1. An individual has a utility function u =(x1)^1/3(x2)^2/3and an income of $60.

a)Solve for MUI and MU2 and use these to determine the MRS. Now use the tangency condition MRS = p1/p2 together with the budget line to solve for the demand functions for $1 and for this consumer.

b)Initially we have PI = 2 and P2 = 1, but then PI falls to 1. Use your demands to solve for points A and C (the optimal points pre and post price change) as done in class. Show these points on a clear well-labelled graph

c)Now determine the Slutsky demand by computing the income that would make point A just affordable with the new prices. Plug this hypothetical income and the new prices into your demands to solve for point B, as done in class. Show both the hypothetical budget line and point B on either your graph in a) or a new graph. Again, make your graphs - including those below completely clear. Show the substitution and income effects on your graph and compute them.

d)Graphically, do the same analysis using the Hicks decomposition method (don't solve explicitly for 'point B'. but show it on a graph). Show the income and substitution effects on your graph.

e)Which substitution effect is larger (in absolute value) the Slutsky one or the Hicks one? Is this true for any set of prices and any income (keeping the same preferences)?