We know that:
M = 20 (in thousands)
Py = 2
Px = 14
Q = 14000
Q = 20000 - 500*Px + 25*M + 250*Py
From Using Calculus To Calculate Price Elasticity of Demand we see that:
we can calculate any elasticity by the formula:
Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z)
In the case of price elasticity of demand, we are interested in the elasticity of quantity demand with respect to price. Thus we can use the following equation:
Price elasticity of demand: = (dQ / dPx)*(Px/Q)
In order to use this equation, we must have quantity alone on the left-hand side, and the right-hand side be some function of price. That is the case in our demand equation of 20000 - 500*Px + 25*M + 250*Py. Thus we differentiate with respect to P and get:
dQ/dPx = -500
So we substitute dQ/dP = -500, Px=14, and Q = 20000 - 500*Px + 25*M + 250*Py into our price elasticity of demand equation:
Price elasticity of demand: = (dQ / dPx)*(Px/Q)
Price elasticity of demand: = (-500)*(14/20000 - 500*Px + 25*M + 250*Py)
Price elasticity of demand: = (-500*14)/14000
Price elasticity of demand: = (-7000)/14000
Price elasticity of demand: = -0.5
Thus our price elasticity of demand is -0.5.
Since it is less than 1 in absolute terms, we say that Demand is Price Inelastic. This means that consumers are not very sensitive to price changes, so a price hike will lead to increased revenue for the industry.
That's the end of this Q&A. I hope everyone found it useful!