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1. (18 points) For each of the following situations, use a graph to indicate the given<br />
bundle and accurately draw the indifference curve that goes through that bundle. Be sure<br />
to label you graph carefully and accurately. In all cases put the amount of good X on the<br />
horizontal axis, and the amount of good Y on the vertical axis.<br />
a) The consumers utility function is given by U(X,Y) = X 2 *Y, and the given bundle is X = 2<br />
and Y = 4.<br />
b) The consumers utility function is given by U(X,Y) = MIN(X, 4Y), and the given bundle is<br />
X = 2 and Y = 1.<br />
c) The consumers utility function is given by U(X,Y) = 4X + 2Y and the given bundle is X =<br />
2 and Y = 6.<br />
2) (18 points) For each of the following situations, draw the consumer’s budget constraint,<br />
indicate the optimal bundle on the graph, and accurately draw the indifference curve that<br />
runs through the consumer’s optimal bundle. Be sure to carefully label your graph.<br />
a) U(X,Y) = XY 2 . The consumer has $24 to spend and the prices of the goods are P X = $2<br />
and P Y = $4. Note that the MU X = Y 2 and the MU Y = 2XY.
) U(X,Y) = MIN(4X,Y). The consumer has $24 to spend and the prices of the goods are P X<br />
= $2 and P Y = $1.<br />
c) U(X,Y) = 3X + Y. The consumer has $20 to spend and the prices of the goods are P X =<br />
$4 and P Y = $2.<br />
3. (14 points) Suppose that Lynn enjoys coconut oil in her coffee. She has very particular<br />
preferences, and she must have exactly two spoonfuls of coconut oil for each cup of<br />
coffee. Let C be the number of cups of coffee, and O be the number of spoonfuls of<br />
coconut oil. Also, let P C be the price of a cup of coffee. Suppose Lynn has $12 to spend<br />
on coffee and coconut oil. Also, the price of coconut oil is $.50 per spoonful.<br />
a) Graph Lynn’s Price Consumption Curve for prices, P C = $1, P C = $2, and P C = $3. Please<br />
put the number of cups of coffee on the horizontal axis, and the number of spoonfuls of<br />
coconut oil on the vertical axis. Be sure to label your graph carefully and accurately.<br />
b) Graph Lynn’s demand curve for coffee. You may assume that both coconut oil and<br />
coffee are continuous variables so she can consume any amount of coffee and coconut<br />
oil that she could afford. Be sure to label your graph carefully and accurately.
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