<p>In the basic "Cobweb Theorem", the assumption is that suppliers must decide now next period production, and that they assume that next period market price will be equal to current period market price.  </p>

<p>$$p^e_{t} = p_{t-1} \tag{1}$$</p>

<p>Now, we know that <em>if</em> price follows a random walk without drift, <em>then</em> the above a priori assumed expectations formation hypothesis coincides with the Rational Expectations Hypothesis:</p>

<p>$$\text {If}\;\;\; p_{t} = p_{t-1} + u_{t} ,\;\;\; u_{t} \sim WN \implies E_{t-1}p_{t} = p_{t-1} \tag{2}$$</p>

<p>But in the cobweb model, the actual price process <em>is determined endogenously</em>, <em>given</em> the a priori assumption $(1)$: we assume $(1)$ and we let the equilibrium of the model give us the model-consistent price process. </p>

<p>Assuming linear demand  (say, with a white noise preference shock), and supply function we have</p>

<p>$$D_t = a-bp_t +u_t,\;\;\; S_t = \gamma + \delta p^e_t$$</p>

<p>Imposing market clearing (an additional assumption no less) we have</p>

<p>$$D_t = S_t \implies p_t = \frac {a-\gamma}{b} - \frac {\delta}{b} p^e_t +u_t$$</p>

<p>and applying the a priori expectations formation assumption $(1)$ we obtain</p>

<p>$$p_t = \frac {a-\gamma}{b} - \frac {\delta}{b} p_{t-1} + u_t\tag{3}$$</p>

<p>$(3)$ is the model-consistent price process here (i.e. given $(1)$), not $(2)$. Only in the case that $a=\gamma, b=-\delta$ do we get that the price process emerges as a random walk without drift and so that the expectations formations hypothesis used in the model coincides with the Rational Expectations hypothesis. </p>

<p>The price that suppliers use is the current market clearing price indeed. But <em>how</em> they use it (hypothesis $(1)$), does not "reflect all available information", which is embodied in $(3)$ which suppliers ignore.</p>

CC BY-SA 3.0
2016-11-05T19:03:47.490Z
2016-12-02T03:12:42.790Z
2016-12-02T03:12:42.790Z
Alecos Papadopoulos
<p>In the cobweb theorem it is assumed that the producers follow an adaptive expectation, however if the price they look to determine their production reflects all the available information at the moment, so this price is in the context of the efficient market hypothesis and therefore it is formed under the rational expectation.
What is wrong here? </p>

CC BY-SA 3.0
2016-08-30T19:17:14.680Z
EMH stems from rational expectations, so without them you don't have that result. Cobweb stems from adaptive, so you don't get EMH.
VCG
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2016-08-30T19:59:50.823Z
Definitely, however what is wrong with my reasoning?
unmark1
CC BY-SA 3.0
2016-08-30T20:01:02.613Z
When you say "price is in the context of EMH and therefore..." I don't see how that seems true.
VCG
CC BY-SA 3.0
2016-08-30T20:11:08.197Z
if you were a producer and you would like to fix your production today, say for example corn, what price you were looking at? Wouldn't it be the price which is being traded at CME? And this price is in the context of EMH.
unmark1
CC BY-SA 3.0
2016-08-30T20:14:18.680Z
I still don't know what "price in context" means.
VCG
CC BY-SA 3.0
2016-08-30T20:31:19.077Z
meaning it reflects all available information.
unmark1
CC BY-SA 3.0
2016-08-30T20:34:08.413Z
Well if it happens to in this case, that doesn't mean expectations are rational. Just that the price happens to have that property. I don't think the EMH is bijectional.   But why do you think the price contains all the information?
VCG
CC BY-SA 3.0
2016-08-30T20:41:26.067Z
because otherwise it would permit an arbitrage. Can we move to chat, i really liked your point about bijectional.
unmark1
CC BY-SA 3.0
2016-08-30T20:44:21.560Z
Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/44701/discussion-between-vcg-and-unmark1).
VCG
CC BY-SA 3.0
2016-09-02T14:40:52.817Z
I've found this which offers a good explanation: http://developing-trade.com/wp-content/uploads/2014/11/DTC-Article-Chapter-2011-4.pdf
unmark1
<microeconomics>
Cobweb theorem and rational expectation
unmark1
# Cobweb theorem and rational expectation

(Asked by: username_0 on 2016-08-30)

In the cobweb theorem it is assumed that the producers follow an adaptive expectation, however if the price they look to determine their production reflects all the available information at the moment, so this price is in the context of the efficient market hypothesis and therefore it is formed under the rational expectation.
What is wrong here?

**Tags:** microeconomics
> **Comments:**
> **username_1**: EMH stems from rational expectations, so without them you don't have that result. Cobweb stems from adaptive, so you don't get EMH.  
> **username_0**: Definitely, however what is wrong with my reasoning?  
> **username_1**: When you say "price is in the context of EMH and therefore..." I don't see how that seems true.  
> **username_0**: if you were a producer and you would like to fix your production today, say for example corn, what price you were looking at? Wouldn't it be the price which is being traded at CME? And this price is in the context of EMH.  
> **username_1**: I still don't know what "price in context" means.  
> **username_0**: meaning it reflects all available information.  
> **username_1**: Well if it happens to in this case, that doesn't mean expectations are rational. Just that the price happens to have that property. I don't think the EMH is bijectional.   But why do you think the price contains all the information?  
> **username_0**: because otherwise it would permit an arbitrage. Can we move to chat, i really liked your point about bijectional.  
> **username_1**: Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/44701/discussion-between-vcg-and-unmark1).  
> **username_0**: I've found this which offers a good explanation: http://developing-trade.com/wp-content/uploads/2014/11/DTC-Article-Chapter-2011-4.pdf  

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## 1 answers

### Answer by username_2 on 2016-11-05. Score: 2

In the basic "Cobweb Theorem", the assumption is that suppliers must decide now next period production, and that they assume that next period market price will be equal to current period market price.

$$p^e\_{t} = p\_{t-1} \tag{1}$$

Now, we know that *if* price follows a random walk without drift, *then* the above a priori assumed expectations formation hypothesis coincides with the Rational Expectations Hypothesis:

$$\text {If}\;\;\; p\_{t} = p\_{t-1} + u\_{t} ,\;\;\; u\_{t} \sim WN \implies E\_{t-1}p\_{t} = p\_{t-1} \tag{2}$$

But in the cobweb model, the actual price process *is determined endogenously*, *given* the a priori assumption $(1)$: we assume $(1)$ and we let the equilibrium of the model give us the model-consistent price process.

Assuming linear demand (say, with a white noise preference shock), and supply function we have

$$D\_t = a-bp\_t +u\_t,\;\;\; S\_t = \gamma + \delta p^e\_t$$

Imposing market clearing (an additional assumption no less) we have

$$D\_t = S\_t \implies p\_t = \frac {a-\gamma}{b} - \frac {\delta}{b} p^e\_t +u\_t$$

and applying the a priori expectations formation assumption $(1)$ we obtain

$$p\_t = \frac {a-\gamma}{b} - \frac {\delta}{b} p\_{t-1} + u\_t\tag{3}$$

$(3)$ is the model-consistent price process here (i.e. given $(1)$), not $(2)$. Only in the case that $a=\gamma, b=-\delta$ do we get that the price process emerges as a random walk without drift and so that the expectations formations hypothesis used in the model coincides with the Rational Expectations hypothesis.

The price that suppliers use is the current market clearing price indeed. But *how* they use it (hypothesis $(1)$), does not "reflect all available information", which is embodied in $(3)$ which suppliers ignore.


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