# Analyzing the given demand function

Management at the Johnston Corporation estimates a demand function for its lawnmower line to be:

Qk = 5-2.4*Pb+0.7*A+0.002*I+0.8*Pv

Where Qk = the quantity of lawnmowers, Pb = the own price of lawnmowers produced by Johnston ($/Unit)

A = the advertising expenditures for Johnson lawnmowers ($/ad unit in a year), I = income in Johnstonâ??s market ($/year), Pv = the price of lawnmowers produced by the Gibson corporation ($/Unit)

1. Explain the coefficients of each explanatory variable.

2. If Pb is $60, A is $200, I is $20,000 and Pv is 100, what is the quantity of Johnston Lawnmowers sold?

3. Determine the own price elasticity of demand for Johnston Lawnmowers.

4. Determine the income elasticity of demand.

5. Determine the cross price elasticity of demand. Interpret this measure.

6. Given the answers of (c) through (e), what is the most important factor in determining the demand for Lawnmowers?

7. If the Johnston Corporation wants to reduce its advertising expense to $190, and wants to offset the lost revenues by changing its price, should the price be increased or decreased?

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#### Solution Preview

1. Explain the coefficients of each explanatory variable.

Coefficient of Pb is negative. It indicates that price and quantity demanded for lawnmowers has inverse relationship for Johnston Corporation. Quantity demanded will increase in case their prices fall and quantity demanded will decrease in case their prices rise. For an increase of $1 in own price, quantity demanded for their lawnmowers will decrease by 2.4 units. For a decrease of $1 in own price, quantity demanded for their lawnmowers will increase by 2.4 units.

Coefficient of A is positive. It indicates that advertising expenditure per ad unit and quantity demanded for lawnmowers has direct relationship for Johnston Corporation. Quantity demanded will increase in case their advertising expenses per ad unit increases and quantity demanded will decrease in case their advertising expenses per ad unit decreases. For an increase of $1 per ad unit in advertising expenditure, quantity demanded will increase by 0.7 units. For a decrease of $1 in advertising expenditure per ad unit, quantity demanded will decrease by 0.7 ...

#### Solution Summary

The solution analyzes the given demand function. It discusses the nature of given coefficients and calculate the various elasticity values.