Với một tiền chi trả dự kiến sẽ được đưa ra bởi thời hạn trong dấu ngoặc vuông phía bên phải bàn tay của (5,15). Nếu đại lý đáp ứng một người giữ hàng hóa cho rằng cô "thích" và sẵn sàng chấp nhận tiền, trao đổi có thể diễn ra và tiền chi trả là tổng hợp của các tiện ích từ U tiêu thụ và giá trị mới được sản xuất hàng hóa VC (t + 1). | COORDINATION AND EXTERNALITIES 183 with an expected payoff given by the term in square brackets on the right-hand side of . If the agent meets a commodity holder who is offering a good that she likes and is willing to accept money the exchange can take place and the payoff is the sum of the utility from consumption U and the value of the newly produced commodity Vc t 1 . This event occurs with probability 1 M xn. With the remaining probability 1 1 M xn trade does not take place and the agent s payoff is simply VM t 1 . For a commodity holder the payoff is Vc t T 1 Vc t 1 1 M x2 U M-xVm t 1 1 r 1 1 M-x Vc t 1 . Again the term in square brackets gives the expected payoff if a meeting occurs and is the sum of three terms. The first is utility from consumption U which is enjoyed only if the agent meets a commodity holder and both like each other s commodity a double coincidence of wants situation so that a barter can take place the probability of this event is 1 M x2. The second term is the payoff from accepting money in exchange for the commodity yielding a value VM t 1 this trade occurs only if the agent is willing to accept money with probability - and meets a money holder who is willing to receive the commodity he offers with probability Mx . The third term is the payoff from ending the period with a commodity which happens in all cases except for trade with a money holder so occurs with probability 1 M-x. To derive the agent s best response we focus on equilibria in which all agents choose the same strategy whereby - n and payoffs are stationary so that VM t VM t 1 VM and Vc t Vc t 1 Vc. Using these properties in and multiplying by 1 1 r and rearranging terms we get rVM 1 M xn U 1 M xn Vc Vm rVc 1 M x2U Mxn Vm Vc . Expressed in this form and are readily interpreted as asset valuation equations. The left-hand side represents the flow return from investing in a risk-free asset. The right-hand side is the flow return from .
