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.
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- You are given the following utility function: ? = ?? The budget is K100 and the price of X is K2 while the price of Y is K5. a) Derive the demand for X and Y by the Lagrange multiplier method. b) What will be the demand when all the prices are doubled and the income is doubled? c) What is the utility when the budget is increased by K1?I 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?What are the determinants for an individual demand? Derive with the help of indifferencecurves and the budget constraint the optimal consumption plan. How do you transfer theoptimal consumption plan into an individual demand function? (use graphs)
- What are the determinants for an individual demand? Derive with the help of indifferencecurves and the budget constraint the optimal consumption plan. How do you transfer theoptimal consumption plan into an individual demand function?A consumer consumes two agricultural products: Red Meat, and Tomatoes according to the following utility function: U = RT That is, the total utility is the multiplication of the quantity consumed of the two products. Given that consumer's income is 210, price of R is 10, and the price of Tis 2, a)Write down the budget constraint (budget line equation) for this consumer. b)Determine the quantities that the consumer should consume of each of the two products c)Calculate the value of the lagrangian multiplier and derive the demand function for Red Meat and for tomatoes.What are the determinants for an individual demand? Receive with the help of indifference curves and the budget outline the optimal consumption plan. How do you transfer the optimal consumption plan into an individual demand function?
- Given f(x,y) = 2x2 - 6xy + 9y2, and Px= 7, Py= 5 and income, I = 175. Construct the budget contraint and Lagrange function and solve for the equilibrium values of x and y. (a) What is the equilibrium value of x? (Give your answer to two decimal places, if required) (b) What is the equilibrium value of y? (Give your answer to two decimal places, if required) (c) What is the value of the determinant of the bordered Hessian matrix? (Give your answer to two decimal places, if required) unanswered d. Based on the value of the Bordered Hessian, comment whether the objective function is maximized or minimized. Answer in one word.Jane has utility function u(x,y)=x4y5. The price of x is px, the price of y is py, and Jane’s income is W. What is the expression of her consumption of y as a function of prices and income (her optimal consumption is determined by the tangency rule)? Qy(px,py,W)= 9W/5py. Qy(px,py,W)= 5W/9py. Qy(px,py,W)= 4W/3py. Qy(px,py,W)= 5W/4py. Qy(px,py,W)= 4W/5py.given f(x,y) = 9x2 - 2xy + 8y2, and Px= 12, Py= 1 and income, I = 165. Construct the budget contraint and Lagrange function and solve for the equilibrium values of x and y. (a) What is the equilibrium value of x? (Give your answer to two decimal places, if required) (b) What is the equilibrium value of y? (Give your answer to two decimal places, if required) (c) What is the value of the determinant of the bordered Hessian matrix? (Give your answer to two decimal places, if required) Question #2 Based on the value of the Bordered Hessian, comment whether the obejective function is maximised or minimised.
- A consumer is maximising her utility function: U(x, y) = (x¹/³+y¹/³)³, subject to the budget constraint x + 3y = 100. (a) Set up the Lagrangian function of this utility maximisation problem and derive the first-order conditions. (b) What are the utility maximizing amounts of x and y? Also, calculate the Lagrange multiplier. (c) What are the utility maximising amounts of x and y if the budget constraint changes to x + 3y = 50? Also, calculate the Lagrange multiplier.Given f(x,y) = 2x2 - 5xy + 5y2, and Px= 7, Py= 6 and income, I = 169. Construct the budget contraint and Lagrange function and solve for the equilibrium values of x and y. (a) What is the equilibrium value of x? (Give your answer to two decimal places, if required) (b) What is the equilibrium value of y? (Give your answer to two decimal places, if required) (c) What is the value of the determinant of the bordered Hessian matrix? (Give your answer to two decimal places, if required) (d) Based on the value of the Bordered Hessian, comment whether the obejective function is maximised or minimised.The consumer's utility function is u(x1,x2) = x1 x2 Graph her budget constraint for P1 = 3, P2 = 2 and M = 900, and write down the equation for her budget Using the MRS= MU1/ MU2 = p11 / P2 tangency condition, find her optimal consumption bundle for these prices and income.