Suppose a consumer’s utility function is u = x_1^(3/2) x_2^(3/2) . She spends her budget of £27 for two goods. The prices of both goods are p1 = 6 and p2 = 6. Derive the Marshallian demand functions for ?1 and ?2 as functions of both prices and income. Then find the optimal consumption point for the given budget constraint.
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Suppose a consumer’s utility function is u = x_1^(3/2) x_2^(3/2) .
She spends her budget of £27 for two goods.
The prices of both goods are p1 = 6 and p2 = 6.
Derive the Marshallian
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- For each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x and x2 are p₁ and p₂ respectively and income is m. i) U(x1x2) = ln(x1+ x2) ii) U(x1x2) = (x1+ x2)Suppose that an individual has a Utility function represented by a CES function. The utility function of the individual is given as: U(x,y) = x1/2 + y1/2 a. Derive the Marshallian Demand for both goods, in terms of Income and the prices of both goodsFor each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x1 and x2 are p1 and p2 respectively and income is m. U(x1 x2) = In (x1 + x2) U(x1 x2) = x1 + x2
- 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? PLEASE ONLY ANSWER PART C, D AND ESuppose 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?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.
- 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)??2I need answers of C,F 1. Think about a utility function U(x,y) =xy, the budget constraint is px*x +py*y= m. a. Please derive the Marshallian demand functions. b. Please derive the indirect utility function. c. Please derive the expenditure function. If originally m = 8, px=1, py=4. d. Now px has increased to 2. f. Based on (c), after the price change, how much should be compensated to maintain his original utility level?Derive the expenditure function for the consumer and the hickson demand function
- 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.A 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?Suppose that i’s preferences over goods x and y are represented by the following utility function Ui(x, y)=x^0.8·y^0.2. Let m denote the consumer’s income, p denote the price of good x and let the price of good y equal 1. a) Find the Marshallian demand functions for goods x and y. b) Show how each of the demand function is affected by a change in the price of good x. c) Which of the goods is an inferior good?