Question

. Goods 1 and 2 are perfect complements. and a consumer always consumes them in the ratio

of 2 units of good 2 per unit of good 1. If a consumer has an income of $120 and if the price

of good 2 changes from $3 to $4, while the price of good 1 stays at $1, then the income effect

of the price change

a) is 4 times as strong as the substitution e ect.

(b) does not change demand for good 1.

(c) is exactly twice as strong as the substitution e ect.

(d) accounts for the entire change in demand.

(e) is 3 times as strong as the substitution effect.

how is the ratio 2x1=x2?

Answer 1

Correct option is (d).

When two goods are perfect complements, they are consumed in fixed proportion with zero substitutability. Since the goods cannot be substituted with each other, substitution effect from a change in price of one good is zero, and total effect of that price change is equal to income effect.

Note on utility function:

A fixed-proportion utility function for complements is:

U = min{ax1, bx2}

Here, 2 units of x2 are used for every 1 unit of good x. Therefore, (x1 / x2) = 1/2, and a = 2 and b = 1.

U = min{2x1, x2}