(4) Consider a Cobb-Douglas utility function U(1,2) = ria, where U is the utilitylevel, x, and 2 are the amounts of two commodities, respectively, and a > 0, b> 0, a+b=1.Suppose that the commodity prices for 1 and 2 are p andP2, respectively.(a) Set up the utility maximization problem subject to the budget constraint such thatPix+P2x2 = I, where I is the income level.(b) Suppose that P1, P2, and I are given exogenously. Solve the utility-maximizing levelsof r and r2. [Hint: Derive the demands for 1 and 2, respectively, as a function of pi. P2,and I.(c) Compute the indirect utility function V (P1, P2, I). [Hint: Write the utility as a func-tion of P1, P2, and I.](d) Verify the Roy's identity such thatav (pi PJ)дрOV (p1.p2.1)arfor i = 1,2.

The utility maximization problem is to choose the amounts of commodities x1 and x2 to maximize the…

Answered: (4) Consider a Cobb-Douglas utility…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Sheila decides to take a trip to Peru for her 60th birthday. She looks forward to the guided tours (T) and the food (F). She is allocating $2,000 to spend on guided tours and food. Sheila's preferences over these two goods T and F is represented by the utility function: U(F, T) = = √F+T Denote prices for tours and food as på and pf, respectively, and take them to be pt = $100 and PF = $20. a. Carefully draw at least two indifference curves to get a sense of Sheila's preferences. Are Sheila's preferences "well-behaved"? [Note: Go ahead and put T on the y-axis and F on the x-axis so that your pictures are consistent with mine.] b. Derive an expression for Sheila's marginal rate of substitution. What is the MRS in words? What does her MRS approach as F→ 0? How about when F→→∞o? How do you interpret these findings, in words? c. In the above analysis, you found that Sheila's MRS does not depend on T. Please show what it means for the MRS to be independent of T either in a new graph in the…
An individual’s utility function is given byU = x1√x2where x1 and x2 denote the monthly consumption of two goods. Unit prices of these goodsare $2 and $4 respectively, and the total monthly expenditure on these goods is $300.(a) Write down the budgetary constraint.(b) Find the optimal quantities of x1 and x2 the maximize U.(c) Verify that the stationary point is a maximum.
Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices (y-good) with the utility function min[4x,5y]. a) Find her Marshallian Demand Functions. b) Find her Hicksian Demand Functions
Which of the following utility functions represents preferences over consumption bundles (X, Y) that violate the assumption of diminishing MRS? (a) U(X,Y) = 3 ln(X) + 5 ln(Y) (b) U(X,Y) = X² + y² (c) U(X, Y) = XY (d) U(X,Y) = X² + Y² (e) U(X, Y) = X¹Y³
Jasper utility function for beer and pizza can be expressed as: U(B,P) = BXP Suppose beer costs $5 per glass, pizzas cost $10 each, and Jasper has a total of $30 to spend. Assume Jaspeer is allowed to purchase fractional amounts of each good. Part A) Based on the above information, what is Jaspeer's optimal amount of beer? Enter the number below. glasses Beer = 3 Part B) Now suppose the price of beer falls from $5 down to $3. Calculate the following and fill in the blanks below. When necessary, round answers to two places after the decimal. (Hint: find the decomposition basket to calculate the substitution and income effects). Jasper's total effect on beer is to increase total consumption by glasses of beer. Jasper's substitution effect is to increase beer consumption by 0.28 Jasper's income effect is to increase beer by 1.12 glasses of beer. glasses of beer.
An individual's utility is given by: U (q1, q2) = a(q1)+ b(q2), where a and b are constants. When prices are P1= 4 and P2=1, the individual can only maximize utility by purchasing all good #2. When the prices are P1=3 and P2=1, the individual can only maximize utility by consuming all good #1. Which of the following statements below must be true? A. Goods #1 and #2 are complements B. a < b C. 3 < a/b <4 D. The indifference curves exhibit diminishing MRS
Christin has a monthly income of $500 that he allocates between two goods: food and clothing. Suppose food costs $8 per pound and clothing cost $5 per piece. a) Draw her budget constraint properly labelling the axes. 0.5 b) Suppose also that her utility function is given by ?( f,c)= 2f ^2 + c^2 . What combination of food and clothing does she buy in order to maximize her utility? Show your work mathematically. Round your answer to two (2) decimal points.
Let a consumer's utility function be U (x, y) = x'/²y/2. The consumer's income is I = 160 and prices for the two goods are, respectively, p, = 1 and py = 4. (a) Write down the utility maximization problem and compute the optimal consumption basket. (b) Suppose now the price of good y is equal to p, = 16 (while the price of good r stays constant). Compute the new optimal consumption basket.
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Given the total utility function for a consumer, consuming two goods is U = x+2y + xy+2 the prices of x and y are 4 TL and 6 TL respectively (Px = 4 and Py = 6), and the total budget of the consumer (B) is 130 TL; a) Write the constraint ( budget) function. b) Write the lagrangian function. c) What are the first-order conditions for utility maximization? d) Find the critical values of x, y and \lambda (x*,y*and \lambda *) according to the first order conditions. e) is the second order suficent condition for maximum utility satisfied 2 4 10 [ [:] 8 Write the appropriate commands to create A and d matrixes in R software. A-1. din R language? Given A = 1 3 And d = How can you formulate the equation X =
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3*. Ms Smith likes to drink wine; in particular, a french bordeaux (f) at $40 per bottle and a California varietal wine (c) priced at $8. She allocates $600 to these two each month; and her utility is: U(ƒ, c) = ƒ²/³ c¹/³ (a) Write out her (constrained) utility maximization problem. Solve for the optimal consumption of wine f and c.

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