If u(x1, x2) = x1 + x2 represents the individual's preferences, then V(x1, x2) = -1/(x1 + x2) also represents the individual's preferences. True, Uncertain or False?
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If u(x1, x2) = x1 + x2 represents the individual's preferences, then V(x1, x2) = -1/(x1 + x2) also represents the individual's preferences.
True, Uncertain or False?
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- There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x₂ measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 11 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary. For parts (a) - (f), let a = 1. Draw Jeff's indifference curves for the utility levels u = 4, 9, 16. Draw a straight line between the bundles (x₁, x₂) = (4, 0) and (x₁, x2) = (0, 4). Now, use your picture to determine whether the following two statements are true or false. Answer "1" for true. Answer "0" for false. a) Statement 1: Jeff's preferences are strongly monotone. 1 b) Statement 2: Jeff's preferences are strictly convex. 0 c) Find the bundle at which one of Jeff's indifference curves is tangent to the budget line. (x₁, x^2) = ( d)…There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x2 measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 5 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary.Consider an agent who has to choose how many donuts to eat. He exhibits the choices C({1, 2}) = {1, 2} and C({1, 2, 3}) = {2, 3}. Can these choices be explained by : (i) maximization of a complete and transitive preference? (ii) satisficing? (iii) regret aversion? %3D
- A consumer buys (x1, X2 , X3 ) at price vector (P,, P2 , P3). We make three observations of his behavior: At (P,P,,P;) = (1,1,2), the consumer chooses (x,,x,,x3) = (5,19,9) At (P, P,,P,) = (1,1,1), the consumer chooses (x,,x,, x3 ) = (12,12,12) At (P, P,,P,) = (1, 2,1) , the consumer chooses (x,,x,,x; ) = (27,11,1) %3D %3D Does the consumer's behavior satisfy WARP? What about SARP?You are maxiimizing utility when :A)(MU of X)/(P of X) < (MU of Y)/(P of Y). B)(MU of X)/(P of X) > (MU of Y)/(P of Y). C)(MU of X)/(P of X) = (MU of Y)/(P of Y). D)(MU of X)/(P of Y) = (MU of Y)/(P of X).b) If U = X0.75 y 0.25 and P = 5 ,P, = 10,Income = 200 then find out the utility maximizing values of X and Y.
- A consumer buys (X1, X2 , x3 ) at price vector (P1, P2 , P3). We make three observations of his behavior: At (P.P,P,)=(1,1, 2), the consumer chooses (x,,x,,x, ) =(5,19,9) At (P.P,,P.) =(1,1,1), the consumer chooses (x,.x,,x, ) = (12,12,12) At (P,P,,P,)= (1,2,1), the consumer chooses (x,.x,,x, ) =(27,11,1) Does the consumer's behavior satisfy WARP? What about SARP?A person with utility function U(x, y) = 5 + y + 2x has nonconvex preferences. True FalseYou have $3,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Suppose that your utility function is U(TM) T1/3M2/3. a. What combination of T and M will you choose? b. Suppose that the price of day trips rises to $50. How will this change your decision?
- 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.Happy Goluki likes tea (good 1) and cookies (good 2). Her preferences are represented by the utility function U(q₁,92) = (q₁)⁰.5+(q₂)0.5, where q₁ is the number of cups of tea and q2 is the number of cookies. Goluki is given I = $180, which she is allowed to spend as she wishes on tea and cookies. a) Calculate Goluki's optimal bundle if the price of tea is p₁=$1 and the price of cookies is p2=$2. Call this bundle A and show it on a graph (put tea on the horizontal axis). b) Suppose that the price of tea increases to $5 (I know, I can't believe it either, but Melbourne does have some very fancy tea places) and the price of cookies stays the same. Calculate Goluki's new optimal bundle of tea and cookies (call it bundle B). Show it on a graph from part a). c) If at new prices (pnew-$5 and p2=$2) Goluki has just enough income to achieve the same utility as in part (a), what bundle will she buy? Calculate this new bundle D and show it on the graph from part a). Calculate the income required…Given the utility function U (x1, x2) = x³x2.7 select all that are true. a) 30% of the budget is spent on good 1. ○b) V (p, I) = 30.370.7 I 10 P1P2 c) If P2 = 2 and I = 60, then $18 is spent on good 21. d) If P1 = 9, P2 = 2, and I = 60 then the consumer enjoys 1.81 utils of utility. e) Half the budget is spent on good 1 and the other half is spent on 2.