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Calculating the Elasticity Values in the Given Case

Suppose the estimated demand equation of good X looks as follows:

QX = 10,000 - 2 PX + 3 PY - 4.5M
Where Px is the price of the product itself
PY is the price of another (related) good
M is buyers' income.

Suppose currently PX = $100, PY = $50, and M = $2,000.
a. What is the price elasticity of demand of good X?

b. What is the cross-price elasticity of good X with respect to the price of good Y?

c. what is the income elasticity of good X?

d. Estimate the demand function (representing the demand curve) of this product.

e. Suppose the local government decides to raise the sales tax on product X, causing the price to rise by 10%. Will sales of the product X rise or fall, and by what percentage amount?

f. If the seller of the product (X) wants to increase her sales quantity by 10% through a price-change, what should she do to price - increase? decrease? By what percentage amount?

Solution Preview

a. What is the price elasticity of demand of good X?

First we calculate the quantity demanded at given parameters.
QX = 10,000 - 2 PX + 3 PY - 4.5M
Put PX=$100, PY=$50 and M=$2000
QX=10000-2*100+3*50-4.5*2000=950

We are given that
QX = 10,000 - 2 PX + 3 PY - 4.5M
Differentiate QX with respect to PX, we get
dQX/dPX=-2

Price elasticity of demand=(dQX/dPX)*(PX/QX)=-2*(100/950)= -0.21

b. What is the cross-price elasticity of good X with respect to the price of good Y?
We have calculated in part (a) that QX=950 at given parametes.

We are given that
QX = 10,000 - 2 PX + 3 PY ...

Solution Summary

Solution describes the steps to estimate the price elasticity of demand, cross-price elasticity of demand and income elasticity of demand in the given case. It also studies the impact of price changes on quantity demanded.

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