Question

Consider two normal goods and suppose the price of good 1 increases.

(a) Show that if the two goods are perfect complements, then the substitution effects for both goods are

zero.

(b) Show that if the two goods are perfect substitutes, then the income effect for good 1 is zero. (You can

assume for simplicity that initially p1< p2 but after the price increase p1' > p2).

Answer 1

A) let we take left shoe and right shoe as complementary goods.

In this diagram as the price increases of one good budget line will shift inward to AB₂ from AB₁ and a new equilibrium will be established at point 'b'. For substitution, we will keep the paying capacity constant so the compensated demand curve will be tangent to the old indifference curve IC₁ parallel to new budget constraint AB₂ as to keep slope equal. As it can be seen there is no other point than a which provides equilibrium quantity so substitution effect is zero. Price effect (Income Effect) can be seen from movement ' point a' to point 'b'

B) let us assume 2 substitute goods be Pepsi and cola.

Let the price of Pepsi be $3 and the price of cola be $4 and income is $12. Therefore he can either purchase 4 units of good Pepsi or 3 units of Good Cola. initially, a consumer is consuming Pepsi at X as its price is less than that of another good. As the price increases, budget constraint will shift from point B₁ to point B₂. For example, let the price of Pepsi be increased to $6, therefore, the customer will move towards good cola which costs $3. Therefore zero income effect.