Assume you spend your entire income on two goods X & Y with prices given as Px & Py, respectively. Prices and income (1) are exogenous and positive. Given hat U= X²Y², derive the Hicksian demand function for good Y.
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- 1. 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,…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.Let x be the number of pizza slices and y the number of Cokes. If John’s utility function is u = min{7x, 4x+ 12y}, then if the price of pizza slices is 20 euros and the price of Coke is 40 euros, John will demand ? a- 2 times as pizza slices as Cokes b- 3 times as pizza slices as Cokes c- 6 times as pizza slices as Cokes d- 4 times as pizza slices as Cokes e- 5 times as pizza slices as Cokes f- only Cokes
- The consumer has an incom Mand a utility function of the form u (x1; x2) = aInx1 + (1 - a)Inx2 If the prices of the two goods are given by p1 and p2, derive the Hicksian demand functions for a given utility level U: Derive the expenditure function. Using the concept of duality, derive the indirect utility function.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 FunctionsSuppose U = 2X + Y, I = 20, Px = 2, and Py = 2. (a) Find Marshallian demand for X and Y . (b) What is Marshallian demand for X and Y if the price of X increases to 5? How much of the change in demand for X is the income effect and how much is the substitution effect? (c) How much is compensating variation for the price change described in part (b)? (d) How much is equivalent variation for the price change described in part (b)? ( Please solve all the subparts ASAP I will give you thumbs up . )
- Assume that the prices of good X, Y and Z are as follows R5,R1 and R4 respectively, and the Judith has an income of R37 to spend. HOW much of each good will judith consume in order to maximise her utility? What will be her total utility and marginal utility of the last rand spent on each good? Show all the calculationsA consumer has the following indirect utility function:U∗(Px, Py, M) = M2/2PxPy1. What is the consumers Marshallian demand for good x?2. What is the expenditure function?3. What is the Hicksian demand for good x?D9) Given current prices, Johnson spends all his free time on pursuing gold (x1) from Danny, which costs (p1) hours of service per coin. His Marshallian demand function can be represented by x1(p1,I) = I/p1 and his Hicksian demand can be represented by xh1(p1,u) = u/5 . (a) Verify that the Slutsky Equation holds for x1 when there is a change in p1. (b) What is the substitution effect of x1 when there is a change in p1? (c) What is the income effect of x1 when there is a change in p1?
- Pankti consumes two goods, x and y. Her utility function is given byU(x, y) = ln(xy).(a) Suppose when Pankti’s income is 12, her optimal bundle consists of 2 units of x and 6units of good y. Without solving for Pankti’s Marshallian demands for x and y,determine how her consumption of x and y would change if her income doubled(holding constant the prices of the goods). Justify your answer as well as you are able.(b) Find an expression for Pankti’s indirect utility function, V (px, py, m), using themethod of Lagrange multipliers. Confirm your answer to part (b) using theMarshallian demands you derive in the process of solving the optimization process.(c) Suppose the price of good x is 2 and the price of good y is 2. Find Pankti’s utilitywhen her income is 24. Now suppose the price of good x doubles to 4. How much extraincome does Pankti need to obtain the same level of utility she had prior to the priceincrease?Consider an economy with 2 goods and 30 agents. There are 10 agentseach with the utility function u (x1; x2) = ln x1 + 2 ln x2 and endowments e = (3; 1).Also, the other 20 agents each have the utility function u (z1; z2) = 2 ln z1 + ln z2 andendowments e = (1; 2). Normalize p2 = 1. Calculate the Walrasian equilibrium pricep1*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.