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Homework 3 Chapter 5: Demand 1. What happens to the amount of x and y consumed...
Homework 3 Chapter 5: Demand 1. What happens to the amount of x and y consumed when income falls if x and y are normal goods? Draw a budget constraint (before the income decrease) and a convex utility curve that corresponds to the optimal consumption bundle. Draw a new budget constraint (after income falls) and a new convex utility curve that corresponds to the optimal consumption bundle. Has the amount of x and y consumed increased or decreased due to...
4. Assume a utility function described by u(x,y)=2/xy. a. Given the utility function, u(x,y)=2xy, sketch the...
4. Assume a utility function described by u(x,y)=2/xy. a. Given the utility function, u(x,y)=2xy, sketch the indifference curves for u = 50, 72 and 98. e indifference Carved forbise banta un b. Sketch budget constraint of 5x +10y = 30. Label intercepts (where it crosses the axes). 00:0 VE c. Solve for calculate) the optimal bundle (x, y) and sketch the optimal solution.
Bob has $36 to spend on tacos and burritos which are both ordinary goods for Bob....
Bob has $36 to spend on tacos and burritos which are both ordinary goods for Bob. Burritos cost $4 each and tacos cost $2 each. a. Draw Bob's budget line with tacos on the x-axis and burritos on the y-axis. b. Draw an indifference curve showing Bob's optimal consumption at 5 burritos and 8 tacos. c. What is the ratio of the Marginal Utility of Burritos to the Marginal Utility of Tacos at Bob's optimal consumption bundle? d. On the...
1. Price of x is 12 and price of y is 8. Answer the following questions...
1. Price of x is 12 and price of y is 8. Answer the following questions for a consumer who earns $600 and whose preference can be represented with the utility functions U(x,y) x0.4y0.6 = a) Write down the utility maximization problem. (2 points) b) Does the utility function represent convex preference? Explain. (2 points) c) Write down the budget constraint. What is the slope of the budget line? (2 points) d) What is the slope of the indifference curve...
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)...
2. Sandra has the following preferences over cookies (x) and tea (y) (x,y) = min(3x, 2y)...
2. Sandra has the following preferences over cookies (x) and tea (y) (x,y) = min(3x, 2y) (a) Graph Sandra's indifference curves that go through points (2,3), (4,6), (6,9), (8,12). Be sure to label the axis and the utility levels of the indifference curves. (Hint: You should be graphing 4 indifference curves) (10 points) (b) On the same graph above, draw a budget constraint where pe=2.py=2 m = 20. (Note, careful attention to precise graphing here will help in partc.) (4...
1. Dorothy's utility function is U(B, O) = (B + 2) (0 + 1) where B...
1. Dorothy's utility function is U(B, O) = (B + 2) (0 + 1) where B is her consumption of bananas and O is her consumption of oatmeal. MUB = 0 + 1, MUo = B + 2. (Place Oatmeal on the y axis.) a. Write down the expression and draw Dorothy's indifference curve through (2,8). b. Suppose po = Pb = $1 and M = $11, draw the budget constraint on the same graph as her indifference curve. c....
Jane commutes to work. She can either use public transport or her own car. Her indifference curve...
Jane commutes to work. She can either use public transport or her own car. Her indifference curves obey the four properties of indifference curves for ordinary goods 1. Draw Jane's budget line (BL,) with car travel on the vertical axis and public transport on the horizontal axis 2. Suppose that Jane consumes some of both goods. Explain how her optimal consumption bundle can be obtained. Then, draw an indifference curve that helps you illustrate that optimal consumption bundle represented by...
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X...
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X is MUx = Y. His marginal utility of Y is MUY = . He has income $12. When the prices are Px - 1 and Py -1, Andy's optimal consumption bundle is X* -6 and Y' = 6. When the prices are Px = 1 and P, = 4, Andy's optimal consumption bundle is X** = 6 and Y* 1.5. Suppose the price of...
2. Zhixiu has the following linear preferences over coffee (x) and candy (y): u(x, y) =...
2. Zhixiu has the following linear preferences over coffee (x) and candy (y): u(x, y) = 2x+4y (a) Graph the indifference curves for Zhixiu that represent each of the following utility levels: 10, 20, 40, and 60. (You should be drawing 4 indifference curves, make sure to label with one represents which utility level) Make sure to show your calculations for how you identified the equation of the indifference curves.(4 points) (b) Setup Zhixiu's utility maximization problem with a general...
Homework 3 Chapter 5: Demand 1. What happens to the amount of x and y consumed when income falls if x and y are normal goods? Draw a budget constraint (before the income decrease) and a convex utility curve that corresponds to the optimal consumption bundle. Draw a new budget constraint (after income falls) and a new convex utility curve that corresponds to the optimal consumption bundle. Has the amount of x and y consumed increased or decreased due to...
4. Assume a utility function described by u(x,y)=2/xy. a. Given the utility function, u(x,y)=2xy, sketch the indifference curves for u = 50, 72 and 98. e indifference Carved forbise banta un b. Sketch budget constraint of 5x +10y = 30. Label intercepts (where it crosses the axes). 00:0 VE c. Solve for calculate) the optimal bundle (x, y) and sketch the optimal solution.
1. Price of x is 12 and price of y is 8. Answer the following questions for a consumer who earns $600 and whose preference can be represented with the utility functions U(x,y) x0.4y0.6 = a) Write down the utility maximization problem. (2 points) b) Does the utility function represent convex preference? Explain. (2 points) c) Write down the budget constraint. What is the slope of the budget line? (2 points) d) What is the slope of the indifference curve...
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)...
2. Sandra has the following preferences over cookies (x) and tea (y) (x,y) = min(3x, 2y) (a) Graph Sandra's indifference curves that go through points (2,3), (4,6), (6,9), (8,12). Be sure to label the axis and the utility levels of the indifference curves. (Hint: You should be graphing 4 indifference curves) (10 points) (b) On the same graph above, draw a budget constraint where pe=2.py=2 m = 20. (Note, careful attention to precise graphing here will help in partc.) (4...
1. Dorothy's utility function is U(B, O) = (B + 2) (0 + 1) where B is her consumption of bananas and O is her consumption of oatmeal. MUB = 0 + 1, MUo = B + 2. (Place Oatmeal on the y axis.) a. Write down the expression and draw Dorothy's indifference curve through (2,8). b. Suppose po = Pb = $1 and M = $11, draw the budget constraint on the same graph as her indifference curve. c....
Jane commutes to work. She can either use public transport or her own car. Her indifference curves obey the four properties of indifference curves for ordinary goods 1. Draw Jane's budget line (BL,) with car travel on the vertical axis and public transport on the horizontal axis 2. Suppose that Jane consumes some of both goods. Explain how her optimal consumption bundle can be obtained. Then, draw an indifference curve that helps you illustrate that optimal consumption bundle represented by...
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X is MUx = Y. His marginal utility of Y is MUY = . He has income $12. When the prices are Px - 1 and Py -1, Andy's optimal consumption bundle is X* -6 and Y' = 6. When the prices are Px = 1 and P, = 4, Andy's optimal consumption bundle is X** = 6 and Y* 1.5. Suppose the price of...
2. Zhixiu has the following linear preferences over coffee (x) and candy (y): u(x, y) = 2x+4y (a) Graph the indifference curves for Zhixiu that represent each of the following utility levels: 10, 20, 40, and 60. (You should be drawing 4 indifference curves, make sure to label with one represents which utility level) Make sure to show your calculations for how you identified the equation of the indifference curves.(4 points) (b) Setup Zhixiu's utility maximization problem with a general...
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