Ian's utility function is given by u = x1x2. His cross-price elasticity of demand for x1 with respect to p2 will be:

The cross-price elasticity of demand measures the responsiveness of the quantity demanded for a good to a change in the price of another good.

Given Ian's utility function u = x1x2, we can derive his demand functions for x1 and x2.

First, we need to set up the Lagrangian for this utility maximization problem:

L = x1x2 + λ(I - p1x1 - p2x2)

where I is income, p1 is the price of good 1, and p2 is the price of good 2.

Taking the partial derivatives of the Lagrangian with respect to x1, x2, and λ, and setting them equal to zero gives us the following system of equations:

x2 - λp1 = 0 x1 - λp2 = 0 I - p1x1 - p2x2 = 0

Solving this system of equations gives us the demand functions for x1 and x2:

x1 = I/(2p1) x2 = I/(2p2)

The cross-price elasticity of demand for x1 with respect to p2 is given by:

η12 = (dx1/dp2)*(p2/x1)

Substituting the demand function for x1 into this equation gives us:

η12 = (d(I/(2p1))/dp2)*(p2/(I/(2p1)))

Solving this derivative, we find that the cross-price elasticity of demand for x1 with respect to p2 is zero. This is because the demand for good 1, x1, does not depend on the price of good 2, p2, in this particular utility function. Therefore, a change in the price of good 2 will not affect the quantity demanded of good 1.