Cobweb Theorems with Production Lags and Price Forecasting

Daniel Dufresne and Felisa Vázquez-Abad (2013). Cobweb Theorems with Production Lags and Price Forecasting. Economics: The Open-Access, Open-Assessment E-Journal, 7 (2013-23): 1—49.
[下載 PDF: Download (pdf, 800.8 kB)](SSCI 期刊)

==noted by yinung==


生產落後期的例子: 挖礦 => 金屬生產
… An important aspect of mining is the lag between the time the decision to increase or decrease production
is made and the time the decision actually takes effect in the market. It takes several years for a planned new mine to start producing, …


Numerical Examples 1. l=落後期變長>=4, 價格波動變成發散


Numerical Examples 2. m=預期價格期數變長, 價格波動變成愈穩定

註: m =0 是典型 cobweb 理論, 即只用當期價格, 預測下一期價格


Numerical Examples 3. c= s/d =供給彈性/需求彈性, c 供需彈性比愈大, 價格波動愈不穩定


==original abstract==

(yinung 翻譯的)

The classical cobweb theorem is extended to include production lags and price forecasts. Price forecasting based on a longer period has a stabilizing effect on prices. Longer production lags do not necessarily lead to unstable prices; very long lags lead to cycles of constant amplitude. The classical cobweb requires elasticity of demand to be greater than that of supply; this is not necessarily the case in a more general setting. Random shocks are also considered.


* Chiarella (1988)studies a system where expected prices follow adaptive expectations, when the demand curve is linear, while the supply curve is non-linear…[The] paper shows that the system is either (1) stable, (2) unstable but cyclical, or (3) chaotic.

* Chiarella and He (2004). That paper studies the cobweb model from a slightly different point of view (in particular, the supply curve is a specific S-shaped function),


總體經濟學實驗文獻回顧 by Duffy

John Duffy (forthcoming) “Macroeconomics: A Survey of Laboratory Research." Handbook of Experimental Economics, Volume 2, Princeton University Press. link to PDF. (本站複本)

Notes by yinung

終於找到文獻回顧了! (哈, 其實以前已經找過了,… 人的記憶力真的很脆弱…)


1) 總體經濟之個體基礎評估
an assessment of the micro-assumptions underlying macroeconomic models,

2) 總體模型中預期形成之理解
a better understanding of the dynamics of expectations which play a critical role in macroeconomic models,

a means of resolving equilibrium selection (coordination) problems in environments with multiple equilibria,

4) 驗證沒有現地之料之總體模型預測結果
validation of macroeconomic model predictions for which field data are not available and

5) 各種總體政策干預對個人形為之影響
the impact of various macroeconomic policy interventions on individual behavior.

1) 總體經濟之個體基礎評估 (to be done)

主題例如: intertemporal consumption and savings decisions, inflation and unemployment, economic growth, bank runs, monetary exchange, monetary or fiscal policy

本文主要內容 (to be done)

2. Dynamic, Intertemporal Optimization

Optimal Consumption/Savings Decisions, Exponential discounting and infinite horizons

3. Coordination Problems

Poverty Traps, Bank Runs, Resolving Coordination Problems: Sunspots, Resolving Coordination Problems: The Global Game Approach

4. Sectoral Macroeconomics

5. Macroeconomic Policies

Ricardian equivalence, Commitment versus discretion, Monetary policy decision-making, Fiscal and tax policies, Exponential or Hyperbolic Discounting, Expectation Formation,

cobweb experiment – Google 學術搜尋

Idea: cobweb + SC: how cobweb market affect SC of upper stream

在 supply chain 中, 引用 cobweb 實驗? 看SC 如何對 cobweb 反應、price exp. formationz、response of quantities supplied by upper streams.

另, 有趣的課 syllabus:Expectations and choice behavior  by Claudia Neri, Assistant Professor in the Department of Economics at the University of St. Gallen

JA Carlson – Southern Economic Journal, 1967 – JSTOR
other, steeper. By the cobweb theorem, one market should have been stable and the
other unstable. Since of the market. They were also told that each of them would be
paid half of his cumulative profit at the end of the experiment.
S Arango… – … commodity cycles based on expanded Cobweb …, 2006 –
ABSTRACT This paper examines market behaviour in a series of Cournot market
experiments with five sellers. Step by step, we add complexity (and realism) to the basic
Cobweb market. First, we introduce long lifetimes of production capacity. Second, we
J Sonnemans, C Hommes, J Tuinstra… – Journal of Economic …, 2004 – Elsevier
Which strategies do agents use when forming expectations about future prices, and how
often does this lead to stable or unstable outcomes? We performed a four-round strategy
experiment in a cobweb economy with expectations feedback. Subjects received
CA Holt… – Atlantic Economic Journal, 1986 – Springer
Introduction Among economists, one of the least fashion- able theories of price adjustment is
the “cob- web theorem" that static expectations will induce a counterclockwise adjustment pattern
of prices and quantities around the intersec- tion of market supply and demand functions.
CH Hommes, J Sonnemans, J Tuinstra… – 1999 –
In our cobweb strategy experiment, subjects are asked to formulate a complete strategy, that
is, a description of all their forecasts in all possible states of the world (eg history of prices). The
(unknown) cobweb model underlying the experiment has a nonlinear, but monotonically
C Hommes, J Sonnemans… – Interaction and market structure, 2000 – Springer
An explanation for this is that the theoretic cobweb model with naive expectations and parameters
as in the experiment, leads to the stable equilibrium value in periods 29-40 . Figure 4 shows the
time series of participant 31 (experiment 1a), a typical example of category 1.
C Hommes, J Sonnemans… – Macroeconomic …, 2007 – Cambridge Univ Press
observations. The realized market price pt in the experiment is determined by the
cobweb market equilibrium equation in which demand equals total supply; that is,
D(pt ) = K ∑ i=1 S ( pe i,t ) , (2) Page 7. 14 HOMMES ET AL.
C Hommes, J Sonnemans, J Tuinstra… – Journal of Economic …, 2008 – Elsevier
There it was shown that, for an unstable cobweb model, the heterogeneity of expectations leads
to excess volatility of realized prices. In particular, in the experiment presented in that paper an
upper bound on prices and predictions is used that is much lower than the one in the
S Arango… – … cycles based on expanded Cobweb …, 2006 –
Arango (2006b) extends the simplest Cobweb market5, step by step, by including a four period
lifetime of production capacity and a two period Arango (2006b) presents a continuation of the
previous experiment replacing the linear demand by a constant elasticity demand.
C Hommes, J Sonnemans, J Tuinstra… – Journal of Economic …, 2005 – Elsevier
see Selten et al. (1997), Keser (1992), Offerman et al. (2001), Sonnemans (1998);
and also the classic work of Axelrod (1984)). Sonnemans et al. (2004) present a
similar strategy experiment for a ‘cobweb‘, corn market model.
R Dieci… – Applied Mathematics and Computation, 2009 – Elsevier
All rights reserved. Permissions & Reprints. Stability analysis of a cobweb model with market
interactions. Available online 4 August 2009. Abstract. This paper explores the steady-state
properties and the dynamic behavior of a generalization of the classical cobweb model.
R Dieci… – Journal of Economic Behavior & Organization, 2010 – Elsevier
doi:10.1016/j.jebo.2010.05.004 | How to Cite or Link Using DOI Copyright © 2010 Elsevier BV
All rights reserved. Permissions & Reprints. Interacting cobweb markets star, open. Abstract. We
enrich the classical cobweb framework by allowing producers to enter different markets.
E Moxnes –
Arango (2006b) extends the simplest Cobweb market5, step by step, by including a four period
lifetime of production capacity and a two period Arango (2006b) presents a continuation of the
previous experiment replacing the linear demand by a constant elasticity demand.
S Casellina, S Landini… – Computational Economics, 2011 – Springer
Credit market dynamics: a cobweb model 1). The specular dynamics of fixed-rate vs
adjustable-rate suggests that the structure of an aggregate cobweb model type is suitable
when based on demand and supply of these two kinds of financial contracts.
G Bottazzi, G Devetag… – Journal of Economic Behavior & …, 2010 – Elsevier
Sonne- mans et al. (2004) use a non linear cobweb model that Their results show rare
convergence to the stable equilibrium while increasing amplitude of price uctuations and the
emergence of chaotic dynamics especially towards the end of the experiment. In Hommes et
R Garratt – The Journal of Economic Education, 2000 – Taylor & Francis
outcomes is the coordination prob- lem that these researchers address.’ The feature that separates
this experiment from decentralized Furthermore, because students can observe each other’s
choices and make adjustments within rounds, cobweb cycles that often occur when
C Hommes… – 2008 –
market scenarios. Finally, Section 6 concludes. 2 The forecasting experiment
Hommes et al. (2007) report on a set of cobweb experiments with k = 6 participants
per session. Their participants were asked to predict next pe-
RH Day… – The Economic Journal, 1969 – JSTOR
possible with economy of means to achieve a simple but powerful generalisation of the cobweb
FH Hahn – The Review of Economic Studies, 1955 –
Page 7. UNCERTAINTY AND THE COBWEB 71 from equilibrium output less than it would
otherwise have been (at the same expected price). utility analysis, the assumptions of a cardinal
index and the maximisation of expected utility can certainly be contradicted by experiment.
A Škraba, D KOFJAˇC, M BREN… – Proceedings of the 4th …, 2005 –
The solution of the periodicity conditions for the 2-d discrete linear cobweb map provided the
means to determine the periodicity The bi- furcation experiment with the nonlinear mapping
provided the example of periodicity transposition to the systems of higher complexities.
F Declerck, LM Cloutier, M Fritz… – … , February 18-22, …, 2008 –
Cobweb strategy experiments have been used by rese- archers interested in the formation of
expectations and of their impacts. Subjects in experiments formulate a complete strategy with
price forecasts for all possible states of the world. From pe- riod-to-period, experiment