Roberto and Emily meet for lunch. Roberto has 23 M&Ms (M) and 10 Starburst (S); Emily has 2 M&Ms and 10 Starburst. Roberto's preferences can be described by the utility function U(M, S) = MS2. While Emily's preferences can be described by the utility function U(M, S) = MS.
a. Draw an Edgeworth box showing the initial consumption bundles for Roberto and Emily. Be sure to label the diagram completely. Draw their indifference curves through these bundles. Calculate their marginal rates of substitution at those bundles, and show graphically what those rates represent.
b. What is the best trade for Roberto that leaves Emily no worse off than she is at her original bundle?