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7. Suppose U(X., X) = X.-X, (12pts) a. Solve for the marshallian demands for x, and...
1. Suppose U(X1, X2) = 2lnx, + 3lnx, and P, = 4, P2 = 1, and...
1. Suppose U(X1, X2) = 2lnx, + 3lnx, and P, = 4, P2 = 1, and m = 20. (15pts) a. Solve for the Utility maximizing amounts of x, and X2. b. Is this an interior or corner solution? c. Is the budget exhausted here? Yes/no d. Assume that the above prices and income have all doubled. How does this change your solution in a? e. Set up the Lagrangian for this problem (but do not solve it) 2. Suppose...
U(x, y) = x,"x:(1-2) a. Solve for the marshallian demands for x, and x, as functions...
U(x, y) = x,"x:(1-2) a. Solve for the marshallian demands for x, and x, as functions of p1, P2, and m. (Hint your solutions will be equations, not numbers). b. For x, find the own-price elasticity and income elasticity. C. Suppose a = 0.2, m = 100, p1 = 2, and p2=8, find the quantities of x, and X d. What happens to these quantities when p1 doubles to $4? e. What does this say about the price consumption curve...
U(x, y) = x1ax2(1-a) Solve for the marshallian demands for x1 and x2, as functions of...
U(x, y) = x1ax2(1-a) Solve for the marshallian demands for x1 and x2, as functions of p1, p2, and m. (Hint: your solutions will be equations, not numbers). For x1 find the own-price elasticity and income elasticity. Suppose a = 0.2, m = 100, p1 = 2, and p2=8, find the quantities of x1 and x2. What happens to these quantities when p1 doubles to $4? What does this say about the price consumption curve (PCC)? 2. Suppose the price...
U(x, y) = x1ax2(1-a) a. Solve for the marshallian demands for x1 and x2, as functions...
U(x, y) = x1ax2(1-a) a. Solve for the marshallian demands for x1 and x2, as functions of p1, p2, and m. (Hint: your solutions will be equations, not numbers). b. For x1 find the own-price elasticity and income elasticity. c. Suppose a = 0.2, m = 100, p1 = 2, and p2=8, find the quantities of x1 and x2. d. happens to these quantities when p1 doubles to $4? e. What does this say about the price consumption curve (PCC)?
NEED Question #2 1. U(x, y) = x1ax2(1-a) a. Solve for the marshallian demands for x1...
NEED Question #2 1. U(x, y) = x1ax2(1-a) a. Solve for the marshallian demands for x1 and x2, as functions of p1, p2, and m. (Hint: your solutions will be equations, not numbers). b. For x1 find the own-price elasticity and income elasticity. c. Suppose a = 0.2, m = 100, p1 = 2, and p2=8, find the quantities of x1 and x2. d. What happens to these quantities when p1 doubles to $4? e. What does this say about...
Show all work please. 1. U(x, y) x,ax,1-a) a. Solve for the marshallian demands for x,...
Show all work please.
1. U(x, y) x,ax,1-a) a. Solve for the marshallian demands for x, and x2, as functions of p1, p2, and m. (Hint: your solutions will be equations, not numbers). (4pts) b. For x, find the own-price elasticity and income elasticity. (4pts) c. Suppose a = d. What happens to these quantities when p1 doubles to $4? (4pts) e. What does this say about the price consumption curve (PCC)? (4pts) 100, p1 2, and p2=8, find the...
Question 3: Suppose there are two people in town. Their individual demands are given by Q4...
Question 3: Suppose there are two people in town. Their individual demands are given by Q4 10 - 3p, Q 15 6p. (1) Sketch the individual demand curves and the aggregate town demand on the same graph, with Q on the horizontal axis and p on the vertical axis. (2) What is the quantity demanded when p = 2? When p = 3? Question 4: For each of the following price-income scenarios, sketch the co budget lines on one set...
7. Jay's Utility function is given by U(x,z) = 3x10.2 x20.8 and P1=$2 and P2=$4 and...
7. Jay's Utility function is given by U(x,z) = 3x10.2 x20.8 and P1=$2 and P2=$4 and his budget is $200. Write out the Lagrange but DO NOT solve it Find the utility maximizing values of x1and x2 8. What does the substitution effect cause a consumer to do if the price of a good increases? 9. What does the income effect cause a consumer to do if the price of a good increases? What else is needed here? 10. What...
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...
A consumer's preferences are given by the following utility function: u(x,y) = xy Assume Pold =...
A consumer's preferences are given by the following utility function: u(x,y) = xy Assume Pold = 1, Py = 1, and I = 8. a. Solve for the Marshallian demand functions of x and y (your answer should have numbers, not variables. You should round your answers to three decimal places): * old 4 y = 4 b. What is the utility associated with these demands, prices, and income? u = 16 c. Suppose the price of x rises to...
1. Suppose U(X1, X2) = 2lnx, + 3lnx, and P, = 4, P2 = 1, and m = 20. (15pts) a. Solve for the Utility maximizing amounts of x, and X2. b. Is this an interior or corner solution? c. Is the budget exhausted here? Yes/no d. Assume that the above prices and income have all doubled. How does this change your solution in a? e. Set up the Lagrangian for this problem (but do not solve it) 2. Suppose...
U(x, y) = x,"x:(1-2) a. Solve for the marshallian demands for x, and x, as functions of p1, P2, and m. (Hint your solutions will be equations, not numbers). b. For x, find the own-price elasticity and income elasticity. C. Suppose a = 0.2, m = 100, p1 = 2, and p2=8, find the quantities of x, and X d. What happens to these quantities when p1 doubles to $4? e. What does this say about the price consumption curve...
Show all work please.
1. U(x, y) x,ax,1-a) a. Solve for the marshallian demands for x, and x2, as functions of p1, p2, and m. (Hint: your solutions will be equations, not numbers). (4pts) b. For x, find the own-price elasticity and income elasticity. (4pts) c. Suppose a = d. What happens to these quantities when p1 doubles to $4? (4pts) e. What does this say about the price consumption curve (PCC)? (4pts) 100, p1 2, and p2=8, find the...
Question 3: Suppose there are two people in town. Their individual demands are given by Q4 10 - 3p, Q 15 6p. (1) Sketch the individual demand curves and the aggregate town demand on the same graph, with Q on the horizontal axis and p on the vertical axis. (2) What is the quantity demanded when p = 2? When p = 3? Question 4: For each of the following price-income scenarios, sketch the co budget lines on one set...
A consumer's preferences are given by the following utility function: u(x,y) = xy Assume Pold = 1, Py = 1, and I = 8. a. Solve for the Marshallian demand functions of x and y (your answer should have numbers, not variables. You should round your answers to three decimal places): * old 4 y = 4 b. What is the utility associated with these demands, prices, and income? u = 16 c. Suppose the price of x rises to...
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