Afirm has estimated the following demand function for its product:
q = 100 - 5 p + 5 i + 15 a
where q is quantity demanded per month in thousands, p is product price, i is an index of consumer income, and a is advertising expenditures per month in thousands. assume that p = $200, i = 150, and a = 30. for simplicity in calculating the results, use the point elasticity formulas to complete the calculations indicated below.
(i) calculate quantity demanded.
(ii) calculate the price elasticity for demand. is demand elastic, inelastic, or unit elastic?
(iii) calculate the income elasticity of demand. is the good normal or inferior?
(iv) calculate the advertising elasticity of demand.

(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

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

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

From the above equation we get:

Replacing in the elasticity formula

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

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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