Answer- Correct option is 'd'
a) The expenditure function is homogeneous of degree one in prices and utility. If u(x) is continuous, strictly quasi-concave and non-satiated, then the associated cost (expenditure) function c(p,u) is homogeneous of degree 1 in p, concave, strictly increasing u, and has a partial derivatives which are the compensated (Hicksian) demand functions.
b) The hicksian demand functions for x and y are homogeneous of degree zero in prices. Homogeneity of degree zero in p follow because the optimal vector. The minimizing p.x is subject to u(x)>=u.
c) The marshallian demand function are homogeneous of degree zero in prices. If all the prices and the consumer's income are multiplied by any number t > 0 then his demand for goods stay the same.
Which of the following statements is correct for an individual who consumes the two goods X...
Consider the following utility function over goods 1 and 2, plnx1 +3lnx2: (a) [15 points] Derive the Marshallian demand functions and the indirect utility function. (b) [15 points] Using the indirect utility function that you obtained in part (a), derive the expenditure function from it and then derive the Hicksian demand function for good 1. (c) [10 points] Using the functions you have derived in the above, show that i. the indirect utility function is homogeneous of degree zero in...
1. Consider the following utility function over goods 1 and 2, (a) [15 points] Derive the Marshallian demand functions and the indirect utility (b) [15 points] Using the indirect utility function that you obtained in part (a), () [10 points] Using the functions you have derived in the above, show that function derive the expenditure function from it and then derive the Hicksian demand function for good 1. iihi İ. the indirect utility function is homogeneous of degree zero in...
. Consider the following utility function over goods 1 and 2, u (ri, 2)- In a 3 ln r2. (a) [15 points] Derive the Marshallian demand functions and the indirect utility function (b) [15 points] Using the indirect utility function that you obtained in part (a), derive the expenditure function from it and then derive the Hicksian demand function for good 1. (c) [10 points] Using the functions you have derived in the above, show that i. the indirect utility...
Q1. Sam consumes two goods x1 and x2. Her utility function can be written as U(x1,x2)=x 1raised to 2/3 and x 2 raised to 1/5 ⁄. Suppose the price of good x1 is P1, and the price of good x2 is P2. Sam’s income is m. [20 marks] a) [10 marks] Derive Sam’s Marshallian demand for each good. b) [5 marks] Derive her expenditure function using indirect utility function. c) [5 marks] Use part c) to calculate Hicksian demand function...
Complete the following statements: Taking the partial derivative of the expenditure function with respect to the price of X yields ____________________________. Substituting the Marshallian demand functions into the utility function yields _____________________________. Marshallian demand functions are homogenous of degree ____ in _________________________. Expenditure functions are homogenous of degree ____ in _________________________
2.Optional Question on duality for those who welcome a challenge Consider the same utility function as given by: U(X, Y) = X-Y For the primal problem, find the Marshallian uncompensated demand functions, X(Px Ру and y(Rs Py, by maximizing utility subject to budget constraint Px. X + Ру.Y - I. After obtaining the optimal consumption choices, write down the indirect utility function. Give a simple diagrammatic and economic interpretation. Illustrate the use of the indirect utility function by plugging in...
Please consider an individual that consumes two goods – Food (F) and Clothing (C) – and has a Cobb- Douglas Utility Function of the form U= 10 F^(2/3)* C^(1/3) a) Write the functions for the demand curves for Food and Clothing b) What is the maximum utility that can be attained when Income=1000, Pf = 5 and Pc = 20? c) What is the minimum expenditure necessary to attain Utility = 500?
just need parts e,f,g 2. Jane's utility function defined over two goods x and y is U (x,y) = x/2y12. Her income is M and the prices of the two goods are p, and p. (a) Find the Marshallian demand curves. (b) Find the Hicksian demand curves. (c) Find the indirect utility function. (d) Find the expenditure function. (e) Determine the substitution and income effects for good r when ini- tially M =$12, P. = $2.P, = $1, and then...
i need help with (b) and (c)!!! thank u!!!! Jeanette has the following utility function: U= a*In(x) + b*In(y), where a+b=1 a) For a given amount of income I, and prices Px. Py, find Jeanette's Marshallian demand functions for X and Y and her indirect utility function. (6 points) b) From now on, you can use the fact that the utility parameters are a=0.2 and b=0.8. Find the Hicksian demand functions and the corresponding expenditure function. (6 points) c) Suppose...
4. Each week an individual consumes quantities x and y of two goods, and works for hours. These three quantities are chosen to maximize the utility function U(x, y,0) = lnx + Bin y + (1 - -B) In(L-1) which is defined for 0 </<l and for x,y > 0. Here a and Bare positive parameters satisfying a+B < 1. The individual faces the budget constraint px + 4y = wl, where w is the wage per hour Define y...