Suppose that a consumer chooses (x1, x2) = (9,2) at prices (pi, p2) = (2,3) and (x,x) (4,5) at prices (pl, p) = (3,2) (note that wealth may be changing along with prices). As- suming that choices satisfy Walras' Law, i.e. the consumer spends her full wealth, are these choices consistent with the Weak Axiom of Revealed Preference? = Solution: The bundle x¹ is affordable at the old wealth wº = pº.x0 = 24 and prices pº, but the bundle xº is not affordable at the new wealth w¹ = p¹.x¹ 22 and prices p¹. This means that is revealed preferred to x¹, and x¹ is not revealed preferred to xº. Therefore, these choices are consistent with WARP.
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- Bob has a utility function U(x, y) = √x1 + 0.8√x2 + 0.64√x3 over his incomes x1, x2, x3 in the next three years. This function is an example of (A) expected utility; (B) quasi-hyperbolic utility function; (C) discounted utility; (D) none of the above. . Which of the following preferences agree with Bob’s utility? (A) (9, 10, 11) ≻ (9, 10, 12); (B) (9, 10, 11) ≻ (11, 10, 9);(C) (9, 10, 11) ≻ (9, 11, 10); (D) none of the above. Bob’s utility function implies (A) time stationarity; (B) transitivity; (C) impatience; (D) all of the above.Which of the FF. statements is correct regarding the preference of the consumers when the income of the consumer can only be spent between apples and oranges? Assume that apples are written on the vertical axis while oranges are written on the horizontal axis A. when the consumer has few oranges, he is willing to trade more apple to get another orange B. when the consumer has so many oranges already, he will only exchange less apples for an orange C. the declining slope of the indifference curve shows the marginal value of oranges is declining D. all are correct E. none is correctExistence of representative consumer Suppose households 1 and 2 have one-period utility functions u(c1) and w(c2), respectively, where u and w are both increasing, strictly concave, twice-differentiable functions of a scalar consumption rate. Consider the Pareto problem: Subject to the constraint c1 + c2 = c. Show that the solution of this problem has the form of a concave utility function vθ(c), which depends on the Pareto weight θ. Show that vθ(c) = θu (c1) = (1 − θ)w (c2). The function vθ(c) is the utility function of the representative consumer. Such a representative consumer always lurks within a complete markets competitive equilibrium even with heterogeneous preferences. At a competitive equilibrium, the marginal utilities of the representative agent and each and every agent are proportional.
- Solve part b and c. There two goods, candy and soda, available in arbitrary non-negative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function:u(x, y) = −|4 − x| − |4 − y|where x is the quantity of candy (in grams), y is the quantity of soda (inliters), and |.| denotes the absolute value: for any real number r ∈ R, |r| = r if r ≥ 0 −r if r < 0. The consumer has wealth of w > 0 Dirhams. The price of candy is p > 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Calculate the utility of the following consumption bundles: (4, 4), (4, 5), (5, 4), (4, 3), (3, 4), and α(4, 5) + (1 − α)(3, 4) for α ∈ [0, 1]. (b) In an appropriate diagram, illustrate the consumer’s map of indifference curves. c) Are the consumer's preferences monotone? Provide an explanation foryour answer.A consumer has a perfect complements utility function, where she prefers to have one unit of H with each unit of G. Also, she has an income of $210. Assume that the price of H is $8 and the price of G is $6. What is the consumer's optimal choice for good G*? Group of answer choices 11 12 15 16A consumer prefers to consume two commodities in fixed proportions. Specifically, she prefers to consume 1 unit of x2 and 4 units of x1 at the same time. Represent her utility function and find the most preferred and affordable consumption bundle for prices p1 and p2
- Solve; a consumer utility function is given as 64q10.5q20.25q30.4 1. what is the marginal utility of consuming commodities q1, q2 and q3 2. derive the second-order partial derivatives of the utility function with respect to the three pairs of commodities 3. show the cross partial derivatives with respect to q1 4.what is her total utility when q1 is 24, q2 is 30, and q3 is 15I. A)MRS=1/3, B)MRS=1/4, C)MRS=4/3, D)MRS=12 II. A)Rhea should buy more bread, less milk, B)Rhea should buy more milk, less bread, C) Rhea maximizes her utility at bundle A, so she should not change her consumptions of either good, D) Rhea cannot afford bundle A, so she should buy less of both goods III. A)Rhea's MRS at bundle A is greater than the price ratio (Pb/Pm), B)Changing her bundle moves Rhea to a higher indifference curve, C)The slope of the indifference curve (where bundle A is found) is not equal to the slope of Rhea's budget constraint, D)All of the above statements explain your answer to part II.When utility function U(q1, q2)=min{ 34.6 q1, 17 q2} and q1= 33 and q2= 60 are given, find utility level consumer gains?
- Solve; a consumer utility function is given as 64q10.5q20.25q30.4 2. derive the second-order partial derivatives of the utility function with respect to the three pairs of commoditiesMichael does not like to mix peanut butter and jelly in the same sandwich. However, he will consume them separately; for him, a sandwich with 1 spoon of peanut butter is exactly the same as a sandwich with 2 spoons of jelly. Michael has an income of m = 50, and the prices per spoonful of peanut butter and jelly are pPB=5 and pJ=11. Please write down Michael’s utility function over peanut butter (PB) and jelly (J). 2. Please determine Michael’s Marshallian demands PB*m and J*m3. Please determine Michael’s new Marshallian demands PB*m and J*m, when the price of peanut butter falls to pPB = 1.4. What are the (Hicks) SE and IE? Draw a diagram to show your analysis, with peanut butter on thehorizontal axis, and jelly on the vertical axis. 5. Recall that there are two different types of substitution effects. For example, in Q2 we have used theHicks SE. Does your answer to the last part change if we use the Slutsky SE? Justify. 6. Nam likes his peanut butter and jelly sandwiches with exactly…Marina decides to purchase a ring made from an alloy composed exclusively of gold (G) and titanium (T). The price of gold is $60 per gram, and the price of titanium is $30 per gram. Her total budget for the ring is $600. Her utility function is given by U(G,T) =GT. Suppose the price of titanium falls to $20 per gram. At the final basket, the optimal amount of titanium is()grams.