If the price of good X increases by 2%, and that causes the quantity demanded of good Y to decrease by 15%, then the cross elasticity of demand for good Y, with respect to the price of good X, is

-7.5%

Explanation:

Cross elasticity of demand is the degree of responsiveness of the quantity of a commodity, Y in this case, to the change in the price of another commodity, X in this case.

Cross elasticity of demand is measured as a percentage change in the quantity of commodity Y divided by the percentage in the price of commodity Y. This can be written mathematically as follows:

Ec = % Change in the quantity of commodity Y divided by the percentage in the prie of commodity X.

Where Ec denoted cross elasticity.

Applying the formula to this question, we have

Ec = - 15%/2% = - 7.5%

Note that under cross elasticity of demand:

1. Two goods are substitute if the value of their cross elasticity of demand is positive. That is, an increase in the price of good one, good X, will lead to an increase in the quantity demand of the second, good Y.

2. Two goods are complimentary if the value of their cross elasticity of demand is negative. That is, an increase in the price of good one, good X, will lead to an decrease in the quantity demand of the second, good Y.

Therefore in this question, goods X and Y are complimentary because the value of their cross elasticity of demand is - 7.5% which is negative.

I wish you the best.