For each of the following situations, i) Find the Marginal Rate of Substitution at the given bundle, and ii) use a graph to indicate the given bundle, and accurately draw the indifference curve that goes through that bundle. Be sure to label you graph carefully and accurately. In all cases put the amount of good X on the horizontal axis, and the amount of good Y on the vertical axis.

1. (18 points) For each of the following situations, i) Find the Marginal Rate of Substitution at the given bundle, and ii) use a graph to indicate the given bundle, and accurately draw the indifference curve that goes through that bundle. Be sure to label you graph carefully and accurately. In all cases put the amount of good X on the horizontal axis, and the amount of good Y on the vertical axis. a) The consumers utility function is given by U(X, Y) = X12*Y1/2, and the given bundle is X = 8 and Y = 2. 1) MRS = ii) For this graph, scale each axis up to 16. Do not go above 16 on either axis. Draw your graph in this space:b) The consumers utility function is given by U(X, Y) = MIN(2X, 3Y), and the given bundle is X = 3 and Y = 1. i) MRS = 1i) Draw your graph in this space:c) The consumers utility function is given by U(X, Y) = 4X + 2Y and the given bundle is X = 3 and Y = 1) MRS = ii) Draw your graph in this space