Question

Lizzie consumes cherries and apples. Her demand function for cherries is qc=m-20pc-40pa, where m is her income, pc is price of a pound of cherries, and pa is price of a pound apples. Are cherries and apples substitutes or complements?

Group of answer choices

cherries and apples are substitutes

cherries and apples are neither substitutes nor complements

cherries and apples are both substitutes and complements

neither one is correct

cherries and apples are complements

Answer 1

The given demand curve for cherries is :

Q_c = M - P_c - 40 P_a

Q_c : quantity demanded of cherries

M : income

P_{c :} price of cherries

P_{a :} price of apples

we know from the definition of compliments that, If the price of the complement falls, the quantity demanded of the other good will increase. and , If the price of the complement rises, the quantity demanded of the other good will decrease.

let us take two cases of price change in apples and see its effects on the quantity demanded for cherries

1. price of apples rise :  quantity demanded for cherries decreases .

2. price of apples fall : quantity demanded for cherries increases .

This tells us that cherries and apples are compliments to each other for Lizzie.