Answer to Question #268309 in Microeconomics for Fliss

Question

Suppose that a Demand Curve is given by QY = 10 – 5PY + PX Where QY is the quantity of the good, PY is the price of the good and PX pertains to the price of a substitutable good. The price of the substitutable good is K2. Suppose the price of the good is K1. Find the own price elasticity of demand? Find the cross-price elasticity of demand?

Answer 1

Given,

Demand curve of good Y:

$QY=10−5P_Y+P_X$

Where,

Q_Y=Quantity of good Y

P_Y=Price of good Y

P_X=Price of good X

P_Y=price of the good Y=K1

P_X=price of the substitute good=K2

The following formulas will be used:

Price elasticity of demand $=\frac{∂Q_Y}{∂P_Y}×\frac{P_Y}{Q_Y}$

Cross−price elasticity of demand $=\frac{∂Q_Y}{∂P_x}×\frac{P_x}{Q_Y}$

Calculation of price elasticity of demand:

$\frac{∂Q_Y}{∂P_Y}=−5$

Let us substitute the values of P_Y and P_X in the demand function for quantity

 of good Y

$Q_Y=10−5×1+2\\Q_Y=10−5+2\\Q_Y=7$

Price elasticity of demand$=-5\times{1}{7}$

Price elasticity of demand=−0.71

Calculation of cross-price elasticity of demand:

$\frac{∂Q_Y}{∂P_X}=1\\P_X=K2\\Q_Y=7$

Cross−price elasticity of demand$=1\times \frac{2}{7}$

Cross−price elasticity of demand=0.29