Let the indirect utility function for two goods be as follows: where m is the exogenous income, p, >0 is the price per unit of good 1, p2 > 0 is the price per unit of good 2, y > 0 and 0> 0 are constants. Find the Hicksian quantity demanded for good 1, h; (P.P2, o). Here ug is the target utility level. Enter your algebraic answer in the box provided: h;(P-P2, 4o)=(
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- The preferences of a typical Californian can be represented by the following utility function: U (x1 , x2 ) = α ln(x1) + (1 − α) ln(x2) Here, x1 and x2 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by p1 and p2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to consume at most 50 units of electricity (x1 ≤ 50). Call this restriction a rationing constraint. (a) If α=0.25, m=100,and p1 =p2 =1, find the optimal consumption bundle of gasoline and electricity. Is the electricity rationing constraint binding (meaning does x1∗ = 50)? (b) Suppose that α = 0.75, but the other parameters are the same. What is the optimal consumption bundle? Is the rationing constraint on electricity consumption binding? (c) Now, assume that there is no rationing constraint. Assume m = 100 and p1 = p2 = 1, but α remains as a generic parameter. Solve for the optimal quantity…Assuming a linear budget constraint, consider the following utility maximization problem:U (x1, x2) = 2x10.5 + 4x20.5 1. Compute the Marshallian demand functions for goods 1 and good 2.2. Find the compensated demand function.3. Derive the expenditure function and verify that h (p, u) = ∇pe (p, u)4. Derive the indirect utility function and verify Roy's IdentitConsider the indirect utility function: v(p1; p2; m) = m /(p1 + p2). What is the Hicksian demand function?
- Which of the following statements is true? Select one or more options: a-If two different individuals have exactly the same budget constraint but different preferences (different appearance of the indifference curves) then they will have different equilibrium conditions for optimal choice b-The marginal substitution ratio is always equal to 1 for perfect substitutes c-If item X costs SEK 10, item Y costs SEK 20 and if the marginal benefit for X is 20 and the marginal benefit for Y is 30, then the individual should buy more of Y and less of X d-In the case of a corner solution for an individual, the marginal substitution ratio for two goods is not equal to the relative price of the two goodsConsider an individual with the following utility function: Derive step-by-step both corresponding Hicksian demand functions depending on the different prices (P₁, P2) and a fixed utility level u. The equation given In picture.do This in 10 minutes.Which of the following statements is true? Select one or more options: -If two different individuals have exactly the same budget constraint but different preferences (different appearance of the indifference curves) then they will have different equilibrium conditions for optimal choice -The marginal substitution ratio is always equal to 1 for perfect substitutes -If item X costs SEK 10, item Y costs SEK 20 and if the marginal benefit for X is 20 and the marginal benefit for Y is 30, then the individual should buy more of Y and less of X -In the case of a corner solution for an individual, the marginal substitution ratio for two goods is not equal to the relative price of the two goods
- (In this question we denote income by Y, not by W as in the lecture notes). The following figure shows a two-good consumption space for an agent. The horizontal axis measures good x and the vertical axis measures good y. There are three budget lines shown in the figure. The first budget line has vertical intercept Y/py and horizontal intercept Y/px. The second budget line has vertical intercept Y/p’y<Y/py, and horizontal intercept Y/px. The third budget line has vertical intercept Y/py, and horizontal intercept Y/p’x< Y/px. There are two indifference curves. These are downward sloping thin curves that do not touch. One of this curves intersects the first budget line only at bundle (3,2). The other curve intersects the second budget line only at (4,0.6) and intersects the third budget line only at (1,2.5). Can we conclude that good y is a Giffen good for some market situation? No. Yes.It is given that a typical consumer has a well-behaved preference structure for his consumption bundle, which includes only two goods, A and B. Further, assume that commodity A is normal and commodity B is Giffen. By keeping commodity A on the x-axis and commodity B on the y-axis, you are required to show the price decomposition for commodity B when $PB decreases exogenously relative to $PA.Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2 individuals are: UA (XA,YA) = X0.25Y 0.75, UB (XB,YB) = X0.75Y 0.25 . Show that pareto-improvement is possible if, initially, goods are divided equally between the two individuals.
- Suppose that BC1 on the following graph represents your initial budget constraint for good X and good Y, and point A represents the best bundle, given this choice set. After a change in the price of good X, your new budget constraint is now BC2. The compensated budget is parallel to BC2, representing the same tradeoff between good X and good Y, and it is tangent to the given indifference curve (U) at point B.(In this question, differently from our lecture notes, income will be denoted by Y, not W). The following figure shows a two-good consumption space for an agent. The horizontal axis measures good x and the vertical axis measures good y. There are three budget lines shown in the figure. The first budget line has vertical intercept Y/py and horizontal intercept Y/px. The second budget line has vertical intercept Y/p’y<Y/py, and horizontal intercept Y/px. The third budget line has vertical intercept Y/py, and horizontal intercept Y/p’x< Y/px. There are two indifference curves. These are downward sloping thin curves that do not touch. One of this curves intersects the third budget line only at bundle (3,2). The other curve intersects the second budget line only at (4,0.6) and intersects the third budget line only at (1,2.5). Then Qx(px,py,Y), the demand of good x for prices px and py and income Y is: 4 1 2.5 2 3(In this question, differently from our lecture notes, income will be denoted by Y, not W). The following figure shows a two-good consumption space for an agent. The horizontal axis measures good x and the vertical axis measures good y. There are three budget lines shown in the figure. The first budget line has vertical intercept Y/py and horizontal intercept Y/px. The second budget line has vertical intercept Y/p’y<2, and horizontal intercept Y/px. The third budget line has vertical intercept Y/py, and horizontal intercept Y/p’x<3. There are two indifference curves. These are downward sloping thin curves that do not touch. One of this curves intersects the third budget line only at bundle (3,2). The other curve intersects the second budget line only at (4,0.6) and intersects the third budget line only at (1,2.5). Then Qy(p’x,p’y,Y), the demand of good y for prices p’x and p’y and income Y is less than 2? True. False.