Question

A firm has estimated the following demand function for its product:

Answer 1

Answer:

(i) Q=300

(ii) Elasticity of Demand=-3.33 (elastic)

(iii) Income Elasticity= 2.5 (normal good)

(iv) Advertising Elasticity: 1.5

Explanation:

The Demand function is given by

$Q=100-5P+5I+15A$

(1) To solve (i) we need to replace P = 200, I = 150, and A = 30 in the demand equation:

$Q=100-5(200)+5(150)+15(30)=300$

(2) To find the price elasticity (how much quantity demanded changes with price) we use the point price elasticity formula

$\eta_{Price}=\frac{\Delta Q}{\Delta P}\frac{P}{Q}$

From the above equation we get: $\frac{\Delta Q}{\Delta P}=-5$

Replacing in the elasticity formula

$\eta_{Price}=-5\frac{200}{300}=|-3.33|>1$

in absolute terms the elasticity is bigger than one so it is an elastic demand.

(3) For income elasticity (how much quantity demanded changes with income), we proceed similarly as above. But the derivative is respect to income

$\eta_{Income}=\frac{\Delta Q}{\Delta I}\frac{I}{Q}=5\frac{150}{300}=2.5>1$[/tex]

Which is bigger than one, denoting this is a normal good because it's bigger than one.

(4) Advertising elasticity (how much quantity demanded changes with expenditures in advertising), we proceed as before

$\eta_{advertising}=\frac{\Delta Q}{\Delta A}\frac{A}{Q}=15\frac{30}{300}=1.5$