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

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) = X1/2*Y1/2, and the given bundle is X = 16 and Y = 4.

i) MRS = __________________________________________________

ii) Draw your graph in this space:

b) The consumers utility function is given by U(X,Y) = MIN(X, 4Y), and the given bundle is X = 3 and Y = 1.

i) MRS = __________________________________________________

ii) Draw your graph in this space:

c) The consumers utility function is given by U(X,Y) = 5X + 4Y and the given bundle is X = 4 and Y = 10.

i) MRS = __________________________________________________

ii) Draw your graph in this space:

2) (18 points) For each of the following situations, draw the consumer's budget constraint and indicate the consumer's optimal bundle on the budget constraint. Make sure your graph is accurate and clearly labeled.

a) U(X,Y) = X1/4Y3/4. The consumer has $24 to spend and the prices of the goods are PX = $2 and PY = $3. Note that the MUX = (1/4)X-3/4Y3/4 and the MUY = (3/4)X1/4Y-1/4.

b) U(X,Y) = MIN(2X,5Y). The consumer has $24 to spend and the prices of the goods are PX = $2 and PY = $1.

c) U(X,Y) = 2X + 3Y. The consumer has $30 to spend and the prices of the goods are PX = $2 and PY = $5.

3. (14 total points) Suppose that Lynn enjoys coconut oil in her coffee. She has very particular preferences, and she must have exactly four spoonfuls of coconut oil for each cup of coffee. Let C be the number of cups of coffee, and O be the number of spoonfuls of coconut oil. Also, let PC be the price of a cup of coffee. Suppose Lynn has $12 to spend on coffee and coconut oil. Also, the price of coconut oil is $.10 per spoonful. 

Graph Lynn's Price consumption curve for prices, PC = $.60, PC = $.80, and PC = $1.10. Please put the number of cups of coffee (C) on the horizontal axis, and the number of spoonfuls of coconut oil (O) on the vertical axis. Be sure to label your graph carefully and accurately.