Shirley thinks a 16-ounce can of beer is just as good as two 8-ounce cans. Lorraine only drinks 8 ounces at a time and hates stale beer, so she thinks a 16-ounce can is no better or worse than an 8-ounce can.

(a) Write-a utility function that represents Shirley's preferences between commodity bundles comprised of 8-ounce cans and 16-ounce cans of beer. Let X stand for the number of 8-ounce cans and Y stand for the number of 16-ounce cans.

(b) Now write-a utility function that represents Lorraine's preferences. u(X, Y ) = X + Y .

(c) Would the function utility U(X, Y ) = 200X+100Y represent Shirley's preferences? (explain/demonstrate)

(d) Would the utility function U(x, y) = (10X + 5Y )2 represent her preferences? (explain/demonstrate)

(e) Would the utility function U(x, y) = X + 3Y represent her preferences? (explain/demonstrate)

(f) Give an example of two commodity bundles such that Shirley likes the first bundle better than the second bundle, while Lorraine likes the second bundle better than the first bundle. Shirley prefers (0,2) to (3,0). Lorraine disagrees.