We had a lecture on calculating elasticity in microeconomics and I need help understanding how the answer was derived. I didn't quite get how we came up with the answer. My classmate said to just substitute, but what happened to .03I - .4P + 2P?
Demand function for goodx:
QxD = 5 - 2Px + .03I - .4P + 2P
Find the ExD where Px = 2 and QxD = 1
ExD = 2QxD / 2Px = 2 * 2/1 = -4
Interpretation: Thus, / ExD /=4, generally means that every 1% increase in the price of goodx will result to a 4% decrease in quantity demanded, ceteris paribus.
An economics question? It might belong in a different exchange, but i find myself partial to this one... we have the demand function for good x: QxD = 5 - 2Px + .03I - .4P + 2P and we want to find the own price elasticity of demand, ExD, where Px = 2 and QxD = 1.
The"2" in the elasticity in formula (2$ Q_x^D$) is really the "$\partial$" sign ($\partial Q_x^D$), representing a partial derivative (partial slope) and the correct formula is:
$ E_x^D = \frac{\partial Q_x^D}{\partial P_x} \frac{ P_x}{Q_x^D} = -2 \frac{2}{1} = -4$
Your interpretation is correct. What happened to .03I - .4P + 2P? When taking a partial derivative, the remaining terms (other than $P_x$), are treated as constants. Now, since the derivative is measuring the rate of change (or slope), and since the constant terms do not change, their rate of change is zero and they ($I, P, $and $P$) drop out of the elasticity term. Does this reply help?