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An individual plots her utility from a consumption bundle based on the three utility structures as...
Suppose that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice...
Suppose that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice cream sundaes (z)-according to the Cobb- Douglas utility function: Suppose also that the prices for these goods are given by Px-1,py-4, and pz-8 and this consumer's income is given by 1-8 If z-0, then the combination of x and y that optimize utility involve x*- utility U and y*- , These values of x* and y result in a level of If z- 1,...
1) Eor each of the utility functions below, find the optimal consumption bundle if pi-3 and...
1) Eor each of the utility functions below, find the optimal consumption bundle if pi-3 and p2-2 and m-240 a. u(x)-2x2 b. u(x)-xix22 c. d, e. u(x)- 2x1+X2 u(x)-min(x1,2%) u(x)-x1-X22 y(x)-max(x1,x2) X(X1,X2 2) Suppose p1-2, p2-7 for the first 2 units and p2 4 for the rest. a) Ifm-54 and u(x) -X1+3x2, then what is the optimal consumption bundle? b) Ifm-22 and u(x) - min(3xı, 2x2), , thenwhat is the optimal consumption bundle? Erom Workouts: 5.3,5.6,5.7 3)
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7...
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7 (a) Does this utility function exhibit diminishing marginal utility in X? Show why or why not. (b) Does this utility function exhibit diminishing marginal rate of substitution? Mathematically show and verbally explain why it has (or doesn't have) such property. Problem 2 (10 marks) Consider the following utility function U(X,Y)= X14734 Suppose that prices and income are given as following Px= 1 Py =...
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...
question #6 P2 = $1 for each Gala. Find her optimal demand and show it on...
question #6
P2 = $1 for each Gala. Find her optimal demand and show it on the graph. (e) Describe Kate's optimal choice(s) when p $1. Consumer Demand For each of the following utility functions, write down a transformation that would turn it into a Cobb-Douglas utility function of the form U(, )"ys where a B-1. (a) U(x, y) γχαν'-a where γ is a constant. (b) U(, y)-y 6. For each of the following utility functions, write down 2 monotonic...
Question: Suppose your utility function from a given bundle of goods, (x.y), isWex.y) (y) (a) Suppose...
Question: Suppose your utility function from a given bundle of goods, (x.y), isWex.y) (y) (a) Suppose y 1. Make a table showing your utility for x 1, x-2x-3' and x (b) Is utility increasing from more units of x? (c) Is marginal utility increasing from more units of x? (d) Derive the equation describing the marginal utility for x, Mu (e) Plot a representative indifference curve that includes 3 bundles of goods of your choosing. Include on your graph the...
Assume that Sam has following utility function: U(x,y) = 2√x+y. Assume px = 1/5, py = 1 and her i...
Assume that Sam has following utility function: U(x,y) = 2√x+y. Assume px = 1/5, py = 1 and her income I = 10. (e) Draw an optimal bundle which is the result of utility maximization under given budget set. (Hint: Assume interior solution). Define corresponding expenditure minimization problem (note the elements for expenditure minimization problem are (i) objective function, (ii) constraint, (iii) what to choose). (f)Describeaboutwhatthedualityproblemis. Definemarshalliandemandfuction andhicksiandemandfunction. (Hint: identifytheinputfactorsofthesefunctions.) (g) Consider a price increase for the good x from...
Cat only buys tomatoes (x) and cucumbers (y) and her preferences can be identified with U(x,x)=6x2y....
Cat only buys tomatoes (x) and cucumbers (y) and her preferences can be identified with U(x,x)=6x2y. a. What is Cat's marginal utility for tomatoes, and what is her marginal utility for cucumbers? How does Cat's utility change when she consumes more tomatoes? How does her utility change when she consumes more cucumbers? b. Find Cat’s marginal rate of substitution (tomatoes are on the x axis and cucumbers on the y axis). What is the slope of Cat's indifference curve that...
X-EC2010-1 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility,...
X-EC2010-1 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(X.y) = x10y10, 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) (6) For product...
2. Consider the following four consumers (C1,C2,C3,C4) with the following utility functions: Consumer Utility Function C1...
2. Consider the following four consumers (C1,C2,C3,C4) with the following utility functions: Consumer Utility Function C1 u(x,y) = 2x+2y C2 u(x,y) = x^3/4y^1/4 C3 u(x,y) = min(x,y) C4 u(x,y) = min(4x,3y) On the appropriate graph, draw each consumer’s indifference curves through the following points: (2,2), (4,4), (6,6) and (8,8), AND label the utility level of each curve. Hint: Each grid should have 4 curves on it representing the same preferences but with different utility levels. 3. In the following parts,...
Suppose that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice cream sundaes (z)-according to the Cobb- Douglas utility function: Suppose also that the prices for these goods are given by Px-1,py-4, and pz-8 and this consumer's income is given by 1-8 If z-0, then the combination of x and y that optimize utility involve x*- utility U and y*- , These values of x* and y result in a level of If z- 1,...
1) Eor each of the utility functions below, find the optimal consumption bundle if pi-3 and p2-2 and m-240 a. u(x)-2x2 b. u(x)-xix22 c. d, e. u(x)- 2x1+X2 u(x)-min(x1,2%) u(x)-x1-X22 y(x)-max(x1,x2) X(X1,X2 2) Suppose p1-2, p2-7 for the first 2 units and p2 4 for the rest. a) Ifm-54 and u(x) -X1+3x2, then what is the optimal consumption bundle? b) Ifm-22 and u(x) - min(3xı, 2x2), , thenwhat is the optimal consumption bundle? Erom Workouts: 5.3,5.6,5.7 3)
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7 (a) Does this utility function exhibit diminishing marginal utility in X? Show why or why not. (b) Does this utility function exhibit diminishing marginal rate of substitution? Mathematically show and verbally explain why it has (or doesn't have) such property. Problem 2 (10 marks) Consider the following utility function U(X,Y)= X14734 Suppose that prices and income are given as following Px= 1 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...
question #6
P2 = $1 for each Gala. Find her optimal demand and show it on the graph. (e) Describe Kate's optimal choice(s) when p $1. Consumer Demand For each of the following utility functions, write down a transformation that would turn it into a Cobb-Douglas utility function of the form U(, )"ys where a B-1. (a) U(x, y) γχαν'-a where γ is a constant. (b) U(, y)-y 6. For each of the following utility functions, write down 2 monotonic...
Question: Suppose your utility function from a given bundle of goods, (x.y), isWex.y) (y) (a) Suppose y 1. Make a table showing your utility for x 1, x-2x-3' and x (b) Is utility increasing from more units of x? (c) Is marginal utility increasing from more units of x? (d) Derive the equation describing the marginal utility for x, Mu (e) Plot a representative indifference curve that includes 3 bundles of goods of your choosing. Include on your graph the...
Cat only buys tomatoes (x) and cucumbers (y) and her preferences can be identified with U(x,x)=6x2y. a. What is Cat's marginal utility for tomatoes, and what is her marginal utility for cucumbers? How does Cat's utility change when she consumes more tomatoes? How does her utility change when she consumes more cucumbers? b. Find Cat’s marginal rate of substitution (tomatoes are on the x axis and cucumbers on the y axis). What is the slope of Cat's indifference curve that...
X-EC2010-1 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(X.y) = x10y10, 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) (6) For product...
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