# Analyzing estimated demand function

The economic analysis division of Mapco Enterprises estimated the demand function for its line of weed trimmers as

Qd = 18,000 + 0.4N - 350Pm + 90Ps

where N= number of new homes completed in the primary market area

Pm = price of Mapco trimmer

Ps = price of its competitor's Surefire trimmer

In 2006, 15,000 new homes are expected to be completed in the primary market area. Mapco plans to charge $50 for its trimmer. The Surefire trimmer is expected to sell for $55.

a) What sales are forecast for 2006 under these conditions?

b) If its competitor cuts the price of the Surefire trimmer to $50, what effect will it have on Mapco's sales?

c) What effect would a 30-percent reduction in the number of new homes completed have on Mapco's sales (ignore the impact of the price cut of the Surefire trimmer)?

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#### Solution Preview

a) What sales are forecast for 2006 under these conditions?

Qd = 18,000 + 0.4N - 350Pm + 90Ps

Put N=15000, Pm=$50 and Ps=$55

Qd=18000+0.4*15000-350*50+90*55=11450

b) If its competitor cuts ...

#### Solution Summary

Solution analyzes the impact of changing values of various parameters on estimated sales.

Demand Equations

1. Using the following equation, what is the demand equation as a function of Ps if the price of other pastas (Po) is $2, the individual's income (Y) in thousands is $25, and tastes (Z) are represented by 20? What happens if the individual's income increases to $30?

Qd= 500 - 10Ps + 5Po + 20Y +40Z

2. Given the regression estimate of the demand equation of

Qx = 1,000 - 3.3Px + 0.001Y

where Y is income, what is the change in demand if price rises by $1, holding income constant? What is the percentage change in demand if price rises by $1 from an initial price of Px = $200 given Y = 10,000? What is the effect on demand of a $1 increase in income, holding price constant?

3. Consider the estimate demand equation of

Qx = 1,000 -3.3Px -0.2Pz + 0.001Y

(3.5) (2.1) (0.5)

with t values in parenthesis, where Pz is the price of another good Z, and Y is income. Is good Z a substitute or a complement? Can we say confidently whether good X is a normal good or an inferior good?

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