Price-taking Strategy Versus Dynamic Programming in Oligopoly

In a quantity-competed duopoly, one firm is a naive price-taker (who responses only to the last period’s price) while the other has all the market information so as be able to optimize its profit stream (either discounted or un-discounted) dynamically over a finite or infinite horizon. With a traditional linear economy, we are able to derive algebraically the optimal policies of all periods for the dynamic optimizer. A counter-intuitive phenomenon is then observed: regardless of the planning horizon and the discounted factor, there exists a relative profitability range of initial prices, starting with which the price-taker make higher profit than the dynamic optimizer. Furthermore, with the increase in the planning horizon, the price-taker’s relative profitability range increases accordingly and finally covers the entire economically meaningful range.Economics; dynamic programming; Bellman’s optimality principle; applied OR; duopoly

Relative Profitability of Dynamic Walrasian Strategies

The advantage of price-taking behavior in achieving relative profitability in oligopolistic quantity competition has been much appreciated recently from economic dynamics and evolutionary game theory, respectively. The current research intends to provide a direct economic interpretation as well as intuitive justification and further to build a linkage between different perspectives. In particular, a detailed illustration of an arbitrary oligopoly that produce a homogenous product is presented. So long as the outputs of other firms are fixed and the residual demand is downward sloping, for any two identical firms whose cost functions are convex, their output space can be divided symmetrically into mutually exclusive relatively profitability regimes. Furthermore, there exist infinitely many relative-profitability reactions for each firm in such “residual” duopoly, all of which intersect at the “residual” Walrasian equilibrium. This suggests that sticking to this dynamical equilibrium output constantly (i.e., the static Walrasian strategy) turns out to be a relative-profitability strategy at each period. On the other hand, regardless of what strategies its rival may take, a firm adopting price-taking strategy or more generally defined dynamic Walrasian strategies can achieve the relative profitability if an intertemporal equilibrium is reached. The methodology adopted and the conclusions arrived clarify the confusions and misunderstandings due to the different usages of same terminologies under different frameworks and generalize the previous available results in the literature to a higher level and a broader context.Price-taking, Walrasian behavior, Relative profit, Oligopoly, Cournot, dynamic Walrasian strategy.

Risk and Predictability of Singapore’s Direct Residential Real Estate Market

This study explores the topic of the predictability of direct real estate prices in the short-run and the risks facing investors via a case study. Two models are estimated using heteroscedastic and autocorrelation robust ML method. Possible structural shifts of the models are examined. The one assuming that the model captures all the economic influences produces slightly better in-sample fitting. The other model assumes that there could be some important information which is not publicly available. Such information can nevertheless be extracted using Kalman filter. The latter has smaller forecast error in general. We found that a rational speculative bubble is an important predictor of short-run price movement, especially when the market is volatile and noisy. Rental is the only fundamental variable which has any important role to play in the short-run price generating process. Further more, the influence of rental is significant only when the market is inactive. Based on the study, we argue that the risk facing market participants comes not from the rational speculative bubble given its predictability, but primarily from unpredictable local policy shifts.Risk; information; rational bubble; Kalman filter

A New Approach to Detect Spurious Regressions using Wavelets

In this paper, we propose the use of wavelet covariance and correlation to detect spurious regression. Based on Monte Carlo simulation results and experiments with real exchange rate data, it is shown that the wavelet approach is able to detect spurious relationship in a bivariate time series more directly. Using the wavelet approach, it is sufficient to detect a spurious regression between bivariate time series if the wavelet covariance and correlation for the two series are significantly equal to zero. The wavelet approach does not rely on restrictive assumptions which are critical to the Durbin Watson test. Another distinct advantage of the graphical wavelet analysis of wavelet covariance and correlation to detect spurious regression is the simplicity and efficiency of the decision rule compared to the complicated Durbin-Watson decision rules.Wavelet analysis, spurious regression

A New Approach to Optimization of Dynamic Reactive Power Sources Addressing FIDVR Issues

Dynamic reactive power (var) sources, e.g. SVCs and STATCOMs, can effectively mitigate fault-induced delayed voltage recovery (FIDVR) issues or even voltage collapse. However, their optimal allocation in a power grid is a complicated nonlinear optimization problem since the post-fault voltage trajectories have to be solved to check constraints on voltage responses. Thus, solvers of both nonlinear optimization and power system differential and algebraic equations (DAEs) are required. Currently, most of existing methods merely achieve dynamic optimization locally with great dependence on the initial operation point. Also, complicated algorithm and time consuming are obstacles for the practical implementation. This thesis proposes a new approach to optimize the sizes of dynamic var sources at candidate locations by efficiently interfacing a heuristic linear programming based searching algorithm with power system simulation software. Within several iterative search steps, the optimal size of dynamic var can be achieved. In order to verify the result obtained from the proposed approach, Voronoi diagram is applied to tackle the feasible solution area, and then to demonstrate the result of heuristic linear programming is the global optimal. Case studies on a 9-bus system and the IEEE 39-bus system have benchmarked the new approach with an existing representative approach and demonstrated that the new approach can quickly converge to an optimal solution. Voronoi diagram is implemented to tackle non-convex feasible solution area of both cases and it shows that the result is global optimal

Estimating Behavioural Heterogeneity Under Regime Switching

Financial markets are typically characterized by high (low) price level and low (high) volatility during boom (bust) periods, suggesting that price and volatility tend to move together with different market conditions/states. By proposing a simple heterogeneous agent model of fundamentalists and chartists with Markov chain regime-dependent expectations and applying S&P500 data from January 2000 to June 2010, we show that the estimation of the model matches well with the boom and bust periods in the US stock market. In addition, we find evidence of time-varying behavioural heterogeneity within-group and that the model exhibits good forecasting accuracy.estimation; heterogeneity; regime switching; boom and bust

Lithium atom storage in nanoporous cellulose via surface induced Li2\rm Li_2 breakage

We demonstrate a physical mechanism that enhances a splitting of diatomic $\rm Li_2$ at cellulose surfaces. The origin of this splitting is a possible surface induced diatomic excited state resonance repulsion. The atomic Li is then free to form either physical or chemical bonds with the cellulose surface and even diffuse into the cellulose layer structure. This allows for an enhanced storage capacity of atomic Li in nanoporous celluloseComment: 5 pages, 6 figure