Question

In: Economics

Lizzie consumes cherries and apples. Her demand function for cherries is qc=m-20pc-40pa, where m is her...

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

Expert Solution

Option E is correct - cherries and apples are complements

Cross price elasticity of demand is the responsiveness of change in quantity demanded of one good because of the change in price of the other. It is given by the following formula:

Cross price elasticity of demand for good X = * (Py/Qx)

Here Qx is the quantity demaned of good X and Py is the price of good Y.

The two goods are said to be substitutues if their cross price elasticity of demand is positive.

The two goods are said to be complementary of their cross price elascticity of demand is negative.

We are given the following equation:

Qc = m-20Pc-40Pa, where, m is the income, Pc is the price of a pound of cherreis, Pa is the price of a pound of apples and Qc is the quantity of cherreis.

Differentiating the eqaution with respect to Pa, we get,

= -40

Cross price ealsticity of demand = -40* (Pa/Qc)

Since the value of cross price elasticity of demand is negative, the goods are complements.

Rahul Sunny answered 1 year ago

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