THIRD-PARTY PAYMENT PLATFORM IN ONLINE SHOPPING. YANG YUCHENG (B.Eng(Cum Laude), The Ohio State University) A THESIS SUBMITTED

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1 THIRD-PARTY PAYMENT PLATFORM IN ONLINE SHOPPING YANG YUCHENG (B.Eng(Cum Laude), The Ohio State University) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF SOCIAL SCIENCES (RESEARCH) DEPARTMENT OF ECONOMICS NATIONAL UNIVERSITY OF SINGAPORE 2018 Supervisor: Assistant Professor: Huang Ji Examiners: Assistant Professor: Chen Chaoran Assistant Professor: Ma Lin

2 Declaration I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Yang Yucheng 19 July, 2018 i

3 Acknowledgement I am deeply grateful to my supervisor Prof. Huang Ji for his guidance, encouragement and immense knowledge. The door of his office was always open to me whenever I ran into trouble. Beside, I would like to thank Prof. Ma Lin, Prof. Chen Chaoran for their thoughtful comments and suggestions during my graduate research seminar. Furthermore, I would like to thank Prof. Serene Tan for her inspirations and corrections. I also thank my friends for the meaningful discussions. Last but not least, I am grateful to my fiancée Yang Shuyan who has supported me along the way. ii

4 Contents 1 Introduction 1 2 Model 4 3 Trade Trade without third-party payment platform Trade with third-party payment platform Term of Trade Fixed Policy One Period baseline model Agents Problems for one period Planner s Problems for one period Multiple Periods extension model Agents Problems for multiple period Planner Problems for multiple period State-contingent Policy Agents Problems for multiple periods Planner s Problems for multiple periods Numerical Example Parameterization Fixed Policy One period Multiple periods State-contingent Policy Conclusion 24 iii

5 SUMMARY This paper explores how a third-party payment platform solves problems between buyers and sellers in online shopping. In this study, I posit a model, characterize desirable allocations and explain the different outcomes of trades with or without a third-party payment platform as well as demonstrate that a third-party payment platform is essential when commitment problems exist between buyers and sellers. Without it, the set of incentive feasible allocations will keep shrinking. Furthermore, I investigate the differences between the optimal transaction fee charged by a third-party payment platform and that charged by social planners. The numerical result shows that in order to maximizing social welfare, the optimal transaction fee set by social planners is less than that set by a third-party payment platform. However, with the accumulation of a third-party payment platform s wealth and stable investment return from precipitation funds, the optimal transaction fee of social planners will decrease and converge to the optimal transaction fee of a third-party payment platform. Once the investment return from precipitation funds is high enough, the optimal transaction fee of social planners and a third-party payment platform will converge to the same value. Finally, if the shock of investment return exists and the transaction fee of a third-party payment platform is changeable along different periods, there is an optimal sequence of transaction fees for the social planner to maximize social welfare. iv

6 List of Figures 1 Trading mechanism density function of preference shocks w Third Party Payment Platform Social Planner Time Period T= Time Period T= Time Period T= Time Period T= Time Period T= Time Period T= Time Period T= Time Period T= Time Period T= Time Period T= Time Period T= Time Period T= Value Functions Policy Function Fee in good state Fee in bad state v

7 1 Introduction Nowadays, online shopping has become more and more popular. 79% of U.S. consumers shop online, up from just 22% in 2000 (TechCrunch, 2016). The latest figure for online retail sales in U.S. in 2017 is US$2,197 trillion; online retail sales is estimated to reach 8.8% of the total retail spending in 2018 as compared to 7.4% in 2016 (Invesp, 2017). This is in contrast to several years ago, when most people still shopped in the local stores regardless of parking and weather problems, long lines, and wobbly shopping carts. In spite of the tremendous expansion of online shopping, the number of studies on online trading is still limited, especially on the modes of payment. In the early days of online shopping, the trust between consumers and sellers was initially minimal. Consumers felt uncomfortable in using their credit cards or in giving their personal information to cyber-shops. In addition, they were also doubtful whether the sellers would keep their promise to ship the items after receiving the payment. Therefore, although e-commerce websites emerged nearly two decades ago, the services offered were limited to bookings tickets, reserving hotel rooms and ordering food or drinks. Payments were made only at the point of delivery or in person. Clearly, the e- commerce websites at that time served only to reduce the friction of searching between consumers and sellers but that did not provide a new channel of shopping. In short, a major problem faced by e-commerce all over the world was the lack of trust, which had often caused online shopping businesses to fail. Gefen and Straub (2003) suggest that one of the main barriers to online shopping is how to convince consumers to use the Internet as their new way of shopping and pay online before they get the goods from the sellers whom they cannot even see. This is known as a limited commitment problem. To address this problem, a set of allocations could be defined for the trade between the consumer and the seller, and then it is not difficult to show that the set of feasible allocations is inferior without a full commitment. 1

8 To solve this commitment problem, some online-shopping websites have developed third-party payment platforms. A third-party payment platform is like a bridge between buyers and sellers. When a purchase happens, the third-party payment platform will receive the payment from the buyer and hold it temporarily. Then the platform will alert the seller to ship the item to the buyer on time. Once the buyer receives the item and confirms that it is the correct one, the third-party payment platform will release the money to the seller. If the item is not delivered to the buyer or the item does not match the description, the buyer will get a refund from the third-party payment platform and the seller will be penalized. Some third-party payment platforms have become well established and function well today; examples are Paypal and Alipay. Take Paypal as an example. From 2002 to 2015, Paypal was a wholly owned subsidiary of ebay, which is one of the biggest online shopping websites in the U.S.. Paypal provided the service as a third-party payment platform for ebay for their online transactions. In the early 2000s, when sellers wanted to sell items on ebay, they had to use Paypal for their transactions, as it was the tool used by ebay to protect the rights of buyers. If there were a problem with a purchase, the ebay Money Back Guarantee would ensure that buyers received their money back through Paypal. With the development of third-party payment platforms, consumers are more confident about the security of online transactions and the timely delivery of their purchases. As online trade continues to gain ground, sellers build up their reputation and gain buyers trust. Consequently, online shopping has become a new sales channel and it has even grown into a major way of shopping in some industries. The main objective of this research is to explore the essential role of a third-party payment platform in online shopping and how a third-party payment platform facilitates online shopping in economic models. The economic literature on third-party platform in online shopping is limited. So far, there are only a few economic models to study the new payment technology or study online shopping separately. To my knowledge, this paper is the first attempt to combine the third-party payment platform and online shopping together. For the third-party 2

9 payment platform, Verdier (2010) studies how banks investments in payment card systems impact the privately and the socially optimal interchange fees but does not mention how it works in online shopping. This research is related to monetary theory literature, especially the literature that developed the model with trading friction in commitment problems. In fact, there are several different ways, which can facilitate the process of exchange between two agents with friction. The most common institution is money, and a famous challenge for economists is what kinds of friction make money essential. Wallace (2001) argues that the set of feasible allocations is bigger, or better, with money than without it. Similarly, I intend to investigate which friction leads to the use of third-party payment and when third-party payment is essential. Furthermore, Kiyotaki and Wright (1989) suggest that the difficulty of pure barter leads to a transaction role for fiat currency, which is money. Money, as a medium of exchange, is intrinsically worthless. However, it is essential when everyone believes that money can be used in future trades. In addition, some other ways have been identified to promote trade between two agents with commitment problems. Cavalcanti and Wallace (1999a, b) show that inside money facilitates trade without involving deposits, delegated investments, loans or endogenous monitoring. Another approach, developed by Kocherlakota (1998), suggests that money is one of the records keeping mechanisms; particularly, money is memory. When credit is not feasible or is limited, money is essential since the set of incentive feasible allocations that is larger with money than that without money. Gu et al. (2013) point out that friction gives rise to a role for banks. In their model, banks are the agents who are relatively trustworthy and have stronger incentive than other agents to keep their promise. Such trustworthy agents are appointed to keep the deposits from Agents type A who have commitment problems and allow Agent type B to claim the deposits to serve as a means of payment to facilitate the trade. Without this process or banking, the set of feasible allocations is inferior if the agent has a commitment problem. In this pa- 3

10 per, the third-party payment platform is treated in a similar way. Furthermore, given that third-party payment is essential for online shopping, I investigate the differences between the optimal transaction fee charged by a third-party payment platform and that charged by social planners. The initial model in this paper without a third-party payment platform is based on the New Monetarist benchmark model, originally proposed by Williamson and Wright (2010a, b). It contains two sub-periods coming one after another within every period. The payment and trade model including the third-party payment platform is built from the model created by Gu et al. (2013). In my model, one more agent, a thirdparty payment platform is added, while the model of Gu et al. (2013) does not require an extra agent to act as the bank. 2 Model Time is discrete and continues forever in the environment where there are three types of agents: buyer, seller and third-party payment platform. Each agent in the different group is assigned a permanent role, which means the role of agents will not change over time. Among these agents, sellers and buyers are equal mass but there is only one third-party payment platform in the economy. Buyers cannot produce and sellers cannot consume. There are two types of goods, one is a general goods and the other is a consumption goods. In each period, the probability of buyer and seller meeting is σ. U b (x, y) = u(x) y is the period utility function of each buyer and U s (x, y) = c(x)+y is the period utility function of each seller. Assuming that u(x) and c(x) are both twice differentiable, u(x) is strictly concave while c(x) is strictly convex. In addition, assuming that u(0) = c(0) = c (0) = 0, u (0) = +, there exists a x > 0 such that u(x) = c(x) and a x > 0 such that u (x ) = c (x ). Since u(x) is strictly concave with u (0) = + and c(x) is strictly convex with c (0) = 0, then x argmax(u(x) c(x)). There is a discount factor β (0, 1) across periods. 4

11 Each period includes two sub-periods. The matches between sellers and buyers are formed in the first sub-period and are maintained in the second sub-period. All matches are broken up at the end of each period. If there is a match between a buyer and a seller, the buyer will pay general goods y to the seller in the first subperiod and the seller will commit to transfer consumption goods x to the buyer in the second sub-period. The terms of trade between buyers and sellers in the first sub-period is determined by the solution of Nash Bargaining. Suppose a third-party payment platform is involved in the trade, it can hold y unit general goods of the buyer from the first sub-period to the second sub-period. During this time, the third-party payment platform can invest this money and yield ρ s y unit of general goods. ρ s is investment return rate, which is random and depends on the aggregate state s, which could be l or h (low and high) with probabilities π l and π h respectively. ρ l ( 1, 0) and ρ h (0, 1). Compared with the risk-free investment return rate r, the expected investment return rate E[ρ s ] is higher. Particularly, ρ l is less than r while ρ h is higher than r. At the end of the second sub-period, if the trade is completed, the third-party payment platform will transfer the general goods to the seller. 3 Trade 3.1 Trade without third-party payment platform Let us assume that the allocations (x, y) are incentive feasible if they satisfy the participation constraints and no-default conditions of buyers and sellers. First of all, we consider agents as being willing to fully commit for one period, and then the incentive feasible allocations entail two participation constraints: U b (x, y) 0 (1) U s (x, y) 0 (2) 5

12 Then the incentive feasible set with full commitment is denoted: F = {(x, y) (1) and (2) hold} In another case, there is no commitment. This means that at the start of every period, there are two participation conditions: U b (x, y) + β V b (x, y) 0 (3) U s (x, y) + β V s (x, y) 0 (4) where V b and V s are the continuation value of the buyer and the seller. In (3) and (4), the left hand side (LHS) of the equation means that the payoff follows the commitment and right hand side (RHS) of the equation is the payoff of derivation. The derivation will result in a punishment of future autarky with payoff 0. Since V s (x, y) = σ U s (x, y) + β V s (x, y) 0 and r = β, we have V s (x, y) = σ U s (x,y) 1 β 1 β. When the seller receives the general goods y from the buyer, he promises to deliver x units of consumption goods to the buyer in the second sub-period, but he may renege to save the cost of production. If he reneges, he will be punished with future autarky, and therefore, he keeps his promise only if β V s (x, y) c(x) where the RHS of the equation is the payoff of reneging. Replacing V s (x, y) by U s (x, y), we get the no default condition σu s (x, y) c(x)r (5) From equation (5), we know that the seller is trustworthy when he has a small production cost. Also, a low r and high meeting rate σ will lower the sellers temptation to default. The incentive feasible set with no commitment is denoted: 6

13 F = {(x, y) (1) and (5) hold} Lemma 1. If r a > r b and σ a = σ b or r a = r b and σ a < σ b then F a F b. Proof. Since σ > 0, r > 0, U s (x, y) 0 and c(x)r 0, it is trivial that when r a > r b and σ a = σ b or r a = r b and σ a < σ b, we have F a F b. 3.2 Trade with third-party payment platform Since the trade under no commitment needs to satisfy (5), from Lemma 1, we know that when the cost of production c(x) and the interest rate r is high enough or the meeting rate σ is close to 0, the no default condition always fails. In other words, since the buyer does not trust that the seller will follow through the commitment, the incentive feasible set may shrink to empty. To solve this commitment problem between buyers and sellers, a third-party payment platform could be brought into the trade. The mechanism works in the following manner: in the first sub-period, after the buyer and the seller reach a mutual agreement, a general goods y will be transferred by the buyer to the third-party payment platform, where a voucher, of no actual value to the buyer, will be given to the buyer. In the meantime, the item will be tracked by the third-party payment platform during the whole transportation process until it is successfully delivered to the buyer. The buyer will receive the item in the second sub-period. In addition, during the first sub-period, the third-party payment platform can invest the general goods y. This investment yields ρ s y general goods in the second sub-period. The value of ρ s depends on the state s, which could be l or h (low or high) with probabilities π l and π h respectively. Moreover, in the second sub-period, the buyer needs to use the voucher to exchange the goods when it arrives. The seller takes this voucher and redeems it for δ y with δ > 0. If δ (0, 1), the seller is charged (1 δ) y as the transaction cost by the third-party payment platform. If δ > 1, the seller receives (δ 1) y from the third-party payment platform as the incentive payment after transaction through the platform. Consider if the buyer and 7

14 Figure 1: Trading mechanism the seller can also have access to either the risk-free or the risky asset, the third-party payment platform are likely to set δ > 1 in order to attract more buyers and sellers trade under the third-payment platform. However, in this paper, I assume only the third-party payment platform can make investment for simplicity. If the third-party payment platform has not received the voucher from the seller at the end of the second sub-period, he will return general goods y to the buyer. If someone rejects a suggested trade, as above, he is punished with future autarky. See Figure 1. The incentive conditions of the buyer, the seller and the third-party payment platform are reduced to U b (x, y) 0 (6) U s (x, y) (1 δ) y (7) (ρ s + (1 δ) )y 0 (8) Equations (6) and (7) are the participation constraints of buyers and sellers and (8) is the repayment constraint of the third-party payment platform. Since there is no 8

15 repayment constraint for the seller or the buyer, the incentive feasible allocation is equal to the one in full commitment when δ is converged to 1 and the repayment constraint of the third-party payment platform is not violated. 3.3 Term of Trade For full commitment scenarios and no commitment scenarios, I assume Nash Bargaining is the trading mechanism and consider the case of Generalized Nash Bargaining. In full commitment scenario, the generalized Nash solution solves max [ U s (x, y)] θ [ U b (x, y)] (1 θ) (x,y) subject to the two participation constraints U b (x, y) 0 U s (x, y) 0 where U b (x, y) = u(x) y, U s (x, y) = c(x) + y, and θ is the bargaining power of the seller, which is exogenous. Assumption 1. Buyer has enough money to consume the first-best quantity level of good. Take the F.O.C and we can get the solution x = x and y = (1 θ) c(x ) + θ u(x ). Since Nash solution is Pareto efficient, the solution lies on the Pareto frontier. In the no commitment scenario, where the incentive constraint of seller has changed, the Nash solution needs to satisfy U b (x, y) 0 U s (x, y) r σ c(x) 9

16 We can obtain the same solution as full commitment scenario only if c(x ) r + σ σ u(x ) If this condition fails, the solution will not be located at the Pareto frontier, which means that the allocation is not efficient. When the trade involves a third-party payment platform, the term of trade problem could be more interesting. Actually, the third-party payment platform keeps the record of trade, which can reveal the seller s past behavior. For example, the record can be measured by the refund rate to show the probability of any unsatisfactory transactions in the past. If buyers are given access to the record, they can update their belief in the sellers at the beginning of every period based on Bayesian Updating. For instance, if the refund rate of the seller is high, it means that this seller has a higher temptation to renege. Or if the item is usually not as good as described, the buyer will lower his or her expected payoff of the trade with this seller. Since the expected payoff is lower, the buyer tends to ask for a lower price. As a result, based on the buyer s belief, we can classify the sellers into three different types: good, neutral and bad. I assume the bargaining power of seller θ is endogenous when the trade includes a thirdparty payment platform and θ depends on the buyer s belief. However, the question of how to determine the value of θ based on the repeated game between buyer and seller is beyond the scope of this paper. For simplicity, suppose the value of θ is given and the types of sellers, which are good, neutral and bad. In other words, in this paper, θ is exogenously fixed. Therefore, based on the different bargaining power of sellers, we will have different equilibrium of allocation. The generalized Nash solution of trades with third-party payment platform can be expressed as: 10

17 subject to three incentive constraints max (x,y) [ U s (x, δy)] θ [ U b (x, y)] (1 θ) U b (x, y) 0 U s (x, y) (1 δ) y (ρ s + (1 δ) )y 0 Take the F.O.C and we can obtain the solution x = x and y = 1 δ (1 θ) c(x ) + θ u(x ). As (ρ + (1 δ) )y 0 and 1 δ (1 θ) c(x ) u(x ). Since 1 δ (1 θ) c(x ) u(x ), the y will increase with the increase of θ. 4 Fixed Policy The policy here refers to the transaction cost which is set by third-party payment platform or social planner among the different periods. 4.1 One Period baseline model Consider that buyers, sellers, the third-party payment platform and the social planner want to maximize their utility in one period trade Agents Problems for one period Buyers and sellers optimal decision max [ U s (x(w), y(w))] θ [ U b (x(w), y(w))] (1 θ) (x(w),y(w)) 11

18 where buyer s preference shock w, is an i.i.d. drawn from CDF F (w) with support [w min, w max ]. From the previous Nash solution, we know that the buyers and sellers will choose allocation (x (w), y (w)), where x(w) = x (w) and y (w) = (1 θ) c(x (w)) + θ u(x (w)). to maximize their utility. Third-party payment platform s optimal decision subject to max (1 δ + ρ s ) δ (y(w))df (w) u(x(w)) y(w) 0 (9) c(x(w)) + δy(w) 0 (10) Definition 1. The one period agents problem under fixed policy with ρ s is given by allocations (x(w), y(w)) and a transaction fee (1 δ) such that 1. every allocation maximizes a buyer s utility; 2. every allocation maximizes a seller s utility; 3. the transaction fee maximizes the utility of third-party payment platform; 4. Condition (9) and (10) are satisfied. 12

19 4.1.2 Planner s Problems for one period Given the buyers and sellers optimal solution, the social planner s optimal decision is: max δ [ u(x(w)) y(w) c(x(w)) + δy(w) + (1 δ + ρ s ) y(w)] df (w) subject to u(x(w)) y(w) 0 (11) c(x(w)) + δy(w) 0 (12) Definition 2. The one period social planner s problem under fix policy with ρ s is given by allocations (x(w), y(w)) and a transaction fee (1 δ) such that 1. every allocation maximizes a buyer s utility; 2. every allocation maximizes a seller s utility; 3. the transaction fee maximizes the social welfare; 4. Condition (11) and (12) are satisfied. 4.2 Multiple Periods extension model Consider that a third-party payment platform can accumulate their profits from every period as asset and invest them in the current period. The return of this investment depends on the shock of investment return ρ st based on the Markov chain. The asset accumulation in the current period can occur in three ways. First of all, the third party payment platform can accumulate the asset from the return of investment of the previous accumulated asset. Secondly, the asset can be accumulated by the investment of the payment received from buyers at the current period. Last by not least, the transaction fee charged from sellers can accumulate to assets. 13

20 4.2.1 Agents Problems for multiple period The decision of all buyers and sellers are independent in every period; in other words, the optimal decision will not change in the different periods given a fix term of trade and bargaining power. Therefore, from the previous Nash solution, we know that the buyers and sellers will choose allocation (x (w t ), y (w t )), where x(w t ) = x (w t ) and y (w t ) = (1 θ) c(x (w t )) + θ u(x (w t )). and where the buyer s preference shock at time t w t, is an i.i.d. drawn from CDF F (w t ) with support[ w tmin, w tmax ] to maximize their utility. The third-party payment platform s optimal decision is: V (a t, ρ st 1 ) = max δ E[ (1 δ + ρ st ) ρ st 1 ] y(w t )df (w t ) + E[ a t ρ st ρ st 1 ] + βe[ V (a t+1, ρ st ) ρ st 1 ] subject to u(x(w t )) y(w t ) 0 (13) c(x(w t )) + δy(w t ) 0 (14) B a t+1 = E[ a t ρ st ρ st 1 ] + E[ (1 δ + ρ st ρ st 1 )] y(w t )df (w t ) a (15) where B is the lowest capital requirement for a third-party payment platform and a t, a t+1 are the asset at time t and time t + 1. Definition 3. The multiple periods agents problem under fixed policy with ρ st is given by allocations (x(w t ), y(w t )) and a transaction fee (1 δ) such that 1. every allocation maximizes a buyer s utility; 14

21 2. every allocation maximizes a seller s utility; 3. the transaction cost maximizes the utility of third-party payment platform; 4. Condition (13), (14) and (15) are satisfied Planner Problems for multiple period Given the buyers and sellers optimal solution, the Social Planner s optimal decision is: V (a t, ρ st 1 ) = max δ E[ [ u(x(w t )) c(x(w t )) + ρ st y(w t ) ρ st 1 ] df (w t )] + E[ a t ρ st ρ st 1 ] + βe[ V (a t+1, ρ st ) ρ st 1 ] subject to u(x(w t )) y(w t ) 0 (16) c(x(w t )) + δy(w t ) 0 (17) B a t+1 = E[ a t ρ st ρ st 1 ] + E[ (1 δ + ρ st ρ st 1 )] y(w t )df (w t ) a (18) Definition 4. The multiple periods social planner s problem under fixed policy with ρ st is given by allocations (x(w t ), y(w t )) and a transaction cost (1 δ) such that 1. every allocation maximizes a buyer s utility; 2. every allocation maximizes a seller s utility; 3. the transaction cost maximizes social welfare; 4. Condition (16), (17) and (18) are satisfied. 15

22 5 State-contingent Policy I now assume that the third-party payment platform and the social planner can choose a different value of δ in every period to maximize the utility. 5.1 Agents Problems for multiple periods Since the decisions of all buyers and sellers are independent in every period, we can obtain the same equation of x (w t ) and y (w t ) as the multiple periods case. The third-party payment platform s optimal decision is: V (a t, ρ st 1 ) = max E[ (1 δ + ρ st ) ρ st 1 ] δ t y(w t )df (w t ) + E[ a t ρ st ρ st 1 ] + βe[ V (a t+1, ρ st ) ρ st 1 ] subject to u(x(w t )) y(w t ) 0 c(x(w t )) + δ t y(w t ) 0 B a t+1 = E[ a t ρ st ρ st 1 ] + E[ (1 δ t + ρ st ρ st 1 )] y(w t )df (w t ) a 5.2 Planner s Problems for multiple periods The planner s problem s optimal decision: V (a t, ρ st 1 ) = max E[ δ t [ u(x(w t )) c(x(w t )) + ρ st y(w t ) ρ st 1 ] df (w t )] + E[ a t ρ st ρ st 1 ] + βe[ V (a t+1, ρ st ) ρ st 1 ] subject to u(x(w t )) y(w t ) 0 c(x(w t )) + δ t y(w t ) 0 16

23 B a t+1 = E[ a t ρ st ρ st 1 ] + E[ (1 δ t + ρ st ρ st 1 )] y(w t )df (w t ) a 6 Numerical Example To the following, I present several examples of both fixed policy and state-contingent policy cases. 6.1 Parameterization I assume that the buyer s utility function is: u(x) = log(x + 1) and that the seller s utility function is: c(x) = x 2 In addition, I assume that the buyers preference shocks follow a normal distribution with mean 0.5 and standard deviation Figure (2) plots the density function of the preference shocks w. 17

24 Figure 2: density function of preference shocks w I pick the following parameter values for the benchmark model. values target β Period length = 1 week B -50 Asset lower bound a 1750 Asset upper bound S 1000 Size of buyers and sellers θ 0.7 Seller bargaining power E[ ρ s ] 0.05 Expected ROC r 0.02 Risk free ROC ρ g1 0.1 ROC in good state in fixed policy case ρ g2 0.1 ROC in good state in state-contingent policy case ρ b ROC in bad state in fixed policy case ρ b ROC in bad state in state-contingent policy case 18

25 where ROC is the return on capital. 6.2 Fixed Policy One period Assume that the third party payment platform and the social planner pick an optimal transaction fee (1 δ) to maximize their utility of one period. For the third party payment platform, given the previous parameter, I obtain the maximum profit when δ = In other words, to maximize the profit, the third party payment platform will pick (1 δ), which amount is 28.4% of every transaction charged as transaction fee. (See Figure 3) Figure 3: Third Party Payment Platform Figure 4: Social Planner For the social planner, I obtain the maximum profit when δ Since in one period case, the social welfare is monotonous increasing with the decrease of transaction cost and achieves its maximum at δ = 0.903, to maximize the profit, the third party payment platform will pick (1 δ), which is less or equal to 9.7% of every transaction charged as transaction fee. (See Figure 4) Multiple periods For multiple periods, I discuss the case with fixed investment return rate and the case with volatile investment return rate separately. For the fixed investment return rate 19

26 case, since the rate should always be greater than 0 when third party payment platform decide to invest its assets, the third-party payment platform repayment condition (equation 3) should always satisfy. In other words, the accumulated assets should always positive. However, for the case that investment return rate with shock, since the third-party payment platform may suffer a capital loss when the investment of assets encounters a bad shock, the third-party payment platform repayment condition may fail when the accumulated asset less than 0. If the repayment condition fail, the third-party payment platform will defaults, then there is no trade in this market in the future. Assume that the fixed investment return rate is the same as the expected investment return of the case with shock. Beside, consider that the third party payment platform and the social planner pick an optimal transaction fee (1 δ) at the beginning of the first period to maximize their utility of multiple periods. For the third party payment platform, since the optimal transaction fee of one period case will generate most profit for asset accumulation, the optimal transaction fee of one period should be equal the optimal transaction fee of multiple periods, meaning that their decision will not change with the length of periods. Nevertheless, the optimal transaction fee of the social planner in multiple periods will change because there is a tradeoff between the surplus and the asset accumulation at every period transaction. Since the optimal transaction fee of the third party payment platform, which represents the transaction fee for the largest asset accumulation, is higher than the optimal transaction fee of the social planner in single period case. Therefore, to increase the asset accumulation, the social planner needs to increase the transaction cost which will decrease the surplus of trade between buyers and sellers. Multiple Periods Without Default Let T represent the multiple periods and I calculate the optimal transaction fee of social planner when T=5, 10, 20, 50, 100 and

27 Figure 5: Time Period T=5 Figure 6: Time Period T=10 Figure 7: Time Period T=20 Figure 8: Time Period T=50 Figure 9: Time Period T=100 Figure 10: Time Period T=200 The results show that the optimal transaction fee of the social planner decrease with the increase of T and the value of the optimal transaction fee of the social planner is convergent to the value of the optimal transaction fee of the third party payment platform. In addition, the speed of convergence depends on the return rate of the investment. The convergence is faster with a higher return rate of investment. 21

28 Multiple Periods With Potential Default Let T represent the multiple periods and I calculate the optimal transaction fee of social planner when T=5, 10, 20, 50, 100 and 200. Figure 11: Time Period T=5 Figure 12: Time Period T=10 Figure 13: Time Period T=20 Figure 14: Time Period T=50 Figure 15: Time Period T=100 Figure 16: Time Period T=200 The results are similar to the case without default. The optimal transaction fee of the social planner decrease with the increase of T and the value of the optimal transaction 22

29 fee of the social planner is convergent to the value of the optimal transaction fee of the third party payment platform. However, the optimal transaction fee of multiple periods with potential default is always higher than the optimal transaction fee of multiple periods without default. Particularly, the difference is smaller with the increase of T. 6.3 State-contingent Policy Since the optimal transaction fee of the third party payment platform will not change in different time periods, I only consider the optimal transaction fee under statecontingent policy of the social planner. Suppose that the social planner selects an optimal transaction fee (1 δ t ) at the beginning of period t to maximize their utility in its whole life. Figure 17: Value Functions Figure 18: Policy Function Figure 19: Fee in good state Figure 20: Fee in bad state The results show that the optimal transaction fee of the social planner will converge 23

30 to a fixed point. The value of the fixed point in the good state is larger than the value of the fixed point in the bad state. The reason behind this is that in the good state, the expected return of an investment is higher than in the bad state, meaning that the asset accumulation is larger than that in the bad state. Thus, given the same asset upper bound, the social planner can lower the transaction fee in the good state and get more social welfare from the surplus of the transaction between buyers and sellers. Besides, another interesting result is that the optimal transaction fee of the social planner is relatively higher when the asset is low. The reason is that when the asset is low, most of the social welfare derives from the surplus between buyers and sellers. Since the surplus increase with the decrease of the transaction fee, the transaction fee is relatively low at the beginning. However, with the increase of assets, the return from asset investment becomes the prior source of social welfare. Since the asset accumulation is fastest at the optimal transaction of the third party payment platform, the social planner will pick a transaction fee, which is closer to the optimal transaction of the third party payment platform than when the asset is low. This allows the social planner to balance the speed of asset accumulation and surplus from trade obtained by buyers and sellers. 7 Conclusion The model illustrates how the third party payment platform works when a commitment problem exists in online shopping. In this model, the third party payment platform keeps the payment to protect the buyer in the transaction, alerts the seller to ship the item on time and record the seller s behavior. These actions of a third-party payment platform enlarge the incentive feasible allocations between buyers and sellers and allow the online shopping to be more efficient. Besides, I calculate the optimal transaction fee of third payment platform and social 24

31 planner for the stationary equilibrium and dynamic equilibrium. The numerical results show that the optimal transaction fee of the third payment platform is always higher than the optimal transaction fee of the social planner. In a stationary equilibrium, the optimal transaction fee of the social planner will converge to the optimal transaction fee of the third party payment platform with the increase of time periods. The optimal transaction fee of social planner in the no-default scenario is slightly lower than that in the potential default scenario. In the dynamic equilibrium, the optimal transaction fee of the social planner in the good state and the bad state will converge in different value. The different value shows that the optimal transaction fee in the good state is slightly higher than the optimal transaction fee in the bad state. Therefore, the social planner can set different policies depending on the economic situation. Finally, since the optimal transaction fee of the third party payment platform is always higher than the optimal transaction fee of the social planner, the social planner could impose some regulations to limit the transaction fee charged by third payment platform in order to increase social welfare. 25

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