1. Suppose you have $24 to spend on either tea (T) or sugar (S). Sugar costs $.10 per and Tea costs $.60 per cup spoonful. Using a graph, Explain your budget constraint. Please put the number of cups of Tea on the vertical axis and the number of spoonfuls of Sugar on the horizontal axis. Assume that you can purchase any amount of sugar or tea (for example, you would buy ½ cup of tea). What is the Marginal Rate of Transformation between sugar and tea?
2. For each of the following situations, use a graph to show the given bundle and accurately draw the indifference curve that goes through that bundle. Be sure to label you graph 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 provided by U(X,Y) = X1/2*Y, and the given bundle is X = 4 and Y = 8.
b) The consumers utility function is provided by U(X,Y) = MIN(X, 4Y), and the given bundle is X = 5 and Y = 1.
c) The consumers utility function is provided by U(X,Y) = X + 3Y and the given bundle is X = 3 and Y = 4.
3) For each of the subsequent situations, find the consumer's optimal bundle. Also, for each case, draw the consumer's budget constraint, show the optimal bundle on the graph, and accurately draw the indifference curve that runs through the consumer's optimal bundle.
a) U(X,Y) = XY2. The consumer has $24 to spend and the prices of the goods are PX = $2 and PY = $4. Note that the MUX = Y2 and the MUY = 2XY.
b) U(X,Y) = MIN(X,3Y). The consumer has $40 to spend and the prices of the goods are PX = $1 and PY = $2.
c) U(X,Y) = 3X + Y. The consumer has $60 to spend and the prices of the goods are PX = $4 and PY = $1.