learning to believe in sunspots a number of authors have shown that competitive economies may possess sunspot equilibria that is rational expectations equilibria in which purely extrinsic uncertainty affects equilibrium prices and allocations 2 such results demonstrate that it does not require a lack of faith in the rationality of market participants to believe that competitive markets may be subject to purely speculative fluctuations driven solely by expectations 3 the mere existence of sunspot equilibria as solutions to a system of marketclearing conditions however might not be judged sufficient to indicate that competitive markets with rational participants could ever be subject to speculative instability the sunspot equilibria represent states of affairs in which agents act differently in the case of different realizations of the sunspot variable and it is rational for each agent to do so but it might be thought unlikely that the beliefs of all the participants in the market could ever come to be coordinated so as to bring about an equilibrium of that kind it is rational to believe that sunspots convey information about future states of affairs once the economy is in a sunspot equilibrium but why would rational agents ever begin to believe in such a thing so as to create the conditions under which the belief is rational in order to address such a question one must go beyond the mere statement of the conditions for equilibrium and discussion of what states of affairs satisfy them one must specify an explicit dynamic process according to which the beliefs of agents adjust when out of equilibrium any exercise of this kind is necessarily unsatisfactory as there is no univocal meaning for the postulate of rational behavior outside of an equilibrium it may well be the case that

instability of sunspot equilibria in real business cycle models under adaptive learning we examine the stability of equilibrium in sunspot driven real business cycle rbc models under adaptive learning we show that the general reduced form of this class of models can admit rational expectations equilibria that are both indeterminate and stable under adaptive learning indeterminacy of equilibrium allows for the possibility that non fundamental sunspot variable realizations can serve as the main driving force of the model and several researchers have put forward calibrated structural models where sunspot shocks play such a role we show analytically how the structural restrictions that researchers have imposed on this type of model lead to reduced form systems where equilibrium is indeterminate but always unstable under adaptive learning we thereby resolve a stability puzzle identified by evans and mcgough 2002

sentiments and aggregate demand fluctuations we formalize the keynesian insight that aggregate demand driven by sentiments can generate output fluctuations under rational expectations when production decisions must be made under imperfect information about demand optimal decisions based on sentiments can generate stochastic self fulfilling rational expectations equilibria in standard economies without persistent informational frictions externalities nonconvexities or strategic complementarities in production the models we consider are deliberately simple but could serve as benchmarks for more complicated equilibrium models with additional features

a note on jit purchasing vs eoq with a price discount an expansion of inventory costs in a previous international journal of production economics article a comparative model was presented for inventory costs of purchasing under economic order quantity eoq with quantity discounts and a just in time jit order purchasing system this paper expands the comparative model to include a relevant cost component not considered in the previous article the results of the revised model show di erences in the conclusions reached in the previous article more speci cally the superiority of jit in virtually any type of inventory ordering purchase decision 2000 elsevier science b v all rights reserved

stable near rational sunspot equilibria abstract we introduce a new class of solutions to nonlinear forward looking models called near rational sunspot equilibria nrse nrse are natural nonlinear extensions of the usual sunspot equilibria associated with the linearized version of the economy and are near rational in that agents use the optimal linear forecasting model when forming expectations generic results for existence and stability under learning are established nrse in indeterminate nonlinear models are found to be stable under learning provided that the corresponding linearized model s minimal state variable solution is e stable nrse are readily computable and our results make it possible to use the standard linear tools to search for stable nrse we illustrate our results using a canonical nonlinear new keynesian model

equilibrium selection observability and backward stable solutions abstract the robustness of stability under learning to observability of exogenous shocks is examined regardless of observability assumptions the minimal state variable solution is robustly stable under learning provided the expectational feedback is not both positive and large while the nonfundamental solution is never robustly stable overlapping generations and new keynesian models are considered and concerns raised in cochrane 2011 2017 are addressed

testing for indeterminacy an application to u s monetary policy reply this paper considers a prototypical new keynesian model in which the equilibrium is undetermined if monetary policy is passive the likelihood based estimation of dynamic equilibrium models is extended to allow for indeterminacies and sunspot fluctuations we construct posterior weights for the determinacy and indeterminacy region of the parameter space and estimates for the propagation of fundamental and sunspot shocks according to the estimated model u s monetary policy post 1982 is consistent with determinacy whereas the pre volcker policy is not we find that before 1979 indeterminacy substantially altered the propagation of shocks

the fragility of sunspots and bubbles abstract expectational stability e stability is used to examine the multiplicity of solutions in a range of rational expectations models of interest including muth s inventory model and an overlapping generations model in these model it is found that sunspot and other rational bubble solutions are either e unstable or weakly but not strongly e stable

from eoq towards zi zero inventory zi is a new and powerful concept to improve production efficiency underpinning zi is set up reduction and this paper examines what eventuates when set up costs are cut the folklore is that set up reduction lowers inventory and costs we obtain results contrary to that reducing set up costs need not reduce inventory for example likewise lowering set up costs need not necessarily lower total production and inventory costs furthermore most investments produce marginally decreasing returns set up cost reduction prompts the opposite it produces marginally increasing not decreasing returns a parametric algorithm that calculates the benefit of set up cost reduction is provided most presentations of zi have been descriptive with very few mathematical models of it yet untaken by modeling certain zi concepts mathematically we scrutinize their validity and sometimes invalidity

coalition formation problem for sourcing contract design in supply networks abstract this article studies a coalition formation problem for cooperative replenishment with a single supplier and multiple firms we consider that a vertical cooperation between the supplier and the set of firms is already set using periodic individual contracts and we investigate the profitability of a horizontal cooperation between firms when designing collaborative contracts given the significant savings that can be realized thanks to horizontal collaboration the main interest of the potential collaborating firms is to figure out how the collaborating group should be formed and how stable alliances and coalitions should be generated in this article the two questions are studied in two business situations focusing either on the collaboration opportunities in the ordering or the transportation process in each collaborative situation a decision making approach is applied to assess the expected profitability of each firm and to determine if firms should form coalitions to maximize their profits an exact solution method based on a game theoretic approach is developed called cooperative replenishment algorithm cra which generates core stable coalitions for cost savings regarding all partner standpoints an analytical study of stability conditions regarding the ordering and transportation cost structures were performed to enhance the cra resolution procedure extensive experiments based on realistic instances are provided to validate the performance of the cra proposed in terms of solution stability and convergence the computational results also confirm the potential benefit of horizontal collaboration between firms in terms of profit maximization compared to the stand alone situation

behavioral learning equilibria we propose behavioral learning equilibria where boundedly rational agents learn to use a simple univariate linear forecasting rule with correctly specified unconditional mean and first order autocorrelation in the long run agents learn the best univariate linear forecasting rule without fully recognizing the more complex structure of the economy an important feature of behavioral learning equilibria is simplicity and parsimony which makes coordination of individual expectations on such an aggregate outcome more likely in a first application an asset pricing model driven by ar 1 ar 1 dividends a unique behavioral learning equilibrium exists characterized by high persistence and excess volatility and it is stable under learning in a second application the new keynesian phillips curve multiple equilibria coexist learning exhibits path dependence and inflation may switch between low and high persistence regimes

the new keynesian liquidity trap abstract many new keynesian models produce a deep recession with deflation at the zero bound these models also make unusual policy predictions useless government spending technical regress capital destruction and forward guidance can raise output moreover these predictions are larger as prices become less sticky and as changes are expected further in the future i show that these predictions are strongly affected by equilibrium selection for the same interest rate path equilibria that bound initial jumps predict mild inflation small output variation negative multipliers small effects of far off expectations and a smooth frictionless limit fiscal policy considerations suggest the latter equilibria

heterogeneous expectations and bond markets this paper presents a dynamic equilibrium model of bond markets in which two groups of agents hold heterogeneous expectations about future economic conditions the heterogeneous expectations cause agents to take on speculative positions against each other and therefore generate endogenous relative wealth fluctuation the relative wealth fluctuation amplifies asset price volatility and contributes to the time variation in bond premia our model shows that a modest amount of heterogeneous expectations can help explain several puzzling phenomena including the excessive volatility of bond yields the failure of the expectations hypothesis and the ability of a tent shaped linear combination of forward rates to predict bond returns the author 2009 published by oxford university press on behalf of the society for financial studies all rights reserved for permissions please email journals permissions oxfordjournals org oxford university press

optimal selling strategies when to haggle when to hold firm a seller encountering risk neutral buyers one at a time should if commitments are feasible quote a single take it or leave it price to each this strategy is superior to any other for finite or infinite buyer populations whether there is learning or the distribution of buyer prices is known at the outset with one object for sale or many although haggling may offer advantages in terms of price discrimination these gains are more than offset by the losses it generates by encouraging buyers to refuse purchases at high prices

bargaining under incomplete information this paper presents and analyzes a bargaining model of bilateral monopoly under uncertainty under the bargaining rule proposed the buyer and the seller each submit sealed offers that determine whether the good in question is sold and the transfer price the nash equilibrium solution of this bargaining game implies an offer strategy of each party that is monotonic in its own reservation price and depends on its assessment of the opponent s reservation price issues of relative bargaining advantage and efficiency are examined for a number of special cases finally we discuss the appropriateness of the nash solution concept

towards a more economic production and just in time delivery system abstract we study a system in which a batch production supplier participates in just in time jit delivery of its products to a jit buyer firm we demonstrate that under certain conditions a small adjustment of previously agreed product selling price can result in a more economic production and jit delivery system with reduced delivery quantity and hence increased delivery frequency in the case when both buyer and supplier share equal profit margin optimal levels of adjustment for price and delivery frequency can be obtained that maximize the profit margin a numerical example is used to illustrate the results

learning about monetary policy rules abstract we study macroeconomic systems with forward looking private sector agents and a monetary authority that is trying to control the economy through the use of a linear policy feedback rule we use stability under recursive learning a la evans and honkapohja learning and expectations in macroeconomics princeton university press princeton new jersey 2001 as a criterion for evaluating monetary policy rules in this context we find that considering learning can alter the evaluation of alternative policy rules

on non uniqueness in rational expectations models an attempt at perspective abstract many macroeconomic models involving rational expectations give rise to an infinity of solution paths even when the models are linear in all variables some writers have suggested that this non uniqueness constitutes a serious weakness for the rational expectations hypothesis one purpose of the present paper is to argue that the non uniqueness in question is not properly attributable to the rationality hypothesis but instead is a general feature of dynamic models involving expectations it is also argued that there typically exists in a very wide class of linear rational expectations models a single solution that excludes bubble or bootstrap effects one that occur only because they are arbitrarily expected to occur a systematic procedure for obtaining solutions free from such effects is introduced and discussed in addition this procedure is used to interpret and reconsider several prominent examples with solution multiplicities including ones developed by fischer black and john b taylor

liquidity traps and expectation dynamics fiscal stimulus or fiscal austerity we examine global dynamics under infinite horizon learning in new keynesian models where the interest rate rule is subject to the zero lower bound as in evans guse and honkapohja 2008 the intended steady state is locally but not globally stable unstable deflationary paths emerge after large pessimistic shocks to expectations for large expectation shocks that push interest rates to the zero bound a temporary fiscal stimulus or a policy of fiscal austerity appropriately tailored in magnitude and duration will insulate the economy from deflation traps however fiscal switching rules that automatically kick in without discretionary fine tuning can be equally effective

modeling stockout risk and jit purchasing in ready mixed concrete batching plants abstract a model for comparing the inventory costs of purchasing under an economic order quantity eoq with a price discount system and a just in time jit order purchasing system concluded that jit purchasing is virtually always the preferable inventory ordering system this claim however contradicts the practices observed in ready mixed concrete rmc batching plants by expanding the eoq model and considering the stockout risks this paper derives new eoq jit cost indifference point equations we show that it is possible for an eoq with a price discount system to be more cost effective than a jit system when the stockout risks associated with the jit purchasing system are high or the annual demand is either too low or too high the case study conducted in the rmc industry in chongqing china supports our proposition

indeterminacy and increasing returns abstract we investigate properties of the one sector growth model with increasing returns under two organizational structures capable of reconciling the existence of aggregate increasing returns with competitive behavior by firms the first involves input externalities the second involves monopolistic competition we show for parameters in close accord with recent literature on real business cycles that the model displays an indeterminate steady state that can be exploited to generate a model of business fluctuations driven by self fulfilling beliefs in our first class of models growth is generated by exogenous increases in factor productivity in the second class the marginal product of capital is large enough for endogenous growth journal of economic literature classification numbers e00 e3 o40

economic growth with bubbles this paper presents a stylized model of economic growth with bubbles this model views asset price bubbles as a market generated device to moderate the effects of frictions in financial markets improving the allocation of investments and raising the capital stock and welfare the model illustrates various channels through which asset price bubbles affect the incentives for innovation and economic reforms and therefore the rate of economic growth the model also offers a new perspective on the effects of financial development on asset price bubbles and economic growth

fiscal policy in an expectations driven liquidity trap we study the effects of fiscal policy interventions in a liquidity trap in a model with nominal rigidities and an interest rate rule in a liquidity trap caused by a self fulfilling state of low confidence higher government spending has deflationary effects that reduce the spending multiplier when the zero lower bound is binding instead cuts in marginal labor tax rates are inflationary and become more expansionary when the zero lower bound is binding these findings contradict popular views about the effects of fiscal policy in a liquidity trap

are low interest rates deflationary a paradox of perfect foresight analysis we argue that an influential neo fisherian analysis of the effects of low interest rates depends on using perfect foresight equilibrium analysis under circumstances where it is not plausible for people to hold expectations of that kind we propose an explicit cognitive process by which agents may form their expectations of future endogenous variables perfect foresight is justified by our analysis as a reasonable approximation in some cases but in the case of a commitment to maintain a low nominal interest rate for a long time our reflective equilibrium implies neither neo fisherian conclusions nor implausibly strong predicted effects of forward guidance

the science of monetary policy an imperfect knowledge perspective this paper reevaluates the basic prescriptions of monetary policy design in the new keynesian paradigm through the lens of imperfect knowledge we show that while the basic logic of monetary policy design under rational expectations continues to obtain perfect knowledge and learning can limit the set of policies available to central banks rendering expectations management in general more difficult nonetheless the desirability of some form of price level targeting inducing inertia in interest rate policy paramount under rational expectations is robust to the assumption of imperfect knowledge

the perils of taylor rules abstract since john taylor s 1993 carnegie rochester conf ser publ policy39 195 214 seminal paper a large literature has argued that active interest rate feedback rules that is rules that respond to increases in inflation with a more than one for one increase in the nominal interest rate are stabilizing in this paper we argue that once the zero bound on nominal interest rates is taken into account active interest rate feedback rules can easily lead to unexpected consequences specifically we show that even if the steady state at which monetary policy is active is locally the unique equilibrium typically there exist an infinite number of equilibrium trajectories originating arbitrarily close to that steady state that converge to a liquidity trap that is a steady state in which the nominal interest rate is near zero and inflation is possibly negative journal of economic literature classification numbers e52 e31 e63

monetary policy indeterminacy and learning abstract forward looking monetary models with taylor type interest rate rules are known to generate indeterminacies with a potential dependence on extraneous sunspots for some structural and policy parameters we investigate the stability of these solutions under adaptive learning focusing on common factor or resonance frequency representations in which the observed sunspot has a suitable time series structure we consider specifications incorporating both lagged and expected inflation in the phillips curve and both expected and inertial elements in the policy rule we find that some policy rules can indeed lead to learnable sunspot solutions and we investigate the conditions under which this phenomenon arises

monetary policy and rational asset price bubbles i examine the impact of alternative monetary policy rules on a rational asset price bubble through the lens of an olg model with nominal rigidities a systematic increase in interest rates in response to a growing bubble is shown to enhance the uctuations in the latter

an optimization approach for supply chain management models with quantity discount policy abstract owing to the difficulty of treating nonlinear functions many supply chain management scm models assume that the average prices of materials production transportation and inventory are constant this assumption however is not practical vendors usually offer quantity discounts to encourage the buyers to order more and the producer intends to discount the unit production cost if the amount of production is large this study solves a nonlinear scm model capable of treating various quantity discount functions simultaneously including linear single breakpoint step and multiple breakpoint functions by utilizing the presented linearization techniques such a nonlinear model is approximated to a linear mixed 0 1 program solvable to obtain a global optimum

a note on the seller s optimal mechanism in bilateral trade with two sided incomplete information it is shown with an example that in bilateral trade problems with two sided incomplete information some seller types may obtain higher expected payos in mechanisms other than the one where they make a take it or leave it oer contrary to popular belief if one looks at the mechanism selection problem of the informed seller then the op timality of a take it or leave it oer for the seller is restored journal of economic literature classi cation numbers c72 c78 d82

just in time component replenishment decisions for assemble to order manufacturing under capital constraint and stochastic demand abstract while just in time ideas have been enthusiastically embraced by manufacturing practitioners the small replenishment batch sizes advocated are difficult to reconcile with the standard management science cost trade off approach in a previous paper by the authors which analysed a multi product manufacturing scenario under deterministic demand this difficulty was diagnosed as being due to the standard assumption that capital for inventory is borrowed and hence boundless when inventory is financed by investors and is thus finite the investment level must be treated as an additional variable in the decision to adopt inventory reduction policies for lean investments which might be chosen to maximise return on investment roi rather than absolute profit or for reasons of flexibility jit replenishment becomes more attractive for certain components than the standard analysis would suggest because the capital formerly invested in these components can be reinvested in the inventory of the remaining batch components to improve efficiencies this paper treats the stochastic version of the same problem develops a tractable solution method for the decision problem and in addition to reinforcing the findings of the previous study reveals several other ways in which jit replenishment and component substitution can improve performance by limiting the cost of dealing with uncertainty the analysis is illustrated using an actual case study of a small manufacturing enterprise seeking to reduce inventory and increase roi

equilibria of the sealed bid mechanism for bargaining with incomplete information we study the nash equilibria of the sealed bid bargaining mechanism with incomplete information a nonzero sum game for the case of uniform priors we describe two uncountably numerous families of equilibria the first has differentiable strategies in the second the strategies are step functions the efficiencies of these equilibria range from second best to zero for independent nonuniform priors we show that a similar situation obtains these results seem discouraging with regard to using the sealed bid mechanism in practice the mechanism might be salvaged however if bargainers turn out to confine themselves to linear strategy equilibria

eoq jit and fixed costs in the ready mixed concrete industry the successful implementation of just in time jit purchasing policy in many industries has prompted many companies that still use the economic order quantity eoq purchasing policy to ponder if they should switch to the jit purchasing policy despite existing studies that directly compare the costs between the eoq and jit purchasing systems this decision is however still difficult to be made especially when price discount has to be considered jit purchasing may not always be successful even though plants that adopted jit operations have experienced or can take advantage of physical space reduction hence the objective of this study is to expand on a classical eoq with a price discount model to derive the eoq jit cost indifference point the objective was tested and achieved through a survey and case study conducted in the ready mixed concrete industry in singapore

optimal policy for an inventory system with backlogging and all units discounts application to the composite lot size model this paper examines an inventory model with full backlogging and all units quantity discounts the practical scenario of a salesperson offering compensation to a client so as not to lose the sale is considered the cost of a backorder thus includes both a fixed cost and a further cost which is proportional to the length of time the said backorder exists a first algorithm is developed to determine the optimal policy while some extensions to this algorithm are obtained that include additional conditions on the model in particular the well known composite lot size model developed by tersine is solved incorporating a new stockout cost and a new all units discount numerical examples are provided to illustrate the application of the algorithms

price markdown scheme in a multi echelon supply chain in a high tech industry this paper studies the price markdown scheme in a supply chain that consists of a supplier a contract manufacturer cm and a buyer retailer the buyer subcontracts the production of the final product to the cm the cm buys the components from the supplier and charges the buyer a service fee for the final product produced the price markdown is made possible by the supplier with the development of new manufacturing technologies that reduce the production cost for the sourced component consequently the buyer adjusts the retail price in order to possibly stimulate stronger demand that may benefit both the supplier and the buyer under this scenario we identify the optimal discount pricing strategies capacity reservation and the stocking policies for the supplier and the buyer we also investigate the optimal inventory decision for the cm to cope with the price discount by considering both demand and delivery uncertainties our results suggest that higher production cost accelerates the effects of higher price sensitivity on lowering the optimal capacity and stocking policies in the supply chain the effect of mean demand error on the optimal prices is relatively marginal compared with that from price sensitivity we also found that increasing the standard deviation of the random demand does not necessarily increase the stocking level as one would predict the results show that delivery uncertainty plays an important role in the inventory carried beyond the price break we discuss potential extensions for future research

monetary policy and rational asset price bubbles comment we revisit gali s 2014 analysis by extending his model to incorporate persistent bubble shocks we find that under adaptive learning a stable bubbly steady state and the associated sunspot solutions under optimal monetary policy are not e stable when deriving the unique forward looking minimum stable variable msv solution around an unstable bubbly steady state we obtain results that are consistent with the conventional views leaning against the wind policy reduces bubble volatility and is optimal such a steady state and the associated msv solution are e stable

bilateral trade with the sealed bid k double auction existence and efficiency for k in the unit interval the k double auction determines the terms of trade when a buyer and a seller negotiate transfer of an item the buyer submits a bid b and the seller submits an offer s trade occurs if b exceeds s at price kb 1 k s we model trade as a bayesian game in which each trader privately knows his reservation value but only has beliefs about the other trader s value existence of a multiplicity of equilibria is proven for a class of trader s beliefs for generic beliefs however these equilibria are shown to be ex ante inefficient

real business cycles and the animal spirits hypothesis abstract we calibrate a quantitative equilibrium macroeconomic model with an aggregate technology that is subject to increasing returns and show that this model may display fluctuations at business cycle frequencies even when there are no shocks to the fundamentals of the economy these fluctuations are due to the self fulfilling beliefs of investors which we call animal spirits we compare the impulse response functions predicted by our model and by two other more standard models with a four variable vector autoregression on u s data our animal spirits economy is the most successful of the three at matching broad features of the dynamic responses in the data journal of economic literature classification numbers e00 e3 e32

expectational stability and the multiple equilibria problem in linear rational expectations models linear models involving expectations of future endogenous variables generally have multiple rational expectations equilibria this paper investigates the stability of solutions in the disequilibrium sense of whether given a small deviation of expectations functions from some rational expectations equilibrium the system returns to that solution under a natural revision rule weak and strong local stability are distinguished stability conditions are calculated for a simple general linear model and applied to two macroeconomic examples in some cases there is a unique stable equilibrium in other cases a continuum of equilibria forms a weakly but not strongly stable class

jit purchasing vs eoq with a price discount an analytical comparison of inventory costs abstract the inventory costs of purchasing under economic order quantity eoq model with a quantity discount is determined and compared to the costs under just in time jit it is shown that at low levels of demand jit is the preferred method whereas eoq has the cost advantage for an item with a high demand the model also predicts that the higher the value of the item the carrying cost or the ordering cost associated with the eoq model and the smaller the quantity discount rate the wider will be the range of demand for which jit remains preferable