dHomework Answers
Cobb Douglas preferences will always result in an interior optimum for utility maximization because Cobb Douglas preferences are well behaved , continuous , homogenous , homothetic and strictly convex which means slope of indifference curve i.e. MRS is downward sloping.
so option (c) is correct.
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d
See Hint Which types of preferences will always result in an interior optimum for utility...
d See Hint Let x1 represent a typical good (i.e., consumers prefer more of good x1...
d
See Hint Let x1 represent a typical good (i.e., consumers prefer more of good x1 to less). Let x2 represent a second good in a two-good world. Both goods have continuous indifference curves and income, m, is greater than $0. Under which of the following situations would consumers spend all of their income on just x1? Choose one or more: A. X1 and x2 are perfect complements. B. The consumer has Cobb-Douglas preferences, and p2 > pi. C. xi...
d @ See page 78 06 Question (2 points) In addition to finding the optimal bundles...
d
@ See page 78 06 Question (2 points) In addition to finding the optimal bundles given prices and income, utility maximization can be used to find individual demand functions at any prices and income. Setting up the problem and solving it are the same, except that the prices of each good and the income will be left in variable form (economists call these parameters or exogenous variables). 1st attempt See Hint Consider the quasilinear utility function u(x, y) =...
d @ See page 78 05 Question (2 points) In addition to finding the optimal bundles...
d
@ See page 78 05 Question (2 points) In addition to finding the optimal bundles given prices and income, utility maximization can be used to find individual demand functions at any prices and income. Setting up the problem and solving it are the same, except that the prices of each good and the income will be left in variable form (economists call these parameters or exogenous variables). 1st attempt See Hint Consider a utility function that represents preferences over...
solve 05 Question (5 points) See page 100 One of the most common functional forms used...
solve
05 Question (5 points) See page 100 One of the most common functional forms used in economics is Cobb-Douglas. A Cobb-Douglas utility function takes the formu(I, y) = zºy , where 0 <a < 1. Note that we have imposed the condition that the exponents sum to 1. A monotonic transformation of the function could change that characteristic and still represent the same preferences. However, you will see below that having the exponents sum to 1 leads to a...
d Part 1 (1 point) See Hint The diagram below shows Juan's preferences for cheeseburgers and...
d
Part 1 (1 point) See Hint The diagram below shows Juan's preferences for cheeseburgers and pizzas. Juan's income is $120. The price of one cheeseburger is $10 and the price of one pizza is $15. Use the line tool to draw Juan's budget line. To refer to the graphing tutorial for this question type, please click here. Cheeseburger and Pizza Preferences Pizzas Cheeseburgers Part 2 (2 points) See Hint Using the indifference curves and the budget line you've just...
Question 2:Donny’s monthly budget for Coffee and Muffins is 60 and the prices of those two...
Question 2:Donny’s monthly budget for Coffee and Muffins is 60 and the prices of those two goods are pC=2 and pM=4, respectively. (a) Make a properly labeled diagram illustrating Donny’s budget constraint withCon the horizontal axis and M on the vertical axis. Indicate the area corresponding to the set of bundles(C,M)that Donny can afford. (b) On the same diagram, illustrate Donny’s budget constraint if pM falls from 4 to 2.Up until this point it is impossible to predict what Donny...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py are the prices and I denotes the constraint be prx + pyy income. (a) Write the Lagrangian for this utility maximization problem. (b) Solve the first-order conditions to find the demand functions for both good a and good y. [Hint: Your results should only depend on the pa- rameters pa, Py, I.] (c) In the optimal consumption bundle, how much money is spend on...
d Ist attempt See Hint The table below shows Khloe's purchases of truffles (x1) and oranges...
d
Ist attempt See Hint The table below shows Khloe's purchases of truffles (x1) and oranges (x2) at varying levels of income. Assuming that Khloe is maximizing her utility, which utility function best represents her preferences? Consumption behavior truffles (lbs.) P1 (per lb.) oranges year P2 т 1.00 1 320.00 20 0.25 100 25 2 1.60 320.00 0.5 200 3 640.00 30 1.33 0.25 200 240.00 3.00 20 4 1 300 5 8.00 400.00 25 0.5 250 Choose one: A....
d See Hint Kasey has income of $20.00. She always consumes 5 ounces of cream cheese...
d
See Hint Kasey has income of $20.00. She always consumes 5 ounces of cream cheese with one bagel. If the price of cream cheese is $0.50 per ounce and the price of a bagel is $1.50, Kasey will maximize her utility by purchasing bagels and ounces of cream cheese.
D X-EC2010-1 M. 1. An individual consumer with Cobb-Douglas preferences over two products, x and y,...
D X-EC2010-1 M. 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(x,y) = x1910, subject to the constraint that all income, M, is spent on x and/or y. Products x and y are priced at px and Py, respectively. (a) Set up the appropriate lagrangian for this maximisation problem, find the appropriate first-order conditions for this lagrangian and solve for X and y in terms of Px. Py and M. (40 marks) (b)...
d
See Hint Let x1 represent a typical good (i.e., consumers prefer more of good x1 to less). Let x2 represent a second good in a two-good world. Both goods have continuous indifference curves and income, m, is greater than $0. Under which of the following situations would consumers spend all of their income on just x1? Choose one or more: A. X1 and x2 are perfect complements. B. The consumer has Cobb-Douglas preferences, and p2 > pi. C. xi...
d
@ See page 78 06 Question (2 points) In addition to finding the optimal bundles given prices and income, utility maximization can be used to find individual demand functions at any prices and income. Setting up the problem and solving it are the same, except that the prices of each good and the income will be left in variable form (economists call these parameters or exogenous variables). 1st attempt See Hint Consider the quasilinear utility function u(x, y) =...
d
@ See page 78 05 Question (2 points) In addition to finding the optimal bundles given prices and income, utility maximization can be used to find individual demand functions at any prices and income. Setting up the problem and solving it are the same, except that the prices of each good and the income will be left in variable form (economists call these parameters or exogenous variables). 1st attempt See Hint Consider a utility function that represents preferences over...
solve
05 Question (5 points) See page 100 One of the most common functional forms used in economics is Cobb-Douglas. A Cobb-Douglas utility function takes the formu(I, y) = zºy , where 0 <a < 1. Note that we have imposed the condition that the exponents sum to 1. A monotonic transformation of the function could change that characteristic and still represent the same preferences. However, you will see below that having the exponents sum to 1 leads to a...
d
Part 1 (1 point) See Hint The diagram below shows Juan's preferences for cheeseburgers and pizzas. Juan's income is $120. The price of one cheeseburger is $10 and the price of one pizza is $15. Use the line tool to draw Juan's budget line. To refer to the graphing tutorial for this question type, please click here. Cheeseburger and Pizza Preferences Pizzas Cheeseburgers Part 2 (2 points) See Hint Using the indifference curves and the budget line you've just...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py are the prices and I denotes the constraint be prx + pyy income. (a) Write the Lagrangian for this utility maximization problem. (b) Solve the first-order conditions to find the demand functions for both good a and good y. [Hint: Your results should only depend on the pa- rameters pa, Py, I.] (c) In the optimal consumption bundle, how much money is spend on...
d
Ist attempt See Hint The table below shows Khloe's purchases of truffles (x1) and oranges (x2) at varying levels of income. Assuming that Khloe is maximizing her utility, which utility function best represents her preferences? Consumption behavior truffles (lbs.) P1 (per lb.) oranges year P2 т 1.00 1 320.00 20 0.25 100 25 2 1.60 320.00 0.5 200 3 640.00 30 1.33 0.25 200 240.00 3.00 20 4 1 300 5 8.00 400.00 25 0.5 250 Choose one: A....
d
See Hint Kasey has income of $20.00. She always consumes 5 ounces of cream cheese with one bagel. If the price of cream cheese is $0.50 per ounce and the price of a bagel is $1.50, Kasey will maximize her utility by purchasing bagels and ounces of cream cheese.
D X-EC2010-1 M. 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(x,y) = x1910, subject to the constraint that all income, M, is spent on x and/or y. Products x and y are priced at px and Py, respectively. (a) Set up the appropriate lagrangian for this maximisation problem, find the appropriate first-order conditions for this lagrangian and solve for X and y in terms of Px. Py and M. (40 marks) (b)...
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