This represents the preference over living space (good 1) and all other goods (good 2) is represented by the utility function u(x1,x2)=x1^(2/3)+2x2^(2/3)

There is income m

You may assume that the preference is monotonic and strictly convex.

Calculate MRS

Do the indifference curves of the consumers preference intersect the good 1 axis or the good 2 axis (or both or neither)?show how

Find an interior candidate for the consumer optimization problem.

Without doing further calculations, can you determine whether the interior candidate you found above is the solution to the consumer optimization problem? Explain why or why not

Draw the budget constraint, of the interior candidate bundle, and the indifference curve that passes through the optimal bundle.