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@ See page 78 06 Question (2 points) In addition to finding the optimal bundles...
d 04 Question (2 points) See page 78 In addition to finding the optimal bundles given...
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04 Question (2 points) See page 78 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 dub these parameters or exogenous variables). 1st attempt See Hint Suppose utility for an average consumer over food and...
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...
2.Optional Question on duality for those who welcome a challenge Consider the same utility functi...
2.Optional Question on duality for those who welcome a challenge Consider the same utility function as given by: U(X, Y) = X-Y For the primal problem, find the Marshallian uncompensated demand functions, X(Px Ру and y(Rs Py, by maximizing utility subject to budget constraint Px. X + Ру.Y - I. After obtaining the optimal consumption choices, write down the indirect utility function. Give a simple diagrammatic and economic interpretation. Illustrate the use of the indirect utility function by plugging in...
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,...
Anna's utility function is given by U (r.y) = (r + 3) (y + 2), where...
Anna's utility function is given by U (r.y) = (r + 3) (y + 2), where I and y are the two goods she consumes. The price of good r is p ,. The price of good y is Py. Her income is m. (a) Write her maximization problem and find her demand functions for the two goods. Is it always possible to have an interior solution? Justify your answer. (b) Are the two goods ordinary or giffen? Are the...
Question 2 (20 points) A consumer purchases two goods x ano y. The consumer's income is...
Question 2 (20 points) A consumer purchases two goods x ano y. The consumer's income is 1. Hi S income is 1. His utility is given by is * and y. Px is the price of x. Py is the price of a) Calculate consumer's optim U(x,y) = xy s optimal choice of x and y under his budget.hu uncompensated demand) b) Derive the indirect utility function. c) Are these two goods normal goods? Why d) Derive the expenditure function....
1 [75 points; Chapter 5] You are to solve the consumer choice problem for three different...
1 [75 points; Chapter 5] You are to solve the consumer choice problem for three different consumers. Each consumer has $150 to spend (income) and faces prices Px = $2 and Py = $3 for goods X and Y. Consumers I, II, and III have utility functions U'(X, Y) = X? + Y, U"(X, Y) = X12 + Yl2, and UTM(X, Y) = X´Y, respectively. For each consumer, do the following steps. a [15 points] Carefully express the consumer's choice...
06 Question (3 points) e See page 149 Douglas consumes two goods, x and y. His utility function is u(x, y) = (x + y. I...
06 Question (3 points) e See page 149 Douglas consumes two goods, x and y. His utility function is u(x, y) = (x + y. In the questions below, give your answers to two decimal places. 1st attempt Part 1 (1 point) See Hint Let the price of good x be $2 and the price of good y be $10. Furthermore, assume that Douglas has $360.00 to spend on these two goods. How much of good x does Douglas demand?...
2. Given the following information; solve the consumer's problem by finding the optimal demand functions for...
2. Given the following information; solve the consumer's problem by finding the optimal demand functions for X and Y: U(X,Y)=min(4X,Y) Also, you are given the the following initial market conditions: Px = $5 Py = $5 M = $100 a. Setup the Optimization Problem b. Find X* and Y* c. Graph the solution and explain the economic intuition behind the graph: i.e. What are the conditions met at the optimal bundle? Introduce another consumption bundle and explain why it is...
d
04 Question (2 points) See page 78 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 dub these parameters or exogenous variables). 1st attempt See Hint Suppose utility for an average consumer over food and...
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...
2.Optional Question on duality for those who welcome a challenge Consider the same utility function as given by: U(X, Y) = X-Y For the primal problem, find the Marshallian uncompensated demand functions, X(Px Ру and y(Rs Py, by maximizing utility subject to budget constraint Px. X + Ру.Y - I. After obtaining the optimal consumption choices, write down the indirect utility function. Give a simple diagrammatic and economic interpretation. Illustrate the use of the indirect utility function by plugging in...
Question 2 (20 points) A consumer purchases two goods x ano y. The consumer's income is 1. Hi S income is 1. His utility is given by is * and y. Px is the price of x. Py is the price of a) Calculate consumer's optim U(x,y) = xy s optimal choice of x and y under his budget.hu uncompensated demand) b) Derive the indirect utility function. c) Are these two goods normal goods? Why d) Derive the expenditure function....
1 [75 points; Chapter 5] You are to solve the consumer choice problem for three different consumers. Each consumer has $150 to spend (income) and faces prices Px = $2 and Py = $3 for goods X and Y. Consumers I, II, and III have utility functions U'(X, Y) = X? + Y, U"(X, Y) = X12 + Yl2, and UTM(X, Y) = X´Y, respectively. For each consumer, do the following steps. a [15 points] Carefully express the consumer's choice...
06 Question (3 points) e See page 149 Douglas consumes two goods, x and y. His utility function is u(x, y) = (x + y. In the questions below, give your answers to two decimal places. 1st attempt Part 1 (1 point) See Hint Let the price of good x be $2 and the price of good y be $10. Furthermore, assume that Douglas has $360.00 to spend on these two goods. How much of good x does Douglas demand?...
2. Given the following information; solve the consumer's problem by finding the optimal demand functions for X and Y: U(X,Y)=min(4X,Y) Also, you are given the the following initial market conditions: Px = $5 Py = $5 M = $100 a. Setup the Optimization Problem b. Find X* and Y* c. Graph the solution and explain the economic intuition behind the graph: i.e. What are the conditions met at the optimal bundle? Introduce another consumption bundle and explain why it is...
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