Final answer:
The OLS estimator for price in the demand equation for coffee could be biased if there are omitted variables that correlate with both price and quantity.
For the estimator to be consistent, all relevant factors must be included in the model. Given that the demand for coffee is inelastic, changes in price have less effect on quantity demanded, but equilibrium is achieved when the quantity demanded equals the quantity supplied.
Step-by-step explanation:
The OLS estimator for price in the regression equation q1 = β1 + β2 P1 + β3 income + ei, where Q is the quantity demanded, P is the store price, and income is the average household income, could be biased if there are omitted variables that correlate with both price and quantity demanded which are not included in the regression.
If such relevant variables are omitted, the estimated coefficient on price, β2, would be capturing not only the effect of the price but also the effects of these omitted variables.
For the estimator to be consistent, the error term ei should not be correlated with the regressors, meaning that all variables that correlate with both price and quantity demanded should be included in the model.
Considering the law of demand and the law of supply, it is evident that as the price changes, consumer behavior also changes. In the case of coffee, the demand is described as inelastic, meaning that a percentage increase in price will result in a smaller percentage decrease in quantity demanded.
However, if there are other factors affecting demand or supply that are not controlled for, such as preferences or the number of stores, these could bias the OLS estimator.