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.
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...