A fall in the price of cheese and the demand for crackers: the decomposition of the price effect

Short answer. Arjun buys fewer crackers. When cheese becomes cheaper, both parts of the price effect, the substitution effect and the income effect, push his consumption of crackers down, so the fall is certain.

The decomposition of a price effect. A change in the price of one good has two effects on what the consumer buys:

• the substitution effect: the good whose price fell is now relatively cheaper, so the consumer substitutes it for the other good, keeping his level of satisfaction the same;
• the income effect: with money income unchanged, a lower price raises the consumer's purchasing power (real income), and he adjusts his purchases as he would to a rise in income. The total (price) effect is the sum of the two. How each good responds to the income effect depends on whether it is normal (bought more as income rises) or inferior (bought less as income rises).

Substitution effect on crackers. After the fall in the price of cheese, cheese costs fewer crackers than before: the budget line becomes flatter in the cheese direction. Holding Arjun on his original level of satisfaction, he moves along his indifference curve towards the now cheaper good: more cheese and fewer crackers. The substitution effect on crackers is therefore negative.

Income effect on crackers. The cheaper cheese leaves Arjun with more purchasing power than before. Crackers are an inferior good for him, so this rise in real income makes him buy fewer crackers (and, since cheese is normal, more cheese). The income effect on crackers is also negative.

Total effect on crackers.

Both effects move crackers in the same direction, so the total effect is an unambiguous fall in Arjun's consumption of crackers. (Cheese also rises without doubt, since for a normal good the two effects reinforce each other.)

Assumptions. Arjun's money income and his tastes stay the same; only the price of cheese changes (the price of crackers is unchanged); he buys only these two goods and spends all his income; his indifference curves are downward sloping and convex, so the substitution effect works as described.

Conclusion. When the price of cheese falls, the substitution effect and the income effect both reduce Arjun's purchases of crackers, so he buys fewer crackers, while he buys more cheese.