For a general Cobb-Douglas utility function U(x,y)=Axayb, please show that the price elasticities of demand for both of good x and y are -1, and that the income elasticities of demand for both of good...
For a general Cobb-Douglas utility function U(x,y)=Axayb, please show that the price elasticities of demand for both of good x and y are -1, and that the income elasticities of demand for both of good x and y are 1.
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For a general Cobb-Douglas utility function U(x,y)=Axayb, please show that the price elasticities of demand for both of good x and y are -1, and that the income elasticities of demand for both of good...
1. When a consumer has a Cobb-Douglas utility function given by u(x, y) = xa yb , their demand for good x is given by x∗...
1. When a consumer has a Cobb-Douglas utility function given by u(x, y) = xa yb , their demand for good x is given by x∗ = m/Px (a/a+b) where m is income and Px is the price of good x. Using this demand function, find the formula for this consumer’s price elasticity of demand. Interpret it in words.
Roger's utility function is Cobb-Douglas, U = 80.67 20.33, his income is Y, the price of...
Roger's utility function is Cobb-Douglas, U = 80.67 20.33, his income is Y, the price of B is PB, and the price of Z is pz. Derive his demand curves. Roger's demand functions are B= and Z= . (Enter any numbers rounded to two decimal places. Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the_ character.)
If you have a Cobb-Douglas utility function U= Xα Yβ, what is your compensated demand function...
If you have a Cobb-Douglas utility function U= Xα Yβ, what is your compensated demand function for good X?
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 =...
Complete parts a-e. 1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint:...
Complete parts a-e.
1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint: MZ PeX+PY *Treat Px, P, M, a, and B as positive constants. Note, a + B < 1. Using these equations, please answer the following questions: a. Formally state this consumer's utility maximization problem and write down the relevant Lagrangian. (6 pts) b. Using your work from part "a.", derive demand curves for X and Y. Show all work. (6 pts) C. Show that...
5. Douglas consumes two goods, x and y. His utility function is u(x) = Vx+y Let...
5. Douglas consumes two goods, x and y. His utility function is u(x) = Vx+y Let the price of good x be $2 and the price of good y be $2. Furthermore, assume that Douglas has $420.00 to spend on these two goods. Find the demand for good x and y. Now suppose that the price of good x decreases to $1.00. What is the income effect and substitution effect of this price change on the demand for x?
A person has a Cobb Douglas utility function for two goods X and Y. If the...
A person has a Cobb Douglas utility function for two goods X and Y. If the price of a X increases and the budget stays the same, the utility maximizing person __________. Cannot be determined from the information will consume less of Y will only consume Y will consume less of both goods will have lower utility
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...
4. Suppose preferences are represented by the Cobb-Douglas utility function, u(x1x2) = xx-. a) Show that...
4. Suppose preferences are represented by the Cobb-Douglas utility function, u(x1x2) = xx-. a) Show that marginal utility is decreasing in X and X2. What is the interpretation of this property? b) Calculate the marginal rate of substitution c) Assuming an interior solution, solve for the Marshallian demand functions.
A person has a Cobb Douglas utility function for two goods X and Y. If the...
A person has a Cobb Douglas utility function for two goods X and Y. If the price of a X decreases and the budget stays the same, then a utility maximizing person O will only consume X* O will consume more of Y Cannot be determined from the information will consume more of both goods will have higher utility
Roger's utility function is Cobb-Douglas, U = 80.67 20.33, his income is Y, the price of B is PB, and the price of Z is pz. Derive his demand curves. Roger's demand functions are B= and Z= . (Enter any numbers rounded to two decimal places. Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the_ character.)
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 =...
Complete parts a-e.
1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint: MZ PeX+PY *Treat Px, P, M, a, and B as positive constants. Note, a + B < 1. Using these equations, please answer the following questions: a. Formally state this consumer's utility maximization problem and write down the relevant Lagrangian. (6 pts) b. Using your work from part "a.", derive demand curves for X and Y. Show all work. (6 pts) C. Show that...
5. Douglas consumes two goods, x and y. His utility function is u(x) = Vx+y Let the price of good x be $2 and the price of good y be $2. Furthermore, assume that Douglas has $420.00 to spend on these two goods. Find the demand for good x and y. Now suppose that the price of good x decreases to $1.00. What is the income effect and substitution effect of this price change on the demand for x?
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...
4. Suppose preferences are represented by the Cobb-Douglas utility function, u(x1x2) = xx-. a) Show that marginal utility is decreasing in X and X2. What is the interpretation of this property? b) Calculate the marginal rate of substitution c) Assuming an interior solution, solve for the Marshallian demand functions.
A person has a Cobb Douglas utility function for two goods X and Y. If the price of a X decreases and the budget stays the same, then a utility maximizing person O will only consume X* O will consume more of Y Cannot be determined from the information will consume more of both goods will have higher utility
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