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 of one good increases. What is the substitution and the income effect of this price change? What else do you need to know to fully answer this?

U(x, y) = x1ax2(1-a) Solve for the marshallian demands for x1 and x2, as functions of...
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 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...
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...
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. 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...
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...
7. Suppose U(X., X) = X.-X, (12pts) a. Solve for the marshallian demands for x, and X, as functions of p1, p2, and m. 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?
Q2 For each of the following utility functions, derive the consumer's Marshallian demand functions, 21(P1, P2, B) and x (P1, P2, B), and calculate 11 (income elasticity of good 1), €1 (own-price elasticity of good 1), and €12 (cross-price elasticity). a U(x1, x2) = 21 b U(x1, x2) = 2.925-a for a € (0,1) CU(21, 12) = ln(21) + x2 where B > P2.
Yam has the following utility function for Apples (X1) and Ice Cream (X2) U(X1,X2) = Min{3X1,X2}. Draw Yam’s indifference curves when she consumes 1 and 2 apples. Derive Yam’s demand functions for Apples and Ice Cream. Suppose Yam has an income of M = $120 and the prices of Apples and Ice Cream are p1 =$1, p2 =$1. What is Yam’s optimal consumption of Apples and Ice Cream? Suppose a quantity tax of $1 is imposed on Apples. Separate out the...