8. In a 2-good model, where the goods are denoted x, and x,, the consumer's utility 1 1 function is as follows: U = x,x3. Money income available is denoted m. All of this income is spent on the two goods. The prices of the two goods are P1 and p2 respectively. (a) By minimising expenditure, subject to the utility function, find the compensated (Hicksian) demand functions; that is, demand for each good expressed in terms of U, P1 and P2. Do not check the second order conditions. (b) Substitute these conditional demand functions back into the objective function to find the expenditure function; that is, m in terms of U, P1 and p2.
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Can you please help awnser 8 b I have attached awnser to 8 a to make it easier to understand and complete.
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- 2. Consider the two-good model of the utility maximization program subject to a budget constraint. The utility function U of a hypothetical rational consumer and his/her budget constraint are given, respectively, by: U = x1x2, (U) B = p1x1 + p2x2, (B) where xi = the consumer’s demand for consumption good i (i = 1, 2), pi = the price of consumption good i (i = 1, 2), and B = the (exogenously given) budget of the consumer. In this maximization program, assume the following data: B = 240, p1 = 10, p2 = 2. (a) Using the Lagrangian function L, derive the first-order (necessary) conditions for a (local) maximum of the utility function. (b) Compute the optimal values of all choice variables, i.e., x*1 , x*2, and λ* , in the program, where λ signifies the Lagrange multiplier. (c) Using the information of the bordered Hessian matrix H¯ , verify the second order (sufficient) condition for a (local) maximum of the utility function. Note:- Do not provide handwritten solution. Maintain accuracy…Consider a budget constraint model with two goods X and Y. Suppose X is an inferior good, and the price of Y decreases. The substitution effect says we’ll demand _____ of good X, while the income effect says we’ll demand ______ of good X. Less; less More; less Less; more More; more Skip this question (or leave all choices blank)Question 3 Consider the utility function of the form: ?=?1?1?2?2 Given the budget constraint: ?1?1+?2?2=? Show that the implied Marshallian demand curves are: ?1=?1(?1+?2)??1 ?1=?2(?1+?2)??2
- Consider the utility functions below of two individuals, A and B, and bundles of goods Q and R. UA=X0.5Y0.5; UB=X+2Y; Bundle Q (10, 10); Bundle R (10, 15). Suppose the total X and total Y available in the economy are both equal to 20. a. If initially both individuals are consuming bundle Q, then a pareto-improvement is possible through reallocation of goods, i.e. individual A gives B some of his good X in exchange for some of individual B’s good Y. (True or False? Explain through mathematical examples).b. Pareto-optimality is achieved if we give individual B Bundle R and the remaining goods X and Y available in the economy is given to individual A. (True or false? Explain through a graphical example)Answer both question (a) and (b) below. (a) State theWeak Axiom of Revealed Preference (WARP). (b) In a two-good model, suppose a consumer always chooses the midpoint of the budget line given any (p1; p2; I), does the demand function satisfy WARP? Why? (HINT: Graphs can be helpful to answer the question.)Suppose a consumer in a competitive market maximises utility subject to a standard budget constraint. a. Given their resulting demand function, what assumptions would be required for one to conclude that when the price of good 1 goes up the consumer buys less of that good?b. Given their resulting demand function, what assumptions would be required for us to conclude that when the price of good 1 goes up the consumer buys more of good 2?
- Which of the following statements is correct? Suppose leisure is a normal good, then an increase in non-labor income always increases labor supply. Suppose leisure is a normal good, then an increase in wage rate increases labor supply if the income effect dominates the substitution effect. Suppose leisure is an inferior good, then an increase in non-labor income increases leisure hours. Suppose leisure is a normal good, then an increase in non-labor income reduces labor supply. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Consider the following function describing the utility of a consumer: U(x1, x2, x3) = a1*ln(x1) + a2*ln(x2) + a3*ln(x3), where ln = natural logarithm and a1, a2, a3 constants a. Pose the primal problem (using Langrange's method), obtaining the Marshallian demands for each good and the individual's indirect utility function. b. From the results obtained from question a., find the minimum expenditure function and the Hicksian demands.Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y 2 , derive the Hicksian demand function for good Y.
- The marginal rate of technical substitution Group of answer choices is the rate at which one input must be replaced by a second input in order to maintain the same level of output. is the rate at which one input must be replaced by a second input in order to expand output. indicates what happens to output when all inputs are increased proportionally. is the slope of the isocost curve. is the rate at which consumers are willing trade one unit of a good for another in order to maintain utility.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 your utility for goods x1 and x2 is represented by the following utility function: U(x1,x2)= x11/5 x24/5 a) What is your marginal rate of substitution, MRS12? b) If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25?