# Computing elasticities

The maker of a leading brand of low calorie microwavable food estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April:

Q = - 5,200 - 42P + 20Px + 5.2I + 0.20A + 0.25M

(2002) (17.5) (6.2) (2.5) (0.09) (0.21)

R^2 = 0.55 n = 26 F = 4.88

Assume the following values for the independent variables:

Q = Quantity sold per month

P (in cents) = Price of the product = 500

Px (in cents) = Price of leading competitor's product = 600

I (in dollars) = Per capita income of the standard metropolitan statistical area (SMSA) in

which the supermarket is located = 5,500

A (in dollars)= Monthly advertising expenditure = 10,000

M = Number of microwave ovens sold in the SMSA in which the

supermarket is located = 5,000

Using the information, answer the following questions:

- Compute elasticities for each variable

How concerned do you think this company would be about the impact of a recession on its sales? Explain.

- Do you think that this firm should cut its price to increase its market share? Explain.

What proportion of the variation in sales is explained by the independent variables in the equations? How confident are you about this answer? Explain.

https://brainmass.com/economics/elasticity/computing-elasticities-141076

#### Solution Preview

Elasticity w.r.t to variable x is dQ/dx * x/Q

First calculate the value of Q for the given values of variables.

Q = - 5,200 - 42P + 20Px + 5.2I + 0.20A + 0.25M

P (in cents) = Price of the product = 500

Px (in cents) = Price of leading competitor's product = 600

I (in dollars) = Per capita income of the standard metropolitan statistical area (SMSA) in

which the supermarket is located = 5,500

A (in dollars)= Monthly advertising expenditure = 10,000

M = Number of microwave ovens sold in the SMSA in which the

supermarket is located = 5,000 ...

#### Solution Summary

Computing elasticities is achieved.

Computing elasticity of demand

Question 1. The demand equation for a certain brand of metal alloy audio cassette tape is: 100 x^2 + 9 p^2 = 3600, where x represents the number (in thousands) of ten-packs demanded each week when the unit price is $p. How fast is the quantity demanded increasing when the unit price per ten-pack is $14 and the selling price is dropping at the rate of 15 cents per ten-packs/week? [Hint: To find the value of x when p = 14, solve the equation 100 x^2 + 9 p^2 = 3600 for x when p = 14].

Question 2a. Suppose the quantity x of Super Titan radial tires made available each week in the marketplace is related to the unit-selling price by the equation: p - (x^2 / 2) = 48, where x is measured in units a thousand and p is in dollars. How fast is the weekly supply of Super Titan radial tires being introduced into the marketplace when x = 6, p = 66, and the price/tire is decreasing at the rate of $3/week?

Question 2b. The demand function for a certain brand of compact disc is given by the equation: p = - 0.01 x^2 - 0.2 x + 8, where p is the unit price in dollars and x is the quantity demanded each week measured in units of a thousand. Compute the elasticity of demand E(p), and determine whether demand is elastic, inelastic or unitary when x = 15.

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