For the given life time budget constraint; C, + C2 = W1 1 +r determine C1 and C2 to maximize the following utility function 1 C Ut 1- 0 + 1+p1 – 0 1 p = 1 r= 0,5 w = 220 220) ||
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- We consider the following decision problem, with 4 decisions di,i∈{1,…,4}, and four possible outcomes ωi,i∈{1,…,4}, with the following table of profits: ω1 ω2 ω3 ω4 d1 30 30 0 30 d2 20 20 20 20 d3 0 50 10 40 d4 15 30 10 25 Which decision should be chosen for rewards depending on four different possible outcomes, according to the maximin rule, maximax rule, and optimism-pessimism rule with α<1/3?1(a)lf we allow for the possibility of satiation, the consumer's budget constraint takes the form pxS pw, Walrus' law then becomes pz(p) s0 for all p2 0. Show that the standard textbook proof of the existence of Walrasian equilibrium still applies for this generalized form of Walrus' law.Question 18 (Still with U(X,Y)=min{2X,Y}, Px=2, Py=1, l=20). Independent of the individual preferences, how many units of y will the consumer be able to afford if he/she were to spend all the income on y? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a 20 b 10 d 8
- The dung beetle gets utility from consuming mud balls which are made out of mud and dung. Both inputs are measured in grams and perfectly divisible. Its utility from balls which contain m grams of mud and d grams of dung is u(m, d) = md. For reasons to do with the structural integrity of the balls, however, it cannot combine the two ingredients in very different quantities. The ratio of mud and dung it uses must fall between 1 : 2 and 2 : 1. Excess amounts of either ingredient are discarded at no cost to the dung beetle. (a) How much utility does the beetle get from the following bundles of mud and dung, (m, d)? i. (2,16). ii. (4,8). iii. (4,16). iv. (6,16/3). (b) Draw an indifference curve between mud and dung that represent the preferences of the dung beetle and gives the beetle a utility level of 32.Question 2An investor is to purchase one of three types of real estate, as illustrated inFigure below. The investor must decide among an apartment building, anoffice building, and a warehouse. The future states of nature that willdetermine how much profit the investor will make are good economicconditions and poor economic conditions. The profits that will result fromeach decision in the event of each state of nature are shown in Table below: Assume that it is now possible to estimate a probability of 0.60 that goodeconomic conditions will exist and a probability of .40 that poor economicconditions will exist. a) Determine the best decision by using expected opportunity loss. b) Develop a decision tree, with expected values at the probability nodes. c) Compute the expected value of perfect information.Given the following utility functions, check if the utility function is homogeneous and if MRS is diminishing: (1) U(x, y) = Vr + y (2) U(x,y) = (x +y")/5.851
- Question Solve the following maximization problem graphically. P(x, y) = 16+ x + 4y; subject to: Provide your answer below: f(x)= 4x + 6y≤ 72 4x + 2y 2 24 x > 3 y> 4(a) Given a utility function of an individual is U(x) = x² - 4x, determine his risk attitude. (b) With a utility function of U(x) = x - 3x², where x is the amount invested. (i) determine if this function satisfy the two properties of utility functions. (ii) compute the utility when the amount invested is 3 and 5 respectively.1(a)lf we allow for the possibility of satiation, the consumer's budget constraint takes the form pxs pw, Walrus' law then becomes pz(p) so for all p2 0. Show that the standard textbook proof of the existence of Walrasian equilibrium still applies for this generalized form of Walrus' law.
- Emma has a utility functionU(x1, x2, x3) = logx1+ 0.8logx2+ 0.72logx3 incomes x1 , x2, x3 in the next three years. This is an example of (A) expected value; (B) quasi-hyperbolic utility function; (C) standard discounted utility; (D) none of the above.If the benefits of a given choice option are delayed further into the future(all other relevant factors remaining constant),then the present value of the option will a) increase b) decrease c) remain the same d) ( unknow, not enough information to say).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.