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- 1) Suppose that a person consumes two goods, x and y, in fixed proportions. He or she always consumes 1 unit of x together with 3 units of y no matter what the relative prices are.a) What is the mathematical form for this person's utility function?b) Calculate the Marshallian demand functions for both goods for this person.c) Calculate the indirect utility function and the expenditure function for this person.d) In class we discussed why expenditure functions are concave in prices. Is the expenditure function you calculated in part (c) concave in ???Consider the utility functionU(x, y) = min{x, 2y}Find(a) the Marshallian demand functions for x and y,(b) the indirect utility function,(c) Use the expression for the indirect utility function that your found in part (b) to findthe expenditure function and the Hicksian demand for good x. [Note: Do not answerthis question by solving the expenditure minimization problem!]I need asnwers of d,e,f. Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. a.Please derive the Marshallian demand function of x. b.Please derive the indirect utility function. c. Please derive the expenditure function If originally m = 40, px=2. d. What is his original highest utility level? Now px has decreased to 1, m and py do not change. e. What is his new maximum utility level? f. Based on (c) (d) and (e), what is his compensating variation? g.Based on (c) (d) and (e), what is his equivalent variation?
- Intermediate Econmics Suppose an agent has a utility function u (x, y) = x2y2(a) Set up the expenditure minimization problem and solve for the Hicksian demand functions asfunctions of prices and utility.(b) Find the expenditure function as a function of prices and utility.A consumer has an original income M to spend on goods X and Y. The market price of these two goods are Px=$10 and Py=$25. Based on the information given in the graph above: 1. Determine the consumer income M. 2. Determine the market rate of substitution between goods x and y? give an interpretation of your answer. Now assumer that the consumer income increases to a new level M' but the prices stay the same. Based on the information given in the graph above: 3. Determine the increased income M'. 4. Does the increase in the consumer income increase the market rate of substitution? Explain your answer.Suppose that we have a utility function involving two goods that is linear of the form U =ax+by.a. Derive demand functions for x and yb. Derive indirect utility functionsc. Derive the expenditure function for this utility function. Hint: The expenditure functionwill have kinks at various price ratios.
- A.) Without solving the expenditure minimization problem, recover the Hicksian demands and the expenditure function from the Mashallian demands and the indirect utility function.(B) Using the Slutsky equation find the total, income and substitution effect on smoothiebowls for a small increase in px when px = 2, py = 1, and I = 72I need asnwers of f,g Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. a.Please derive the Marshallian demand function of x. b.Please derive the indirect utility function. c. Please derive the expenditure function If originally m = 40, px=2. d. What is his original highest utility level? Now px has decreased to 1, m and py do not change. e. What is his new maximum utility level? f. Based on (c) (d) and (e), what is his compensating variation? g.Based on (c) (d) and (e), what is his equivalent variation?1. Suppose David spends his income (I) on two goods, x and y, whose market prices are px and py, respectively. His preferences are represented by the utility function u(x, y) = lnx + 2lny (MUx = 1/x, MUy = 2/y). a. Derive his demand functions for x and y. Are they homogeneous in income and prices? b. Assuming I = $60 and px = $1, graph his demand curve for y. c. Repeat part (b) for the case in which px = $2
- Ma1. Please give only typed answer. Assume the following expendiexpenditure function. (a) Interpret this function. In particular, what will happen to the optimal expenditure, if the consumer wanted to maintain a high level of utility? (b) Calculate Hicks demand for good 2. (c) Suppose that p1 = 1, p2 = 1 and that U = 28. Calculate and interpret the variation compensation if the price of good 2 increases by $1.The individual's utility is given by the following function: ?(?,?)=−1/?−1/? a) Calculate the Marshallian demand functions for both goods.b) Determine whether x and y are gross substitutes or gross complements. Is there any asymmetry in the gross definitions?c) Without actually doing so, determine whether x and y are net substitutes or net complements. Please explain.1. Think about a utility function U(x,y) =xy, the budget constraint is px*x +py*y= m. A. Please derive the expenditure function. If originally m = 8, px=1, py=4. Now px has increased to 2. B. Based on (A), after the price change, how much should be compensated to maintain his original utility level? C. Use the Shaphard's Lemma to derive the Hicksian demand functions.