03 Jun Question 1. (8 points) Suppose you have $24 to spend on either tea (T) or sugar (S). Tea costs $.80 per cup and
Question
1. (8 points) Suppose you have $24 to spend on either tea (T) or sugar (S). Tea costs $.80 per cup and
sugar costs $.5 per spoonful. Using a graph, illustrate 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. You may
assume that you can purchase any amount of tea or sugar (for example, you could buy ½ cup of tea).
What is the Marginal Rate of Transformation between tea and sugar?
2. (18 points) For each of the following situations, 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*Y1/2, and the given bundle is X = 2 and Y = 16.
b) The consumers utility function is given by U(X,Y) = MIN( X, 3Y), and the given bundle is X = 3 and Y
= 2.
c) The consumers utility function is given by U(X,Y) = 2X + 5Y and the given bundle is X = 5 and Y = 2.
3) (24 points) For each of the following situations, find the consumer’s optimal bundle. Be sure to show
your work. Also, for each case, draw the consumer’s budget constraint, indicate 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 P X = $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 P X = $1 and PY
= $2.
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