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The utility function of the consumer is u(x1, x2) = VX1 + X2. a) Let P1...
Question 1 (20 points). The utility function of the consumer is u(x1, x2) = x1 +...
Question 1 (20 points). The utility function of the consumer is u(x1, x2) = x1 + x2. a) Let pı = 2 ,P2 = 20 and m = 24. Calculate the optimal quantity demanded of good 1 and 2. (7 points) b) Let p1 = 1,P2 = 4 and m = 100. Calculate the optimal quantity demanded of good 1 and 2. (6 points) c) Let P1 = 1, p2 = 4 and m = 4. Compared to point b),...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the consumption bundles that gives the consumer utility 100. (3 points) b) Plot all the consumption bundles that gives the consumer utility 144. (3 points) c) Plot the budget constraint when p. = 10,P2 = 10 and m = 100 (3 points) d) Plot the budget constraint when P1 = 20, P2 = 5 and m = 60 (3 points) e) What is the optimal...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). e) What is the...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). e) What is the optimal quantity demanded of x, and x2 when pı = 10,p2 = 10 and m = 100? (4 points) f) What is the optimal quantity demanded of x, and x2 when Pı = 20,P2 = 5 and m = 60 ?(4 points)
The utility function of the consumer is ?(?1,?2)=√?1+?2.a) Let ?1=2,?2=20????=24. Calculate the optimal quantity demanded of...
The utility function of the consumer is ?(?1,?2)=√?1+?2.a) Let ?1=2,?2=20????=24. Calculate the optimal quantity demanded of good 1 and 2. (7 points)b) Let ?1=1,?2=4????=100. Calculate the optimal quantity demanded of good 1 and 2. (6 points)c) Let ?1=1,?2=4and ?=4. Compared to point b), by how much would the consumer decrease the quantity demanded of good 1 and good 2? (7 points).
Problem 3 Text: Suppose the utility function of the consumer is u(x1,x2)=min{x1,x2}. Further, suppose pi=$4, P2=$2...
Problem 3 Text: Suppose the utility function of the consumer is u(x1,x2)=min{x1,x2}. Further, suppose pi=$4, P2=$2 and 1=$18. Based on this information, answer the following questions (questions 16-25). Questions: 16. What is the optimal quantity of Good 1 chosen by the consumer? 17. What is the optimal quantity of Good 2 chosen by the consumer? 18. What is the optimal quantity of Good 1 chosen by the consumer if pı decreases to $1?
Question-3 Suppose the consumer’s utility function is given by U (x1 , x2 ) = x1x...
Question-3 Suppose the consumer’s utility function is given by U (x1 , x2 ) = x1x 2 2 . Let the prices of good 1, good 2 be p1 , p2 , and suppose this consumer wants to reach a level of utility U (a) [2] Formulate the consumer’s problem in terms of the Lagrangian (b) [5] Derive the Hicksian demands for this consumer (c) [3] What is the expenditure for this consumer. (d) [5] Show that x H (...
(10 points) Wendy's utility over consumption bundles (x1, x2) is given by u(x1,x2) = VX1 +...
(10 points) Wendy's utility over consumption bundles (x1, x2) is given by u(x1,x2) = VX1 + 21X2. If the price of good 1 is $2/unit, the price of good 2 is $1/unit and income is $120, what is Wendy's optimal consumption of Good 2? (You can use the 5 step method to solve this problem). (10 points) When u(x1, x2) = min ), at prices and income P1, P2, and I, demand for good 1 is given by xi (P1,...
The utility function is u = x1½ + x2, and the budget constraint is m =...
The utility function is u = x1½ + x2, and the budget constraint is m = p1x1 + p2x2. Derive the optimal demand curve for good 1, x1(p1, p2), and good 2, x2(m, p1, p2). Looking at the cross price effects (∂x1/∂p2 and ∂x2/∂p1) are goods x1 and x2 substitutes or complements? Looking at income effects (∂x1/∂m and ∂x2/∂m) are goods x1 and x2 inferior, normal or neither? Assume m=100, p1=0.5 and p2=1. Using the demand function you derived in...
1.) Liz has utility given by u(x2,x1)=x1^7x2^8. If P1=$10, P2=$20, and I = $150, find Liz’s...
1.) Liz has utility given by u(x2,x1)=x1^7x2^8. If P1=$10, P2=$20, and I = $150, find Liz’s optimal consumption of good 1. (Hint: you can use the 5 step method or one of the demand functions derived in class to find the answer). 2.) Using the information from question 1, find Liz’s optimal consumption of good 2 3.) Lyndsay has utility given by u(x2,x1)=min{x1/3,x2/7}. If P1=$1, P2=$1, and I=$10, find Lyndsay’s optimal consumption of good 1. (Hint: this is Leontief utility)....
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given 1) Find the demand functions for x1 and x2 assuming -> 1. What is special about Р2 these demand functions? Are both goods normal? Are these tastes homothetic? <1. You probably P2 2) Now find the demand functions for x1 and x2 assuming assumed the opposite above, so now will you find something different. Explain....
Question 1 (20 points). The utility function of the consumer is u(x1, x2) = x1 + x2. a) Let pı = 2 ,P2 = 20 and m = 24. Calculate the optimal quantity demanded of good 1 and 2. (7 points) b) Let p1 = 1,P2 = 4 and m = 100. Calculate the optimal quantity demanded of good 1 and 2. (6 points) c) Let P1 = 1, p2 = 4 and m = 4. Compared to point b),...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the consumption bundles that gives the consumer utility 100. (3 points) b) Plot all the consumption bundles that gives the consumer utility 144. (3 points) c) Plot the budget constraint when p. = 10,P2 = 10 and m = 100 (3 points) d) Plot the budget constraint when P1 = 20, P2 = 5 and m = 60 (3 points) e) What is the optimal...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). e) What is the optimal quantity demanded of x, and x2 when pı = 10,p2 = 10 and m = 100? (4 points) f) What is the optimal quantity demanded of x, and x2 when Pı = 20,P2 = 5 and m = 60 ?(4 points)
Problem 3 Text: Suppose the utility function of the consumer is u(x1,x2)=min{x1,x2}. Further, suppose pi=$4, P2=$2 and 1=$18. Based on this information, answer the following questions (questions 16-25). Questions: 16. What is the optimal quantity of Good 1 chosen by the consumer? 17. What is the optimal quantity of Good 2 chosen by the consumer? 18. What is the optimal quantity of Good 1 chosen by the consumer if pı decreases to $1?
(10 points) Wendy's utility over consumption bundles (x1, x2) is given by u(x1,x2) = VX1 + 21X2. If the price of good 1 is $2/unit, the price of good 2 is $1/unit and income is $120, what is Wendy's optimal consumption of Good 2? (You can use the 5 step method to solve this problem). (10 points) When u(x1, x2) = min ), at prices and income P1, P2, and I, demand for good 1 is given by xi (P1,...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given 1) Find the demand functions for x1 and x2 assuming -> 1. What is special about Р2 these demand functions? Are both goods normal? Are these tastes homothetic? <1. You probably P2 2) Now find the demand functions for x1 and x2 assuming assumed the opposite above, so now will you find something different. Explain....
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