# Calculating Elasticity Values and Demand Curve

1. The demand curve for a product is given by Qdx =1,000 - 2pPx +.02Pz where Pz = $400.

a. What is the own price elasticity of demand Px = $154? Is demanded elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $154?

b. What is the own price elasticity of demand Px = $354? Is demanded elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $354?

c. what is the cross-price elasticity of demand between good X and good Z when Px = $154? Are goods X and Z substitutes or compliments?

2. Suppose the demand function for a firm's product is given by

In Qdx =3-0.5 In Px - 2.5 In Py+In M+2 In A

Where

Px = $10

Py = $4

M = $20,000, and

A =$250

a. Determine the own price elasticity of demand, and state whether demand is elastic, inelastic, or unitary elastic.

b. Determine the cross-price elasticity of demand between good X and good Y, and state whether these two are substitutes or complements.

c. Determine the income elasticity of demand, and state whether good X is a normal or inferior good.

d. Determine the own advertising elasticity of demand.

#### Solution Preview

1. The demand curve for a product is given by Qdx =1,000 - 2Px +.02Pz where Pz = $400.

a. What is the own price elasticity of demand Px = $154? Is demanded elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $154?

Qdx =1,000 - 2Px +.02Pz

On, differentiating with respect to Px, we get

d(Qdx)/dPx=-2

Value of Qdx at Px=$154 and Pz=$400

Qdx=1000-2*154+0.02*400=700

Own price elasticity of demand= [d(Qdx)/dPx]*[Px/Qdx]

=-2*(154/700)=-0.44

Absolute value of own price elasticity of demand is less than 1, we can say that demand is inelastic at Px=$154.

In case of inelastic demand, total revenue will decrease if price decreases. We can say that total revenue will fall if firm changes a price below $154.

b. What is the own price elasticity of demand Px = $354? Is demanded elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $354?

Qdx =1,000 - 2Px +.02Pz

On, differentiating with respect to Px, we get

d(Qdx)/dPx=-2

Value of Qdx at Px=$354 and Pz=$400

Qdx=1000-2*354+0.02*400=300

Own ...

#### Solution Summary

There are two problems. Solutions to these problems describe the step by methodology to calculate price elasticity of demand, cross price elasticity of demand, income elasticity of demand and own advertising elasticity of demand. It also predicts the nature of goods based upon calculated elasticity values.