Question

the value of cross price elasticity of demand between goods x and y is 2.00, while the cross price elasticity of demand between goods x and z...
which of the following are true?
a. x and y and x and z are substitutes.
b. x and y are complements and x and z are substitutes.
c. x and y and x and z are complements.
d. x and y are substitutes and x and z are complements.
e. none of the above.

Explanation:

Cross - price elasticity of demand ($E_{XY}$) is calculated as $E_{XY}=\frac{\%\text{ change in quantity demanded of }X}{\%\text{ change in price of }Y}$. If $E_{XY}> 0$, goods $X$ and $Y$ are substitutes (when the price of $Y$ increases, the quantity demanded of $X$ increases, as consumers switch from $Y$ to $X$). If $E_{XY}<0$, goods $X$ and $Y$ are complements (when the price of $Y$ increases, the quantity demanded of $X$ decreases, as they are consumed together).

The cross - price elasticity between $X$ and $Y$ is $2.00>0$, so $X$ and $Y$ are substitutes. For the cross - price elasticity between $X$ and $Z$, although the value is not fully given in the problem statement (assuming a typical case where if we follow the same logic, if we assume the cross - price elasticity between $X$ and $Z$ is negative, then $X$ and $Z$ are complements. Among the options, option D states that $X$ and $Y$ are substitutes and $X$ and $Z$ are complements, which matches the logic of cross - price elasticity.

Answer:

D. X and Y are substitutes and X and Z are complements.