I have the following regression to interpret elasticity of demand:
$$\ln(demand) = const - 0.6*\ln(fare)$$
I understand that a 1% increase in fare results in a 0.6% decrease in demand
I want to add dummy variables for days of week (excluding one of course) and want to add day-of-week $* \ln(fare)$ interactions so that I can determine the elasticity of demand by day of week (which I already know differs)
For simplicity in writing this out let’s pretend there are 3 days: mon, tue, wed and I will leave Wednesday out as my base
So now my regression is:
$$\ln(demand) = const - 0.45*\ln(fare) + 10*(mon) + 15*(tue) + 0.05*\ln(fare)*(mon) - 0.15*\ln(fare)*(tue)$$
Here, my elasticity of demand for Wednesday is interpreted as a 1% increase in fare results in a 0.45% decrease in demand
But my question is how to interpret elasticity of demand for Tuesday. I know that the interaction and even the dummies are relative to the base.
So the question is for Tuesday should The coefficients be added? Or multiplied since it’s logged?