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The following is the demand schedule for cement over a period of one week:-

NOTE: I have written the Price and Quantity demanded in tuples of the following form (Price, Quantity). So in the first case, the price is Rs 275 and the quantity demanded is 80 bags of cement.

Monday-(275,80)

Tuesday-(275,30)

Wednesday-(275,60)

Thursday-(275,70)

Friday-(275,50)

Saturday-(275,80)

Sunday-(275,100)

From the above data, you can see that the price is invariant over one week and that all consumers pay this price. However, after further investigation, I found that the price changes after a period of 15 days. Using this limited sample can one conclude that the demand for cement is perfectly elastic in the short run?

EDIT1: After @Ubiquitos' advice I came up with the following idea, which is partly described in a comment. Nevertheless here is the full argument:

Suppose that the equation of the Demand curve is given by the following equation$$q=\beta_0+\beta_1P+\epsilon_1$$ and the equation for the supply curve is given by$$q=\gamma_0+\gamma_1P+\epsilon_2$$. Notice that there is no other exogenous variable in any of the equations except $P$. I know that this quite a crude assumption as we know that there are non-price determinants such as taste and preferences that affect the quantity demeanded.Thus, it is possible that the error term, $\epsilon_1$ and $\epsilon_2$ are related to $P$ and thereby create a Selection Bias. Therefore, the parameters in both the equations cannot be determined. But I am still not sure how does this reasoning directly answer my initial question.

PS: If there are loops in my arguments, then please do suggest some rectifications as I am a beginner in econometrics...

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No, you do not have sufficient information to conclude that the demand is perfectly elastic.

The following figures show two ways that demand curves that are not perfectly elastics could have generated the first two data points in your series:

enter image description here

enter image description here

It should be easy to see how to add other demand curves to generate the rest of the data points.

This is actually a common and more general problem: price and quantity are jointly determined by the interaction of supply and demand. Given two data points, it is impossible to determine whether they were caused by a shift in supply or demand or both. There are two solutions to this dilemma:

  1. estimate a simulatenous equation model that accounts for both supply and demand. You can read about simultaneous equation models in a good econometrics textbook or, for example, in Dan McFadden's lecture notes.
  2. work in a context where you know either the supply or the demand curve are fixed. If you know the supply curve didn't move then any change in price or quantity must have come from a shift in demand and you know that all of your data points lie on (and characterise) the supply curve. The converse is true if you that the demand curve did not move.
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  • $\begingroup$ I'm curious how you produced those figures. A particular software? $\endgroup$ – Herr K. Dec 16 '15 at 16:49
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    $\begingroup$ @HerrK. Those were drawn in Illustrator for convenience. But if you are serious about producing nice figures then you should learn TikZ and PGFPlots. $\endgroup$ – Ubiquitous Dec 16 '15 at 21:54
  • $\begingroup$ I know that the supply remained constant during the time period I measured the demand. Will that be sufficient to conclude that Price is perfectly elastic. $\endgroup$ – Shrey Aryan Dec 17 '15 at 19:24
  • $\begingroup$ @ShreyAryan No. For example, in the top plot the supply doesn't shift but the demand curves are not perfectly elastic. As a practical matter, it is very unlikely to ever encounter perfectly elastic demand. That would mean that consumers are willing to buy any quantity (even an infinite amount) at a fixed price. Eventually, they will run out of money so the demand must eventually decrease to zero. $\endgroup$ – Ubiquitous Dec 17 '15 at 20:20
  • $\begingroup$ @Ubiquitous, I followed your advice and tried to gather as much information regarding the simultaneous equations models. For the purpose of my project I am supposed to disprove the validity of my data mathematically. Although I clearly understand your argument, I can't see how to translate it into mathematics? My modest attempt: Let the supply be given by $q=\beta_0+\beta_1P+\epsilon_1$ and the demand $q=\gamma_0+\gamma_1P+\epsilon_2$, then I can claim that the error term in both equations is dependent on price then, the parameters $\gamma_1$ and $\beta_1$ cannot be measured correctly. $\endgroup$ – Shrey Aryan Jan 22 '16 at 17:53

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