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# Calculating the Elasticity Coefficients

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The demand curve for a product is given by QXd = 1,200 - 3PX - 0.1PZ where Pz = \$300.

a. What is the own price elasticity of demand when Px = \$140? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below \$140?

Instruction: Round your response to 2 decimal places.

Own price elasticity:

Demand is:

If the firm prices below \$140, revenue will:

b. What is the own price elasticity of demand when Px = \$240? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price above \$240?

Instruction: Round your response to 1 decimal place.

Own price elasticity:

Demand is:

If the firm prices above \$240, revenue will:

c. What is the cross-price elasticity of demand between good X and good Z when Px = \$140? Are goods X and Z substitutes or complements?
Instruction: Round your response to 2 decimal places.

Cross-price elasticity:

Goods X and Z are:

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#### Solution Preview

The demand curve for a product is given by QXd = 1,200 - 3PX - 0.1PZ where Pz = \$300.

a. What is the own price elasticity of demand when Px = \$140? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below \$140?

QXd=1200-3PX-0.1PZ
Put Pz=300
QXd=1200-3PX-0.1*300=1170-3PX

Differentiate with respect to PX we get
d(QXd)/dPX=-3

Now calculate QXd at Px=\$140
QXd=1170-3PX=1170-3*140=750

Own price elasticity of demand=Ep=d(QXd)/dPX*(Px/QXD)=-3*(140/750) =-0.56

Own ...

#### Solution Summary

Solution depicts the steps to estimate the elasticity coefficients in the given case.

\$2.19

## Interpret the coefficients in the estimated regression equation.

We believe that the quantity of hamburger (Qh) purchased within a market is a function of its own price (Ph), the price of chicken (Pc), advertising expenditures (A) and household disposable income (I). Using data available to the research team, we have estimated the following linear regression relationship:

Qh = 205.2 - 200*Ph + 100*Pc + 0.023*A + 0.0005*I

(a) How might we interpret the coefficients in the estimated regression?

(b) What is the forecasted demand for hamburger when Ph is \$1.00, Pc is \$1.20, A is \$5,000 and I is \$20,000?

(c) Calculate the own price elasticity for hamburger. If price were to decrease by 1% would the total revenue for hamburger increase or decrease? Explain.

(d) Calculate the cross price elasticity with respect to chicken price, the advertising elasticity and the income elasticity using the information listed and calculated in (b). Interpret the economic meaning of these measures.

(e) Which of the explanatory variable has the greatest impact on hamburger demand? Explain.

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