precious comb. Jim wants to present Della a comb which may be useful to take care of her beautiful hair on Christ Mass era. On the contrary, Della wants to present Jim a platinum chain for his wonderful watch. Jim bought a splendid comb, made of tortoise shell, enriched of different gems. But to buy this comb (as he has no money) Jim sold his precious wrist-watch. And Della to buy her husband‟s platinum chain for his wrist-watch she sold her cascade like beautiful hair. When Jim entered into his home he became astonished because he noticed that Della has cut her hair. Della tried to console Jim and showed him that she bought for him. But when she comes to know that Jim has sold his favorite watch she became speechless. They consoled each other and felt their depth of love. Labour market Perfect information is not satisfied in the labour market (i.e. in labour contract). Employers often do not know the quality of potential hires and hiring can be risky, especially if it is difficult to hire employees or if they require costly training. Hence the asymmetric information adversely affects the labour market between the employer and the potential employee. A worker might have a better idea of how much he could produce (i.e. his productivity) than his employer. But by careful observation of the workers behavior, the employer might be able to get some idea about his Bairagya Ramsundar & Sarkar Shubhabrata productivity. The quality of a labour can be judged by his types of payment. In the labor market the skilled laborers earn higher wage rate than the unskilled one and thus there is wage discriminations in the labor market. Here the employer measures the labour productivity by educational levels of the employee. It is commonly belief that there is positive correlation between educational level and labour productivity. But in reality this may not be true and unfair wage discriminations occur in the labor market. There may be some situation where the educational level is higher though the labor productivity is lower and also the reverse. The various methods used to measure productivity are signaling, self-selection or by screening. Moral hazards The main problems of asymmetric information before transactions are adverse selection and create moral hazards and information monopoly. Adverse selection may occur when an immoral behavior like a person who has not an optimal health or has critical diseases inclined (hidden information) to purchase more life insurance than someone who feels fine. Moral hazards take place when a person who has fire insurance may behave recklessly or be more likely to commit arson to reap the benefits of the insurance. Another example is that a person with insurance against automobile theft may be less cautious about locking his car, because the negative consequences of vehicle theft are now (partially) the responsibility of the insurance company. A party makes a decision about how much risk to take, while another party bears the costs if things go badly, and the party isolated from risk behaves differently from how it would if it were fully exposed to the risk. A man will generally invest on insurance to reduce safety and security in future. Suppose a kitchen has well equipped and electrified and have fire extinguisher. Then the cook takes much risk in fire preventive measures. CAR MARKET It is commonly belief that the owner of a car knows more than any potential buyer. The various car 34 Euro-Asian Journal of Economics and Finance ISSN: 2310-0184 Volume: 1, Issue: 1, Pages: 33-40 manufactories industries establish various showrooms in various parts of a country to cover the entire market. Generally the buyer thinks the quality of a product depends upon its own price. They employ many agents, advertising agencies, media, and news papers to show their superiority of high quality and facility at a low price than other companies and earn more profit through asymmetric information. As a result of asymmetric information‟s the potential buyers due to relative ignorance assumed that any used car have a low quality (after all the seller of the car may secretly have a good reasons to get rid of). Finally, a high quality car even after one day of buying if the owner wants to sell it, the buyer bid down the price of one day used car judging either the car is of a low quality or any defect. This due to adverse selection, a high quality car does not get actual price in case of repeated sale. Here we consider a consumer who purchases two commodities good used car and bad used car (here the quality is judged according to information collect to him i.e. the bad used car may not be originally bad). Now the budget line can be written as: P_gX + P_bY = M where P_g = the price of the bad used car X, P_b = the price of the good used car Y. M = money income of the consumer (after saving and borrowing) (shown in figure-2) and bad used car increases (shown in figure-3). DISCUSSIONS There are fixed numbers of cars of different quality and a set of agents (i.e. sellers). Each car is assigned a quality index q>0. The utility function of each agent is Von Neumann- Morgenstern type i.e. U(c, q: θ) = c+θq where θ is the slope or utility index. Assumptions i. Buyers are risk neutral w.r.t. q i.e. utility is linear in q. ii. For any given q of a car higher the θ, higher is the reservation value a buyer assign to a car. iii. Higher the θ implies higher a buyer‟s marginal rate of substitution between quality and consumption of other goods. Thus, q=0 for agents having no cars. The utility index θ is such that h (θ)>0 on [θ0, θ1], where θ0>0 and H (θ) =∫_θ0^θ▒h(x)dx are the no. of buyers with utility index less than θ. For the ownership set q>0, the agents or sellers have same utility index θ, but they differ in the quality of the cars they own. The quality q is such that f (q)>0 on [q0, q1], where q0>0 and F (q) =∫_q0^q▒f(x)dx are the no. of sellers with cars of quality less than q. The budget equation can be written as: Y =M/ P_g – (P_g/P_b ) x where – (P_g/P_b ) <0 asP_g, P_b>0 is the slope of the budget line which is downward (shown in figure-1). Suppose in case of symmetric information the original budget line is PQ. Now to asymmetric information and due to adverse selection the consumer re-allocate his budget constraint in such a manner that he wants to purchase more of X and less of Y i.e. P1Q1. Derivation of the demand car We derive the demand curves for two types of car used. The demand for good used car decreases Proposition 1 For any expected quality function q*(p) defined on a set of prices, if a buyer with θ1 chooses to purchase at p1 then any buyer θ2> θ1 will choose at least p¬1. Proof Let, q*(p) be the expected quality function over set of prices p, and θ1 be a typical indifference curve for a buyer with positive sloped straight line. Let, q* and p* be equilibrium price at a given level of quality arrived by q*(p) = θ. the buyer with θ1 will have an equilibrium quality q1 and price p1. Thus any other buyer with 35 Consumer behavior and Market Equilibrium Bairagya Ramsundar & Sarkar Shubhabrata θ2> θ1 will enter into the market with a least expectation of q1 and p1. Since, θ2 > θ1 and q2 >q1, so p2>p1. Equilibrium with adverse selection Buyers are price setter Buyers cannot determine the quality of the cars rather they perceive the average quality of the cars sold and the prices at which they are sold. Equilibrium is defined as the price at which quality of cars supplied is equal to the quantity of cars demanded. Let, θq be the value assigned by an owner of a car of quality q and price p. thus an owner will sell his car iff p≥ θq. The supply of cars at price p is S (p) which is equal to the no. of cars for which q≤ p/ θ. S (p) = ∫_q^(p/ θ)▒f(q)dq, p>θ q0 , otherwise 0. And the average quality of cars offered for sale at price p is q*(p), since no seller will offer their cars at prices less than θq0 and q* is defined at prices at or above θq0. This implies, [{qf(q)dq}/S(p) ] q*(p) = ∫_q0^(p/ p>θq0 , or q0 p>θq0. θ)▒ Since, the buyers can only observe the average quality of the cars sold at each price, the expected benefit of buying a car at price p with an utility index θ is θq*(p). Thus, buyers will enter into the market when θq*≥p. Thus, demand for cars D (p) is equal to the no. of cars for which the utility θ ≥ p/θq*(p). So the demand function can be written as: D (p) = ∫_(p/θq*(p))^( θ1)▒ p<θ1q*(p), otherwise 0. p/(q*(p)) (dq*(p))/dp > 0. In addition to this condition the density of buyers at the marginal value of θ is sufficiently high and hence the demand curve may become even flatter than the supply curve. h( θ) dθ for Thus the equilibrium price pe is at D (pe) =S (pe). The demand function is not necessarily downward sloping. The demand depends on the price and as it raises the average quality is also high and these results much more benefit to the marginal buyer than the price. This is due to the utility index of the marginal buyer θ=p/q*(p). Thus the necessary and sufficient conditions for an upward sloping demand function is; Assumptions i. Each buyer may announce at most one price. ii. After the announcements seller may offer his/her car to any buyer he/she wishes. iii. For any excess supply at any price sellers are rationed at random. iv. Sellers unable to sell at the higher price may offer their cars at lower price or may stay out of the market. Buyers’ demand The price buyer choose mainly depend upon the average quality of the cars for sale and the seller will accept the buyer‟s price. Since the search cost is nil the seller may opt for the most favorable price. Thus a buyer may always expect an offer at price ‘p‟, provided that there is an excess supply at prices higher than „p‟. So „p‟ may be chosen as the cutoff price at or above which the subjective probability of buying is 1 and below which is 0. Sellers’ supply In absence of search cost each seller has the opportunity to offer his car to as many buyer as he wish until the car is sold. The supply of cars is an increasing function, because; with high price sellers are less interested to withdraw their cars and greater the no. of sellers with low reservation values. Equilibrium The market is in equilibrium when the expectations of a buyer are right. That is a buyer can anticipate both the set of prices at which a car can be purchased and the average quality of cars at each price. The equilibrium is characterized by two conditions: (i) at every price where sale occurs the buyers‟ expected quality function should equate the actual quality function. 36 Euro-Asian Journal of Economics and Finance ISSN: 2310-0184 Volume: 1, Issue: 1, Pages: 33-40 (ii) at every price at or above „p‟ the excess supply of cars should be positive. Proposition 2 Let, p* be the highest equilibrium price and let, (p, q*) be the buyers‟ equilibrium. Then, given quality function q*, buyer θ1, prefers to purchase at p* than any higher price. Then all active buyers announce p* and p=p*. Proof Let, p* be an equilibrium price, θ the highest utility index and p be the cut off price. If a buyer prefers to buy at p* than any other higher price, then by proposition 1 all buyer will prefer p*. Thus the cut off price is p=p*. Similarly, if p** is the next higher equilibrium price then the cutoff price p*=p** for all active buyers. Thus, the ordering of cutoff price is p<p*<p**. If p is the equilibrium cutoff price, then from proposition 2 p ≤ p* the price is determined by the point on the average quality curve at or above p which reaches his highest indifference curve which will be at p or θq ( since, no owner will sell at p≤ θq) or a point of tangency of θ and q. Thus, at p enough buyer enters the market eliminate excess supply and there is a distribution of price. There are two points for conclusion: i. No buyer announces a price in the interval where the demand curve is positively sloped and hence buyers will prefer to purchase at even higher price. ii. Most buyers will announce p. Therefore, any price below p will make the excess supply negative and the buyers will be forced to raise their prices to attract sellers until all have announced p. Thus, p is the most buyers‟ announced price. Therefore the buyers‟ equilibrium is (p, q*) if: i. q*(p) = q(p) for all p≥ θq0. ii. E (p; p**, q*) = 0 iff p< p**. 2.4 Sellers set the price Here each and every seller has the option of announcing a price or staying out of the market. For any excess supply of a car (at any price) the probability of selling a car at that price is the ratio of demand to supply. Given the set of prices sellers have announced, buyers must have an expectation about the quality of cars at each price and they purchase at a price where their expected utility is maximized. Equilibrium is at a point where expected probability function for sellers and expected quality function for buyers are same, such that it generate a realized probability function and realized quality function which are consistent with the original expectation functions. Given the above conditions seller equilibrium may be of two types: i. Where all sellers announce the same price. ii. Where all sellers announce a distinct price. Let, ψ*(p) be the expected probability of making a sale at price p, such that ψ (p) =0 means seller announces no price and P (ψ*) be the set of prices announced by sellers. Then the expected quality function for buyer = q*(p; P (ψ*)). Thus the demand function is D (p; P (ψ*), q*), which is no. of buyers at each price. The supply function is then S (p; ψ*). For S (p; ψ*) ≥ D (p; P (ψ*), q*), then the probability of making a sale is (D(p; P(ψ*),q*))/(S(p; ψ*)). Thus, probability of making a sale at each price is ψ** (p; ψ*, q*). Therefore seller equilibrium is then defined as an expectation function (q*, ψ*) for all p belongs to P (ψ*) if: i. q**(p, ψ*) = q*(p; P(ψ*)) and ii. Ψ*(p, ψ*, q*) = ψ*(p) ≤ 1. Now for i. All sellers with same price announcement (i.e. single price equilibrium): Let at p0, D (p0) < S (p0) Then, ψ*(p) = D (p0) / S (p0) for p≤ p0 otherwise 0. Since a new seller will always choose to announce p0 so P (ψ*) = {p0}. Thus given the action of sellers the buyers need only to formulate their expected 37 Consumer behavior and Market Equilibrium Bairagya Ramsundar & Sarkar Shubhabrata quality function at p0. Let qb(p) be the quality expectation of buyer. Since at p0, q*(p0) =qb(p0) and the no. of buyers is equal to the demand function, Therefore, ψ (p0) = D (p0) / S (p0) = ψ*(p0). Thus seller equilibrium (q*, p*) is at p0 = p*. ii. All sellers with distinct price announcement (multiple price equilibrium); Let, the seller‟s realized probability function be ψ* and he is offering cars with quality q. He will choose the price (p) that maximizes ψ*(p) [p – θq (p)]. The First Order Condition for maximization requiresΨ*(p) + ψ*‫( ׳‬p) [p – θq (p)] = 0 (i) Let, θ*(p) be the utility index of a buyer. His objective is to choose a price that maximizes his utility. Therefore, CONCLUSION It is quite evident that when both buyers and sellers are price takers the market may have multiple equilibria. That is, it might not be certain that the demand and supply meet at a single point. All these equilibria are distinct from a full information competitive equilibrium, where each quality of cars will have a distinct price. Which means cars will be allocated such that highest quality cars are allocated to agents with highest marginal rate of substitution (MRS) of quality for price. However multiple price equilibrium is quite similar to it. But they differ only due to asymmetric information. Thus, in a buyers‟ equilibrium no seller will be benefited for announcing his own price. But in a seller‟s equilibrium (when all sellers have distinct price) some buyers may be benefitted by announcing their price. This is because the presence of adverse selection may induce a bias towards the market adopting a convention in which the buyers act as price setters. Max. θq*(p) – p The First Order Condition for maximization requiresθ*(p) q*‫(׳‬p) – 1 = 0 (ii) Since, buyers and sellers are continuously distributed, the buyers and sellers per unit interval is h (θ*(p) θ*‫( ׳‬p) and f (q*(p) q*‫( ׳‬p)) respectively. Therefore, ψ*(p) = ([h(θ*(p)θ* ‫(׳‬p)] )/([f(q*(p)q* ‫( ׳‬p))] ) (iii) From (i), (ii) and (iii); Ψ*‫( ׳‬p) = (ψ*(p))/(p- θq*(p) ) (iv) q*‫( ׳‬p) = 1/(θ*(p)) (v) θ*‫(׳‬p) = (ψ*(p)[f(q*(p)q*‫(׳‬p))] )/(h(θ*(p))) = (ψ*(p)f(q*(p)))/(θ*(p)hθ*(p)) (vi) Now for price interval [p0, p1] (because sellers are announcing different prices), and from equation (v) and (vi) no seller would love to quote price lower than his reservation value. Similarly, θ*(p) is also increasing in p (since, p ≥ θq). Thus for p0 the equilibrium will be [q*(p¬0), ψ*(p0)] and for p1 it will be [q*(p¬1), ψ*(p1)]. REFERENCES Akerlof G (1970). The Market for Lemons: Qualitative Uncertainty and the Market Mechanis. Quarterly Journal of Economics, vol. 84, 488-500. Dowling E. T. (1986). Theory and Problems of Mathematics for Economists. International edn. Schaum‟s Outline Series, McGraw-Hill, Singapore, p 242-43 Henderson J. M., & Quandt R.E. (1984). Microeconomic Theory-A Mathematical Approach. 3rd edn. McGraw-Hill, Singapore, 136-137 Henry O. (1906). The Gift of the Magi. New York, USA Levin J. (2001). Information and the Market for Lemons. RAND Journal of Economics, vol. 32, no., 657-666. Milgram P. (1979). A Convergence Theorem for Competitive Bidding with Differential Information. Econometrica, pp 679-688. 38 Euro-Asian Journal of Economics and Finance ISSN: 2310-0184 Volume: 1, Issue: 1, Pages: 33-40 Salvatore D. (1983). Theory and Problems of Microeconomic Theory. International edn. Schaum‟s Outline Series, McGrawHill, Singapore, 1-5 Schilee E. (2001). The Value of Information in Efficient Risk – Sharing Arrangements. The American Economic Review, vol. 91, no. 3, 509-524. Schilee E. (2001). The Value of Information in Efficient Risk – Sharing Arrangements. The American Economic Review, vol. 91, no. 3, 509-524. Silberberg E. (1990). The Structure of Economics-A Mathematical Analysis, 2nd edn. Tata McGraw-Hill, Singapore, 1-15 Varian H. R. (1984). Microeconomic Analysis. 2nd edn. WW Norton & Company, New York, 694-715 Wilson C. (1978). “The Welfare Benefits of Price Maintenance in Markets with Adverse Selection. University of Wisconsin, SSRI Discussion Paper 7817. 39 Consumer behavior and Market Equilibrium Bairagya Ramsundar & Sarkar Shubhabrata APPENDIX Price P P1 O Q Q1 Figure-1 P OO P Q Q1 Q Figure-2 Good used car O Q Q Q1Q1 Bad used car Figure-3 40