Final answer:
To find Paige's demand functions for x and y, take the partial derivatives of the utility function with respect to x and y, and set them equal to zero.
Step-by-step explanation:
To find Paige's demand functions for x and y, we need to maximize the utility function U(x,y)=x0.5, y0.5. We can do this by taking partial derivatives of the utility function with respect to x and y and setting them equal to zero. Taking the partial derivative with respect to x, we get 0.5x-0.5y0.5 = 0. Taking the partial derivative with respect to y, we get 0.5x0.5y-0.5 = 0. Solving these two equations simultaneously, we find that x = 0 and y = 0. Therefore, Paige's demand functions for x and y are x = 0 and y = 0.