Question

8. Suppose Bob consumes e-bikes and scooters. If Bob’s income and prices of both goods
increase by the same percentage,
A) Bob will buy more of both goods.
B) Bob will buy more of both goods if they are both normal goods.
C) Bob will buy less of both goods if they are both inferior goods.
D) Bob’s utility maximizing bundle stays the same.

9. Suppose Bob spends his entire income on e-bikes and scooters. Every month he spends
half of his income on each of these goods. Bob's income elasticity of demand for e-bikes is
-.75. What is the income elasticity of demand for scooters?
A) 2.75
B) 0.36
C) -2.75
D) Unknown with the information provided

Answer 1

Suppose Bob consumes e-bikes and scooters. If Bob’s income and prices of both goods increase by the same percentage Bob’s utility maximizing bundle stays the same. This is because the increase in income will get absorbed by the same percentage increase in price. Thus there will be no change in utility max level.

The weighted income elasticities of two goods will be

W1X1+W2X2 = 1

where W1 and W2 are weights or percent expenditure on the goods. Half of the income is spent on both goods so W1=W2=0.5

0.5*X1+0.5*(-0.75) = 1

0.5*X1 = 1+0.375

0.5X1= 1.375

X1 = 1.375/0.5 = 2.75 (the income elasticity is 2.75)