Suppose you have two goods: pencils and coffee. You like both of the goods. Initially, you...
Suppose you have two goods: pencils and coffee. You like both of the goods. Initially, you spend your income on both goods, but once your income is $10 or higher, you no longer purchase additional pencils. The price of coffee and the price of pencils stays fixed.
(a) Graphically describe these preferences. Graph at least 3 optimal bundles of pencils and coffee. (You must show both the budget constraint and indifference curve for each optimal bundle).
(b) Graph the Engel curve described for pencils.
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Suppose you have two goods: pencils and coffee. You like both of
the goods. Initially, you...
3. Michael has preferences over two goods, z1 and r2, represented by the utility function (a)...
3. Michael has preferences over two goods, z1 and r2, represented by the utility function (a) Find the MRS12 associated with this utility function. (b) Use the MRS12, the price ratio, and the budget constraint to find Michael's optimal bundle when m 3000, P50, and 10. for r2. (You will need to calculate the utility at the optimal point in order to do this.) a single graph. Be sure to label the curves, the optimal point, and the axes. (c)...
Imagine a representative consumer, whose utility for apples (X) and all other goods (Y) can be...
Imagine a representative consumer, whose utility for apples (X) and all other goods (Y) can be represented in a Cobb-Douglas form. 1) Please graphically represent consumer indifference curves, given prices Px and Py and the budget constraint M. 2) What will happen to consumer utility and optimal bundle if consumer income (budget) increases and apples are a necessity good? Please show graphically and explain the intuition. 3) How would the Engel curve look like for point #2?
- Mordecai consumes only coffee (C) and video games (G), and his utility function is U(C,G)=C1/2G1/2....
- Mordecai consumes only coffee (C) and video games (G), and his utility function is U(C,G)=C1/2G1/2. The price of coffee is p, and the price of video games is 10. Mordecai’s income is m. In this problem, you will find Mordecai’s utility maximizing combination of coffee and video games. a.Suppose m=100 and p=10. How much of each good does Mordecai consume? Draw a graph showing his budget constraint and indifference curve passing through the chosen bundle. (2 points) b.Suppose m=100...
1. Suppose a consumer is maximizing utility consuming a bundle apples and bananas x and has...
1. Suppose a consumer is maximizing utility consuming a bundle apples and bananas x and has standard preferences. Her budget constraint is given by the equation 1000-2a-2b0. Apples are normal goods and bananas are normal. a) plot the optimal bundle, showing the proper indifference curve and budget constraint. Call this bundle x1 b) show the effect of an increase of a single price increase for apples on the budget constraint. Use a hypothetical budget line to identify substitution effects for...
3. (10 total points) Suppose that Lynn enjoys sugar in her coffee. She has very particular...
3. (10 total points) Suppose that Lynn enjoys sugar in her coffee. She has very particular preferences, and she must have exactly four spoonfuls of sugar for each cup of coffee. Let C be the number of cups of coffee, and S be the number of spoonfuls of sugar. Also, let Pc be the price of a cup of coffee. Suppose Lynn has $24 to spend on Coffee and Sugar. Also, the price of Sugar is $.30 per spoonful. Graph...
1. Sally has preferences represented by the utility function UC, M) = 3 + 61rC M, where C is coffee and M is meals....
1. Sally has preferences represented by the utility function UC, M) = 3 + 61rC M, where C is coffee and M is meals. Her income is S100, and she pays $2 per coffee and S10 per meal a. Distinguish (the concepts of) diminishing marginal rate of substitution from diminishing marginal uty Your answer does not have to be specific to Sally's preferences. (4 points) Use the Lagrangian method to derive Sally's utility maximizing bundle given her budget constraint. Circle...
2. Suppose Matt has $20 to spend on movies and books. The price of one unit...
2. Suppose Matt has $20 to spend on movies and books. The price of one unit of movie and the price of one unit of book are both $2. Assume movies and books are normal goods. a) Draw Matt’s budget line (Draw Movies on the X-axis). Suppose Matt optimally consumes 6 movies and 4 books. Label this bundle as point A on your graph, and draw the indifference curve associated with this bundle. b) Consider the bundle (5 movies, 5...
Long Question #2 Consider preferences over food and housing represented by the utility function U F2/3H1/3...
Long Question #2 Consider preferences over food and housing represented by the utility function U F2/3H1/3 A. Let Income 1200, PE 2 and PH6. Find the quantity demanded of housing and food. Graph the budget constraint and the optimal bundle that you found. Make sure to include an indifference curve. Let the price of food increase to 4. Add the new budget constraint, find the new optimal bundle and add it to your graph. B.
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose...
2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose Py, and the consumer has $300 to spend. Draw the Price-Consumption Curve for this consumer for income values Px-1, Px 2, and Px- 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw the indifference curve that goes through...
3. Michael has preferences over two goods, z1 and r2, represented by the utility function (a) Find the MRS12 associated with this utility function. (b) Use the MRS12, the price ratio, and the budget constraint to find Michael's optimal bundle when m 3000, P50, and 10. for r2. (You will need to calculate the utility at the optimal point in order to do this.) a single graph. Be sure to label the curves, the optimal point, and the axes. (c)...
1. Suppose a consumer is maximizing utility consuming a bundle apples and bananas x and has standard preferences. Her budget constraint is given by the equation 1000-2a-2b0. Apples are normal goods and bananas are normal. a) plot the optimal bundle, showing the proper indifference curve and budget constraint. Call this bundle x1 b) show the effect of an increase of a single price increase for apples on the budget constraint. Use a hypothetical budget line to identify substitution effects for...
3. (10 total points) Suppose that Lynn enjoys sugar in her coffee. She has very particular preferences, and she must have exactly four spoonfuls of sugar for each cup of coffee. Let C be the number of cups of coffee, and S be the number of spoonfuls of sugar. Also, let Pc be the price of a cup of coffee. Suppose Lynn has $24 to spend on Coffee and Sugar. Also, the price of Sugar is $.30 per spoonful. Graph...
1. Sally has preferences represented by the utility function UC, M) = 3 + 61rC M, where C is coffee and M is meals. Her income is S100, and she pays $2 per coffee and S10 per meal a. Distinguish (the concepts of) diminishing marginal rate of substitution from diminishing marginal uty Your answer does not have to be specific to Sally's preferences. (4 points) Use the Lagrangian method to derive Sally's utility maximizing bundle given her budget constraint. Circle...
Long Question #2 Consider preferences over food and housing represented by the utility function U F2/3H1/3 A. Let Income 1200, PE 2 and PH6. Find the quantity demanded of housing and food. Graph the budget constraint and the optimal bundle that you found. Make sure to include an indifference curve. Let the price of food increase to 4. Add the new budget constraint, find the new optimal bundle and add it to your graph. B.
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose Py, and the consumer has $300 to spend. Draw the Price-Consumption Curve for this consumer for income values Px-1, Px 2, and Px- 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw the indifference curve that goes through...
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