Consider a 2-good economy with a rational consumer who has weakly monotone and weakly convex preferences. He lives for one period, has some fixed income M, and doesn't have any initial endowment of goods. Which of the following is true?
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- Question 3 A consumer spends her income M on two goods (X1 and X2) and the prices of these goods are P1 andP2. If the Marshallian demand for X, is: P1 X2 P2 Find her Marshallian demand for X1 b. What is the slope of the Hicksian or Compensated demand for good 1 (X,) c. Is good 1 a substitute or complement to good 2 d. Is good 2 a substitute or complement to good 1 e. Is X, a normal good f. Is X, a Giffen good а. с. е.1. Suppose that a representative individual has the following utility function U(x, y) = xªyß The price of good x is Php 40 and the price of good y is Php 20. The individual's income is Php 160. a. Find the Marshallian Demands and Indirect Utility function. Use the "Varian" solution to find the Marshallian Demands. Also, find the Expenditure function and Hicksian Demands via the Duality theory and the Shephard's Lemma. Do not use the prices and income given. Assume that a = 0.5 and ß = 0.5K should be used to TL? 3. A consumer's preferences are represented by the utility function, U(X,Y)= Xay. Budget constraint is M = PxX+ P,Y. Based on this information; E a) Derive the Marshallian demand function. b) Calculate zero degree homogeneity for Marshallian demand for X. c) Derive the Hicksian demand function.
- Consider the utility function U = 2 In x₁ + In x2, where the x₁ are consumption goods. 1. Set up the budget-constrained utility-maximization problem, and derive the Marshallian demand functions. 2. Suppose prices are p₁ = 3 and p₂ = 1, and income m = 100. Use your answer from #1 to calculate the specific numerical solutions. Calculate the specific utility value for your solution. 3. Use your answers to #1 to derive the indirect utility function. 4. Use Roy's Identity to derive the Marshallian demand functions from the indirect utility function found in #3. 5. Set up the expenditure-minimization function, which is the dual version of the primal consumer maximization problem you set up in #1, and derive the Hicksian demand functions. 6. Use the same prices and calculated utility value in #2 to calculate the specific numerical solutions to #5. 7. Use your answer to #5 to derive the expenditure function. 8. Use Hotelling's Lemma to derive the Hicksian demand functions from the expenditure…A consumer can consume two goods, A and B, and has the utility function U-15A1/281/2, The consumer's budget is $900, the price of good A is $15 per unit and the price of good B is $45 per unit. (Assume A is the horizontal axis good and B is the vertical axis good. Both goods are infinitely divisible, but round numerical answers to 2 decimal places as necessary) What is the consumer's marginal rate of substitution? What is the consumer's marginal rate of transformation? What is the formula for the consumer's budget constraint? What is the consumer's utility-maximizing bundle given the utility function and budget constraint? A B H1. 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 = X2 + Y2 , derive the Marshallian demand function for good Y and evaluate the type of good. 2. 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= X2Y2 , derive the Hicksian demand function for good Y.3. Suppose that initially PX = 2, PY = 8, I = 96 and the Marshallian demand function for good Y is given by Y∗ = (0.5I/ PY)+(0.5PX/PY)− 0.5. Calculate the own price & income elasticities of demand for good Y. Interpret your computed values and say something about the type of good.4. 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) = X0.25Y0.75, UB (XB,YB) = X0.75Y 0.25Show that pareto-improvement is possible if,…
- Suppose i's preferences are represented by the following utility function: u= x-y. Which of the following statements is true? O i's Marshallian demand for good x is x = - Px i will consume more good y than good x i will consume the same amounts of good x and good y i's Marshallian demand for good y is y=- РуWhy are compensated demand curves always downward sloping? a. Compensated demand curves are always downward sloping because they only show the substitution effect of a price change. b. Compensated demand curves are always downward sloping because they only show the income effect of a price change. c. Compensated demand curves aren't always downward sloping. They can be upward sloping if the good is a Giffen good. d. Compensated demand curves are always downward sloping because Hicks assumed that they would be downward sloping when he developed the model. e. Compensated demand curves are always downward sloping because the substitution effect is always greater than the income effect on compensated demand curves.Given the utility function and budget constraint z= 3X, +X;X; +2x; M= P;X1 + P:X: i. Obtain Marshallian demand curve equations. ii. Estimate the demand for X, at P; 2,4.P2 4 and M 60 iii. Estimate the demand for X, at P2= 2,4, P 4 and M -60
- 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 = X + Y, derive the Marshallian demand function for good Y and evaluate the type of good. Assume you spend your entire income on two goods X & Ywith prices given as Px & Py, respectively. Prices and income (I) are exogenous and positive. Given that U= X²Y², derive the Hicksian demand function for good Y. Suppose that initially Px = 2, P = 8, I = 96 and the Marshallian demand function for good Y is given by . Calculate the own price & income elasticities of demand for good Y. Interpret your computed values and say something about the type of good.Consider the following Marshallian Demand Function derived from the utility maximization problem, X = a M P where X is the quantity consumed, Mis income of the consumer, P is the price of the good, and α is some number between 0 and 1 which represents the relative importance of the good. Does this demand function satisfy the law of demand? (_ Why or why not? (*Suppose that X is an inferior good. A. Show using well labeled diagrams how you would derive the Marshallian Demand curve and compensated demand curve holding utility constant for a consumer maximizing her welfare subject to a budget constraint. B. Derive the consumer's compensated demand curve and draw the demand curve carefully for X, Under the two following rules to measure the amount of compensation required to estimate the substitution and income effects. (1) holding real income constant. (2) holding production possibilities constant (assume linear). C. Under what real model circumstance would you employ these scenario for measuring the compensated demand function for a good?