A consumer has the utility
function U = x1x2 , faces
prices p1 = 2 and p2 =1, and has
given income m = 100 . The
consumer also faces a rationing constraint
that x2 ≤ 50.
Write down the non-linear programming problem. Use the Lagrange
method to solve for the utility maximizing choices
of x1 , x2 , the marginal utility of
income λ1 , and the marginal utility of relaxing
the rationing constraint. Show the graph of your solution, the
constraints, and the relevant indifference curve.