Homework

1. 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) = X^1/2*Y^1/2, and the given bundle is X = 4 and Y = 16.

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) = 4X + 2Y and the given bundle is X = 1 and Y = 3.

i) MRS = __________________________________________________

ii) Draw your graph in this space:

2) 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) = X^1/3Y^2/3. The consumer has $24 to spend and the prices of the goods are P_X = $2 and P_Y = $8.  Note that the MUX = (1/3)X^-2/3Y^2/3 and the MUY = (2/3)X^1/3Y^-1/3.

b) U(X, Y) = MIN(5X, Y). The consumer has $24 to spend and the prices of the goods are P_X = $3 and P_Y = $1.

c) U(X, Y) = 2X + 3Y. The consumer has $20 to spend and the prices of the goods are P_X = $2 and P_Y = $4.

3. Suppose that Lynn enjoys coconut oil in her coffee.  She has very particular preferences, and she must have exactly two 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 $.50 per spoonful.

a) Graph Lynn's Price consumption curve for prices, P_C = $1, P_C = $2, and P_C = $3. Please put the number of cups of coffee on the horizontal axis, and the number of spoonfuls of coconut oil on the vertical axis. Be sure to label your graph carefully and accurately.

b) Graph Lynn's demand curve for coffee. You may assume that both coconut oil and coffee are continuous variables so she can consume any amount of coffee and coconut oil that she could afford. Be sure to label your graph carefully and accurately.