U(x,y) = x^0.5y^0.5 Write the maximization Problem Solve to get Marshallian demand functions for x and y Get Hicksian demand function for x Get Indirect Utility function Get price effect, substitution effect, income effect using Slutsky equation (calculus method) Prove that the Slutsky equation holds.
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- Individual that consumes two goods (X and Y) and has a CES Utility Function of the form: U = 100(X^(0.75) + Y^(0.75)). Income of 1000, the price of Good X is 10 and the Price of Good Y is 20 a) Find the Marginal Rate of Substitution as a function of the quantities consumed of Good X and Good Y. b) Write out the Lagrangian for this problem. c) Solve to find the demand for Good X, the demand for Good Y, and the highest level of utility for this individual. d) Now consider an increase in the price of Good X to 20. What is the demand for Good X and Good Y? What is the Utility of the consumer following the price change? e) Considering the change in demand for each good between parts c) and d), how much is due to the substitution effect and how much is due to the income effect? f) Show your answers on a graph.Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should begiven to Eren to offset his change un utility due to the price increase of an expensivemeal. Calculate the compensative variation (CV).Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate for the equivalent variation (EV) for the price change.
- Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate the change in consumer surplus from consuming the expensivemeals considering the price change (Hint: you need to compare his optimalconsumption bundle before and after the price change to get the change in CS).a good is normal, then an increase in the price of the good will lead to which of the following to be true for this good? (Assume that there are only two goods, the individual's preferences lead to well-behaved preferences with strictly convex indifference curves and an interior solution for all budgets). Let SE = substitution effect, IE = income effect) (a) The magnitude of the IE for this good must be larger than the magnitude of the SE (b) The magnitude of the SE for this good must be larger than the magnitude of the IE (c) The good could be a Giffen good d) The good must be an ordinary good ( (e) None of the aboveUtility Function: U(X,Y)=X1/2Y1/2 Budget Constraint: X+2Y=12 If the price of good Y changes to Py=3, what is the compensating variation? (Round to the nearest one-tenth) 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.
- Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices (y-good) with the utility function min[4x,5y]. a) Find her Marshallian Demand Functions. b) Find her Hicksian Demand Functionshe Calculus of Utility Maximization and Expenditure Minimization -End of Appendix Problem uppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two onsumers, A and B. The utility functions for the consumers are UA(X,Y)= X05.05 UB(X,Y)= X0.8y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is X = 25 and Y* = 50 - b. The optimal bundle for consumer B is X = 120 and Y* = 60I am unsure the direction the utility functions would go in , with this specific scenario
- Suppose that a consumer has the utility function given by U(X,Y) = 20X + 8Y + XY the prices of good X and Y are given by px = 5 TL and py = 1 TL the total budget the consumer has is / = 200 TL a) write down the consumer's optimization problem (formally) b) apply the langrangian method and solve the optimization problem (find the quantities of goods X and Y that maximizes consumer's utility subject to the budget constraint. apply the following steps: b.1) write the langrangian function b.2) write the first order conditions (FOC) b.3) find the values of X and Y that satisfy the (FOC).A utility function is called separable if it can be written as U(x, y) = U (x) + U,(y), where U > 0, U" < 0, and U1, U, need not be the same function. a. What does separability assume about the cross-partial derivative U„? Give an intuitive discussion of what word this condition means and in what situations it might be plausible. b. Show that if utility is separable then neither good can be inferior. c. Does the assumption of separability allow you to con- clude definitively whether x and y are gross substitutes or gross complements? Explain. d. Use the Cobb-Douglas utility function to show that separability is not invariant with respect to monotonic transformations. Note: Separable functions are examined in more detail in the Extensions to this chapter.Let Utility be given by U(x,y)=x^2 y^2 With a budget contraint p_x x+p_y y=Y Let px = 10 Let py = 2 Y = 100 Walk through the optimization process and identify the optimal choice for this consumer in both x and y (Hint: the MUx = 2xy2 and MUy = 2x2y) How much utility is this consumer receiving by consuming the optimal level of x and y? Use your answer in part b,the information from this problem, and excel to draw the budget constraint and the indifference curve at the optimal choice of x and y.