A consumer's preferences over quantities of goods x1,x2 z20 are represented by the utility functionu(x1, 22) = min{2·x1, 22}It has initial endowment w-(3,8). The price of good 1 is given by p1>0 and the price of good 2 is given byp2=3.Note: For the optimal decision is3(P +8)21 (P1, P2, m) =Pi +6Which of the following statements is correct?a.The consumer's net demand for good 1 is given by d1(p1)=88+p1.b.The consumer's net supply of good 1 is given by s1(p1)=66+p1.CThe net demand of the consumer of good 1 decreases in pl1.d.The net supply of the consumer of good 1 increases in p1.

Utility Function : U = min {2x1 , x2 } Endowments : w = (3 , 8 ) Price of good (x2) = 3 Price of…

Answered: A consumer's preferences over…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A gambling game requires people to place bets on either "Big" or "Small" or "Seven" designating the result of two dice throws. Big represents a sum of 8 to 12, while small is from 2 to 6. The special space "seven" is reserved for, of course, 7. Betting on "Big" provides a 1:1 betting win ratio amount. (Ex: Any bet amount of X, will net the winner another amount X, and still get his bet amount X back. ) Betting on "Small" also provides a 1:1 betting win ratio. The space "Seven" gives a 1:5 win ratio amount: Betting 100 money units on "Seven" and having a result of 7 nets the bettor 500 money units, and still have his 100 money units returned to him. If your bet does not appear, then the player loses his/her bet. What is the net Expected value of the strategy of betting 100 money units on "Big" ? Give your answer to two decimal places.
Suppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 2 -2 -2 Guitars 24 Losses Losses -600 -2 What is the least amount of money Jimi is willing to accept to sell one of his guitars? (just enter a dollar amount, i.e., "1000", not "$1000"
In a two-good market, a consumer starts with an initial endowment of (x₁, x2) = (15.00, 5.00), while the market prices for these goods are given by (P1, P2) = (7.00, 3.00). The consumer has the following utility function: U 0.52 0.48 - Given this information, what will this consumer's final choice of quantity for each good be? x1 = x2 =
A pirate is about to set sail on a 2-period journey (trip). He has 100 bags of barley (food). He must decide how much to consume in period 1 and how much to consume in period 2: (C1, c2). He gets all the barley in period 1 and none in period 2. Unfortunately, rats will eat 50% of any barley that he saves to consume in period 2. If the pirate's utility function is U(C1, C2) = C1C2, what levels of consumption does he choose in each period? (Hint: The "price" of barley in each period can be assumed to be 1.)
A consumer has preferences over two goods, carrots and turnips, each measured in kilograms. For each of the following scenarios, identify which, if any, of the standard assumptions of preferences are violated. (a) The consumer will never eat more than ten kilograms of carrots per day. (b) The consumer cares only about the total weight of the two vegetables consumed, and always prefers more to less. (c) The consumer cares only about the product of the respective weights of the two vegetables consumed, and always prefers a greater product to a lesser one.
For each of the utility functions below derive the own-price demand functions for x₁ and x₂. The price of x₁ and x2 are p₁ and på respectively. The consumer has income from endowment (3, 3). (a) u(x₁, x₂) = min{2x1, x₂} (b) u(x1, x₂) = x² + x1²2 (c) u(x₁, x₂) = ln(x₁) + In(x₂) (d) u(x1, X2) = 2x1+x2 (e) u(x1, x₂) = 10x0.5 + x2 (f) u(x₁, x₂) = x₁ + 10x2.5
3.7 Suppose that A> B> C> D and that the utilities of these alternatives satisfy U(A) + U (D)=U (B) + U(C). Is it true that U (B+C) is greater than U (A + D) because the former has a smaller variance? Why or why not?
A consumer has the following utility function: U(x.y)=x(y+1), where x and y are quantities of two consumption goods whose prices are Px and Py, respectively. The consumer also has a budget of B. Therefore, the Lagrangian for this consumer is x(y + 1) + X(B – Prx – Py) (a) Verify that this is a maximum by checking the second-order conditions. By substituting x* and y* into the utility function, find an expression for the indirect utility function U* = U(Pr, Py, B) and derive an expression for the expenditure function E = E(Pr, Py, U*) (b) This problem could be recast as the following dual problem Min Prx + Pyy Subject to æ(y + 1) = U* Find the values of x and y that solve this minimization problem and show that the values of x and y are equal to the partial derivatives of the expenditure function, ðE/ðP, and ðE/ðP, respectively.
Suppose that consumer has the following utility function: U(X,Y) - X1/2y1/4. Suppose also that P 2, P -3 and 1=144. What would be the optimal consumption of X and Y at the equilibrium. respectively? 36, 24 12,40 24,32 48.16
What is the optimal decision for a consumer with perfectly complementary preferences U = min (4X, 2Y] MRS = 4X+2Y MRS = 4/2 Y = 2X 2X=4Y

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