Consider the utility function U(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 find the expenditure function and the Hicksian demand for good x. [Note: Do not answer this question by solving the expenditure minimization problem!]
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Consider the utility function
U(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 find
the expenditure function and the Hicksian demand for good x. [Note: Do not answer
this question by solving the expenditure minimization problem!]
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- 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.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?I 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?
- 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?Derive the expenditure function for the consumer and the hickson demand functionIntermediate 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.
- Consider a consumer with utility function u(x1, x2) = α_1x_1^( 2) + α_2x_2^( 2) where α1 > 0 and α2 > 0. Assume that p1, p2 > 0.? (a) Derive expenditure function e(p, u). Verify that it is homogeneous of degree 1 in p and increasing in u. (b) Using expenditure function and Hicksian demand, calculate Walrasian demand and indirect utilitySuppose James has a Cobb Douglas utility function of U = qaqa where q₁ = live music and q₂ = music tracks. Let a = 0.4 and label på the original price of qi and p2 the original price of q2. a. Derive expressions for James' optimal consumption levels of qı and q2 b. Derive James' expenditure function. Note: You will need to solve for U* and then derive an expression that relates U* to e(p, U), where e is the expenditure function for a given level of utility and prices pi and p2. Recall that Y = e(p, U") at qi and q2. For the remainder of the problem, let James have a monthly music budget of Y = $30 that he spends on qi and q2. Suppose that a new economic development policy is put in place in James' city that seeks to encourage arts and entertainment by subsidizing live music and that this causes the price of live music to decrease from pi = 1to pl = 0.5. The price of music tracks remains constant at p₂ = 1. C. Calculate the benefits that accrue to James from this new policy by…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.
- 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 goodsSuppose 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 . )The utility function of a certain consumer is U =(x1,x2)= x11/3 x22/3 , x 1and x 2 is the consumption of two kinds of goods, and the consumer's income is 100. The current prices of the two kinds of goods are P 1 =1 and P 2=2 respectively, ask: 1. If the price of the first commodity increases from 1 to 2, and other factors remain unchanged, what is the total effect of the price increase on the consumption of the first commodity? According to the Slutsky decomposition principle, what are the income effect and substitution effect? 2. Calculate the amount of income compensation that changes the price of the first commodity from 1 to 2, keeping the original effect unchanged