Econ 302 Homework #1 Assignment

1. (8 points) Suppose you have \$24 to spend on either tea (T) or sugar (S). Tea costs \$.80 per cup andsugar costs \$.5 per spoonful. Using a graph, illustrate your budget constraint. Please put the number ofcups of Tea on the vertical axis and the number of spoonfuls of Sugar on the horizontal axis. You mayassume that you can purchase any amount of tea or sugar (for example, you could buy Â½ 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 andaccurately draw the indifference curve that goes through that bundle. Be sure to label you graph carefullyand accurately. In all cases put the amount of good X on the horizontal axis, and the amount of good Yon 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 consumerâs optimal bundle. Be sure to showyour work. Also, for each case, draw the consumerâs budget constraint, indicate the optimal bundle onthe graph, and accurately draw the indifference curve that runs through the consumerâ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.c) U(X,Y) = 3X + Y. The consumer has \$60 to spend and the prices of the goods are P X = \$4 and PY =\$1.
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Econ 302 Homework #1 Assignment

1. (8 points) Suppose you have \$24 to spend on either tea (T) or sugar (S). Tea costs \$.80 per cup andsugar costs \$.5 per spoonful. Using a graph, illustrate your budget constraint. Please put the number ofcups of Tea on the vertical axis and the number of spoonfuls of Sugar on the horizontal axis. You mayassume that you can purchase any amount of tea or sugar (for example, you could buy Â½ 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 andaccurately draw the indifference curve that goes through that bundle. Be sure to label you graph carefullyand accurately. In all cases put the amount of good X on the horizontal axis, and the amount of good Yon 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 consumerâs optimal bundle. Be sure to showyour work. Also, for each case, draw the consumerâs budget constraint, indicate the optimal bundle onthe graph, and accurately draw the indifference curve that runs through the consumerâ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.c) U(X,Y) = 3X + Y. The consumer has \$60 to spend and the prices of the goods are P X = \$4 and PY =\$1.
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