A consumer with a fixed income buys two goods, X and Y. If her demand for both X and Y are unitary elastic, she must spend an equal amount on each good.

take a shot, what do you think, and why?

i think false, she doesn't have to spend equal amount??

I agree

You are correct, the statement "If her demand for both X and Y are unitary elastic, she must spend an equal amount on each good" is not true. The fact that the demand for both goods is unitary elastic does not necessarily mean that the consumer must spend an equal amount on each good.

To understand why, let's first clarify the concept of unitary elasticity. Elasticity measures the responsiveness of the quantity demanded (or supplied) when there is a change in price. Unitary elastic demand occurs when the percentage change in quantity demanded is equal to the percentage change in price. In other words, when the elasticity is equal to 1.

If a consumer's demand for both goods X and Y is unitary elastic, it means that a 1% increase in price would result in a 1% decrease in the quantity demanded for each good. However, it does not specify the initial quantities or prices of the goods.

Consider the scenario where the consumer initially spends more on good X than on good Y. If the prices of both goods increase by the same percentage, the consumer's expenditures on each good will still be unequal.

For example, suppose the consumer initially spends $100 on good X and $50 on good Y. If the prices increase by 10%, the consumer's expenditures on good X would increase to $110, while the expenditures on good Y would increase to $55. Even though the demand for both goods is unitary elastic, the consumer does not spend an equal amount on each good.

In conclusion, the statement is false, and the consumer's spending on each good does not have to be equal even if the demand for both goods is unitary elastic.