# Regression and Price Elasticity

The Pilot Pen Company has decided to use 15 test markets to examine the sensitivity of demand for its new product to various prices, as shown in the following table. Advertising effort was identical in each market. Each market had approximately the same level of business activity and population.

a. Using a linear regression model, estimate the demand function for Pilot's new pen.

b. Evaluate this model by computing the coefficient of determination and by performing a t-test of the significance of the price variable.

c. What is the price elasticity of demand at a price of 50 cents?

Test Price Quantity Sold Market Charged (thousands of pens)

1 50¢ 20.0

2 50¢ 21.0

3 55¢ 19.0

4 55¢ 19.5

5 60¢ 20.5

6 60¢ 19.0

7 65¢ 16.0

8 65¢ 15.0

9 70¢ 14.5

10 70¢ 15.5

11 80¢ 13.0

12 80¢ 14.0

13 90¢ 11.5

14 90¢ 11.0

15 40¢ 17.0

https://brainmass.com/economics/elasticity/regression-and-price-elasticity-294956

#### Solution Summary

Regression and Price Elasticity are explored.

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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