2) For the following utility functions, using the budget constraint M = Pgx & Pyy, find the compensated (Hicksian) demand functions. Note: For a, minimize expenditure; For b, maximize utility and use the Shepard's Lemma. a) U(x,y) = x0.5 + 2y0.5 b) U(x, y) = min{2x,5y}
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- A consumer utility function is U=(x1,x2) Where X1 is the quantity of good 1 that is bought, X2 is the quantity of good 2 that is bought. The price of good 1 is $10 and the price for good 2 is $2. If the consumer's income is $100 what will the consumer's optimal utility level be? b. Using Lagrange multilplier method. optimise the utility function x0.25 y0.25 subject to the budget constraint 24=x/10+yA 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.A consumer's preferences are represented by the utility function If the budget constraint is P1X1 + P2X2 = M, determine the demand functions q1(P1, P2, M) and Q2(P1, P2, M). Determine also the indirect utility function V(P1,P2,M).
- You are given the following utility function and price of commodities q1 and q2: U = 3q1+q1q2-5q2-15 P1=3 and p2=2 If the corresponding bugdet is 20. i. Write the consumer's budget equation,augmented objective function, ii.construct a constrained utility maximization problem out of the information given above, Is the second order condition for a maximum satisfied? Iii. Find the optimum level of U and the levels of q1 and q2 that will satisfy the first order condition for a maximum.You have £20 per week to spend, and two possible uses for this money: telephoning friends back home, and drinking coffee. Each hour of phoning costs £2, and each cup of coffee costs £1. Your utility function is U(X,Y) = XY, where X is the hours of phoning you do, and Y the number of cups of coffee you drink. What are your optimal choices? What is the resulting utility level? You can use the standard result on the constrained maximization of such a function, but must state it clearly. Now suppose the price of telephone calls drops to £1 per hour. What are your optimal choices? What is the resulting utility level? How much income per week will enable you to achieve the same quantities at the new prices as the ones you chose before? What income will enable you to attain the same utility as you did before? Comment on your answer in the context of equivalent variation and compensating variation.Q)Suppose we have two goods, x1 and x2, with price p1 and p2, respectively. Consider the budget constraint x1p1+x2p2≤m. If both p1 and m double (i.e. p’1=2p1 and m’=2m), the area of the feasible consumption set: a) doubles B)stays the same D) quadruples C)none of the above E) falls by half
- Assume a consumer has a utility function U(x1, x2) = x1x2 where x1, x2 represents the amount of two goods 1 and 2 consumed in a given time period, find the utility-maximizing consumption function subject to the budget constraint5x1 + 4x2 <= 50Individuals in a market each have a total budget y to spend on two goods q1 and q2 at the prices p1and p2 respectively. Their preferences are described by the utility function below. I need help with question b) Find the expenditure function corresponding to these preferences.1. Consider a consumer who chooses bundles consisting of two commodities, x and y. Suppose that, regardless of the prices px and py (which are always positive), the consumer chooses to consume x and y in a ratio of 2:1. This behavior is consistent with: a. A consumer having Cobb-Douglas utility function. b. The consumer’s utility function exhibiting perfect complements. c. The consumer’s utility function exhibiting perfect substitutes. d. Any of the above could be correct.
- Which of the FF. statements is correct regarding the preference of the consumers when the income of the consumer can only be spent between apples and oranges? Assume that apples are written on the vertical axis while oranges are written on the horizontal axis A. when the consumer has few oranges, he is willing to trade more apple to get another orange B. when the consumer has so many oranges already, he will only exchange less apples for an orange C. the declining slope of the indifference curve shows the marginal value of oranges is declining D. all are correct E. none is correctA utility maximizing consumer purchases two commodities, Q1 & Q2. The consumer’s utility function is described by the following expression: U = Q1 Q2 + Q1 + 2Q2. The prices of the commodities are P1 = $2 and P2 = $5. Suppose the income of the consumer is $51 (a)Form the Lagrangian function that defines the combination of both commodities the consumer could buy subject to the budget constraint imposed by the prices of the commodities and the income of the consumer. (b)Find the combination of both commodities that maximizes the utility of the consumer. (c)Write and evaluate the Bordered Hessian for this utility maximization problem.I need asnwers of e,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?
