Consider the utility function uu(xx, yy) 10 for all bundles (xx, yy) (a) What are strict preferences? What are the indifferences? (b) Argue that the preferences represented by this utility function are strictly convex or that they are not. (c) Árgue that the preferences represented by this utility function are complete or that they are not. (d) Argue that the preferences represented by this utility function are strongly monotonic or they are not.
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- (a) A consumer with income I=120 facing prices pX = 4 and pY = 8 for two goods X and Y (for each good she prefers more to less, with diminishing MRS) chooses optimally to consume 12 units of X. If the prices change and now pX = 6 and pY = 4, what is the possible range for her new optimal X consumption? (b) Forget about (a). A consumer with I=$240 budget is shopping for apples (x) and oranges (y). Apples cost $1 each up until 60 units; thereafter each apple costs $2. Similarly, oranges cost $1 each up until 60 units, and thereafter $2 each. Draw the graph of feasible set of bundles for the consumer with relevant points and numbers (shade the feasible area), no explanation needed. (c)(HARD!) In (b), calculate the optimal bundle assuming the consumer’s utility function is u(x,y) = x5y.No written by hand solution Assume Fred has the following preference relation on [0, 1]: x ≿ y if and only if x ≤ y for all x ̸= 1 and y ̸= 1; and 1 ≻ z for all z ∈ (0, 1), 1 ∼ 1 and 0 ≻ 1. Does there exists a utility representation for this preference relation? If yes, provide a utility function. If no, explain. Show your work.ayesha derives utility from travelling and outdoor dinning o weekends as given utility function U(t,d)=TD.the price of a day spent travelling is $160{Pt=160} and price of dining outdoor $200{Pd=200}.ayesha annual budget for this is $8000. find ayesha's utility maximizing choice of days travelling and dining outside. and alsoo find uutility level from consuming that bundles .show findings graphically
- Mr. Dogan has 4000 TL to spend. He considers buying meat whose price is 400 TL per kg. and cheese whose price is 160 TL /kg. Given this a) What condition (equality) leads him to a utility maximization. State the condition numerically and tell clearly what each of the variables mean in that equation b) Now suppose that income of Mr. Dogan and price of meat does not change but price of cheese is down to 130 TL/kg. Do the equality and optimal basket found in a still maximize the utility? If not; what is the new condition for utility maximization (write the condition as a numerical equation defining the variables in the equation)a) Show the derivation of the individual demand function for a utility maximizer consumer and b) explain the common properties for the points on this function.In ordinal Utility approach, let a consumer's utility function is given by TU X³Y. If price of X is 2 birr and price of Y is 3 birr and if budget of the consumer is 100 birr for consumption of X and Y. then what are the utility maximization X and Y?
- part D E F solution needed Question 1Elmira has a monthly income of $200 that she allocates between two goods: Beef (B) andPotatoes (P). Beef costs $6 per pound while Potatoes cost $1 per pound. Elmira’s utilityfunction is given by: U(B, P) = 2B + P Assume that both Beef and Potatoes are finelydivisible goods (so your answer may or may not be a whole number). This questioncontains 6 parts, (a)-(f)) (a) Write down the equation for Elmira’s indifference curves. (Assume Beef is measuredon x-axis and Potatoes on y-axis) (b) Depict Elmira’s budget line graphically and mention its slope. (Again, assume Beef ismeasured on x-axis and Potatoes on y-axis) (c) Illustrate some indifference curve(s) for Elmira. (d) Find MRSBP . Do Elmira’s preferences have a diminishing Marginal Rate of Substitution? (e) What combination of Beef and Potatoes should Elmira buy to maximize her utility? (f) Determine Elmira’s utility at the utility maximizing choice.A consumer’s preferences between goods x and y are representedby the utility function u(x, y) = 2min{x, y}+10. Suppose this consumer hasincome of $16, the price of good x is $3 and the price of good y is $1. Suppose the price of good x increases to $7 while the price of good y andthe consumer’s income stay constant. Calculate the magnitudes of the compensating and the equivalent variations. Explain what each measures.True/False/Uncertain: 1. In taking an exam, Atack, a rational student, allocates his time to the various questions so as to equalize hismarginal point utility per minute on all questions. 2. The marginal utility of food to Zecher depends only on the amount of food (and not on the amount ofhousing) and the marginal utility declines as more food is consumed; likewise for housing. Therefore,both food and housing are normal goods. (Hint: Express the optimality condition for Zecher’s [UMP], MUF/MUH = PF/PH. Notice that PF/PH is fixed. If all of an increase in income is spent on F, can the equality be maintained?)
- Wherein:TU = Total Utilityf= is a function ofMU = Marginal UtilityO = units of consumptionA= infinitesimal change EMV= Expected Monetary Valuea) You are given a utility function described as:U= U(K, L, M) = 10LogK + SLogL. + 2LogMWhere K, L and M are goods consumed. The individual has K100 to spend on the threeitems. Furthermore, you are informed that monthly salary is $500 and the prices of K, Land M are $2, $10 and $4 respectively. Calculate the consumer's optimal bundle.D.b) Provided a demand curve for Beans is as followsO = 4000 - 255PWhere Q is the quantity demanded and P is the price. Find the elasticity at K7, K10 and K15.Consider the following utility function belonging to “Consumer A”. UA(x,y,z,v) = x0.1y0.2z0.3v0.4. Suppose that prices of x, y, z and v are 1$, 2$, 3$ and 4$. The consumer’s income is 10$. a. Find the values of x, y,z and v that maximize the consumer’s utility subject to his/her budget constraint. b. Suppose that “Consumer B” has a utility function which is a logarithmic transformation of the consumer A’s utility function, i.e. UB =ln UA. Suppose that prices and income are the same. Would the amounts of x, y, z and v consumed by “Consumer B” be the same as the amounts consumed by “Consumer A”?