Question

A. Suppose Company A is selling notebooks in California, and the demand function for the notebooks in California is

QC = 100 − p. When the price elasticity of demand is equal to 1, what are the corresponding price and quantity sold in the market?

b. Now suppose Company A decides to sell the identical notebooks in Texas, and the demand function for the notebook in Texas is QT = 80 − 2p. When the price of notebook is equal to $5 each, what will be the price elasticity of demand in each market?

Answer 1

A).

Here the demand curve is given by, => Qc=100-P, => dQc/dP = (-1). Now, the price elasticity is “-1”.

=> e = (-1), => (dQc/dP)*(P/Qc) = (-1) , => (-1)*(P/Qc) = (-1), => P/100-P = 1, => P=100-P, => P=50, => Q=50. So, here the price and the quantity sold are given by, => “P=50” and “q=50” respectively.

B).

In Texas the demand curve is given by, => QT = 80 - 2P, => dQt/dP = (-2), => the elasticity is given by, => e=(dQt/dP)*(P/Qt) = (-2)*(5/80-2*5) = (-2)*(5/70) = (-0.1428).

In California the demand curve is given by, => Qc = 100 - P, => dQc/dP = (-1), => the elasticity is given by, => e=(dQc/dP)*(P/Qt) = (-1)*(5/100-5) = (-1)*(5/95) = (-0.0526). So, here the price elasticity of demand for “P=5” are given.