The consumer has the utility function U(x1 , x2) = (x1-2)4 (x2-3)3, subject to her budget constraint 10 = 4x1 + 3x2. Write the utility maximization of this consumer using the Lagrangian method and find the optimal value of x1 and x2.
Homework Answers
Suppose a person has a utility function U(x1,x2)= xa1+xa2, which she maximizes subject to her budget...
Suppose a person has a utility function U(x1,x2)= xa1+xa2, which
she maximizes subject to her budget constraint, px1 + qx2 = m,
where p, q, m are all positive. Use the Lagrangian method to solve
the maximization problem, and find the demand functions for the
consumer. Show that the demand functions are homogeneous of degree
zero in prices (p, q) and income (m)
(2.5 marks) Suppose a person has a utility function U(x1, x2) = xq +xm, which she maximizes...
U = 8x10.5+ 2x2, where x1 is the quantity of good 1 consumed, and x2 is...
U = 8x10.5+ 2x2, where x1 is the quantity of good 1 consumed, and x2 is the quantity of good 2 consumed. (Yes the x is raised) 8x1.5 Suppose that the consumer has a budget of M = $400 to spend and that good 1 has a price of p1= 2, and good 2 has a price of p2= 8. Answer the following questions, and write your answers in the Answer Sheet. Write the person’s budget constraint as an equation,...
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...
Luke's choice behavior can be represented by the utility function u(x1,x2)= x1 + x2
Luke's choice behavior can be represented by the utility function u(x1,x2)= x1 + x2.The prices of x1 and x2 are denoted as p1 and p2, and his income is m. 1. Draw at least three indifference curves and find its slope (i.e. MRS). Is the MRS changing depending on the points of (x1, x2) at which it is evaluated, or constant? 2. Draw a budget constraint assuming that p1 < P2. Find the optimal bundle (x1*,x2*) as a function of income and prices. 3....
A consumer has utility function: u(x1 , x2 ) = x1 + 2x2 . The consumer...
A consumer has utility function: u(x1 , x2 ) = x1 + 2x2 . The consumer has income m > 0 tospendongood1andgood2. Ifthepriceofx1 isp1 =1andthepriceofx2 isp2 =0.5, then, in order to maximize her utility, the consumer must consume: a) x1 = x2 (b) x1 = 2x2 (c) 2x1 = x2 (d) x1 = 4x2 (e) None of the above
Cursue a consumer with preferences described by (x1, x2) = x1 + x2 Suppose she faces...
Cursue a consumer with preferences described by (x1, x2) = x1 + x2 Suppose she faces prices pi 1 and P2 = 1/2 and that she has an income of I = 2. For your reference, the marginal utilities at a bundle (x1, x2) in this setting are given by MU (x1, x2) = 1 MU?(x), x2) = 2V x2 3(a) Write down the two equations which characterize the consumer's utility-maximizing bundle (X1.3) in this situation. In other words, write...
6. Consider a consumer with the utility function u(x1,x2) = In(x) x2 and the budget constraint...
6. Consider a consumer with the utility function u(x1,x2) = In(x) x2 and the budget constraint px + p2x2 = m. Derive the consumer's demand functions for x1 and x2. (25 marks)
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min...
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min . If P. = $1. P. = $1. and I = $100. find the value of xı* (Hint: This is Leontief utility, the kind with right-angled indifference curves) 2. (10 points) If P, = $4, P2 = $2, and I = $20, and my utility is given by u(x1, x2) = 4x1 + 3x2, find x* (Note: I'm asking for optimal consumption of Good...
Suppose that a consumer has a utility function given by u(x1, x2) = 2x1 + x2. Initially the consumer faces prices (2, 2) and has income 24. i. Graph the budget constraint and indifference curves. Find...
Suppose that a consumer has a utility function given by u(x1, x2) = 2x1 + x2. Initially the consumer faces prices (2, 2) and has income 24. i. Graph the budget constraint and indifference curves. Find the initial optimal bundle. ii. If the prices change to (6, 2), find the new optimal bundle. Show this in your graph in (i). iii. How much of the change in demand for x1 is due to the substitution effect? How much due to...
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?
Suppose a person has a utility function U(x1,x2)= xa1+xa2, which
she maximizes subject to her budget constraint, px1 + qx2 = m,
where p, q, m are all positive. Use the Lagrangian method to solve
the maximization problem, and find the demand functions for the
consumer. Show that the demand functions are homogeneous of degree
zero in prices (p, q) and income (m)
(2.5 marks) Suppose a person has a utility function U(x1, x2) = xq +xm, which she maximizes...
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...
Cursue a consumer with preferences described by (x1, x2) = x1 + x2 Suppose she faces prices pi 1 and P2 = 1/2 and that she has an income of I = 2. For your reference, the marginal utilities at a bundle (x1, x2) in this setting are given by MU (x1, x2) = 1 MU?(x), x2) = 2V x2 3(a) Write down the two equations which characterize the consumer's utility-maximizing bundle (X1.3) in this situation. In other words, write...
6. Consider a consumer with the utility function u(x1,x2) = In(x) x2 and the budget constraint px + p2x2 = m. Derive the consumer's demand functions for x1 and x2. (25 marks)
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min . If P. = $1. P. = $1. and I = $100. find the value of xı* (Hint: This is Leontief utility, the kind with right-angled indifference curves) 2. (10 points) If P, = $4, P2 = $2, and I = $20, and my utility is given by u(x1, x2) = 4x1 + 3x2, find x* (Note: I'm asking for optimal consumption of Good...
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?
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