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7. Suppose U(X., X) = X.-X, (12pts) a. Solve for the marshallian demands for x, and...
4. Suppose U(x1, x2) = 2lnx1 + 3lnx2 and P1 = 4, P2 = 1, and...
4. Suppose U(x1, x2) = 2lnx1 + 3lnx2 and P1 = 4, P2 = 1, and m = 20. (4pts) Set up the Lagrangian for this problem (but do not solve it) 5. Suppose U(x1, x2) = min{5x1, x2}. (8pts) Write out the Marshallian demands for x1 and x2, as functions of p1, p2, and m. Now, solve for these when P1 = 3, P2 = 1, and m = 16. Is this an interior or corner solution? Is the...
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...
Suppose Philip’s utility function over two goods, 1 and 2, is given by the quasilinear form,...
Suppose Philip’s utility function over two goods, 1 and 2, is given by the quasilinear form, U(q ,q )=2q0.5 +q. Let p1, p2, and Y denote the prices of the two goods and Philip’s income. In the first few parts of the problem, you will solve for Philip’s demand functions for the two goods. (a) To start with, suppose the solution is interior and use the tangency condition, or equal marginal principle, to solve for q1∗ (and separately, q2∗) as...
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...
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...
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