Question

So, suppose the elasticity of demand for jelly beans is

Q_D= 7 - 3p + 0.7p_s– 1.4p_P+ 0.00005Y

Q_D is the quantity of jelly beans demanded (‘000 in kilograms per person)

p is the price of jelly beans ($/kg)

p_S is the price of lollipops ($/kg)

p_P is the price of candy hearts ($/kg)

Y is the per capita income ($)

Suppose p=$1.5/kg, p_S=$1.20/kg and p_P=$0.6/kg and Y=$25,000,

1. Calculate and interpret the own-price elasticity of demand

2. Calculate and interpret the cross-price elasticity with respect to other kinds of candy.

3.Calculate and interpret the cross-price elasticity with respect to candy hearts

4.Calculate and interpret the income elasticity

Answer 1

Plugging in given values,

QD = 7 - (3 x 1.5) + (0.7 x 1.2) – (1.4 x 0.6) + (0.00005 x 25,000)

QD = 7 - 4.5 + 0.84 - 0.84 + 1.25

QD = 3.75

(1) Own price elasticity = (QD/p) x (p/QD) = -3 x (1.5/3.75) = -1.2

Since absolute value of elasticity is higher than 1, demand is elastic.

(2) Cross price elasticity = (QD/pS) x (pS/QD) = 0.7 x (1.2/3.75) = 0.22

Since cross price elasticity is positive, jelly beans and other candy (lollipops) are substitutes.

(3) Cross price elasticity = (QD/pP) x (pP/QD) = -1.4 x (0.6/3.75) = -0.22

Since cross price elasticity is negative, jelly beans and candy hearts are complements.

(4) Income elasticity = (QD/Y) x (Y/QD) = 0.00005 x (25,000/3.75) = 0.33

Since income elasticity is positive, jelly beans are normal goods.