,consider the following description of a two-goods example: Assume two consumers with utility functions of the form UX ("1, r2) = x/2y and U (1, /2) = n2- 1/2 1/2 Further, suppose that consumer X is endowed with wX = (6,2) and consumer Y with wY = (2, 6).
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A: Given, U=100x0.85y0.10
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Q: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3
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A: U (x1 , x2 ) = α ln(x1) + (1 − α) ln(x2) α=0.25 U (x1 , x2 ) = 0.25 ln(x1) + 0.75 ln(x2)
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Provide general formulations of the First and Second Welfare Theorems for an exchange economy and, using the specific exchange economy of this section, illustrate the theorems in a diagram.
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- A consumer is willing to trade 4 units of x for 1 unit of y when she is consuming bundle(8, 1). She is also willing to trade in 1 unit of x for 2 units of y when she is consumingbundle (4, 4). She is indifferent between these two bundles. Assuming that the utilityfunction is Cobb-Douglas of the form U(x,y)=xα yβ, where α and β are positiveconstants, what is the utility function for this consumer?Consider a hypothetical consumer named Hayden who is shopping for bread and brie. The graph with bread and brie on the axes presents the utility‑maximizing combinations of bread and brie that Hayden chooses when the price of bread is $1.00$1.00 per loaf and the price of brie is $4.00$4.00 and $6.00$6.00 per wheel, respectively. The other graph shows Hayden's demand curve for brie. The two points and associated values in the graph for bread and brie combinations correspond to points A and B in the graph of the demand curve for brie. What are the specific prices and quantities of brie associated with points A and B on Hayden's demand curve? price of brie at point A: $$ quantity demanded at point A: price of brie at point B: $$ quantity demanded at point B:Consider two individuals whose utility functions are given by
- Suppose that consumer I has the utility function u(x,y) = x + 2y and consumer II has the utility function u(x,y) = min{x, 2y}. Consumer I initially has 12 units of y and zero units of x, while consumer II has 12 units of x and zero units of y. It is correct to state that, in competitive equilibrium, the agents' consumption basket will be:Heather and Jeremiah both enjoy sunflower butter (s) and jelly (j) sandwiches, but they have varying preferences regarding the optimal ratio of the two. Heather prefers her sandwiches to have 6 spoonfuls of sunflower butter for every 3 scoops of jelly, whereas Jeremiah prefers 3 scoops of sunflower butter for every 5 scoops of jelly. They both would prefer as many sandwiches as possible, but derive no utility from sandwiches without their preferred ratio of s and j. A) Write down a utility function for both Heather and Jeremiah regarding consumption of s and j (U(s,j)) B) On the same graph, draw a set of indifference curves for both Heather and Jeremiah, labeling which is which. C) In addition to s and j, Heather and Jeremiah now need bread, b, to make sandwiches. Heather prefers to separate her sunflower butter and jelly and therefore uses 3 slices of bread per sandwich. Write down Heather’s utility function Uh(s,j,b) as a function of the three inputs.First household m=$2,500 per month, spends $125 dollars per month on electricity. Second household m=$10,000 per month and spends $200 per month on electricity. p1=0.1 and p2=1 x1=consumption of electricity and x2=everything else The preferences over electricity and other goods is described by a Cobb- Douglas utility function. What are the parameters of the utility function for each of the two households?
- Describe the two approaches of utility analysis !I am unsure the direction the utility functions would go in , with this specific scenarioCeja has utility function U=A2*B2 , where A equals the number of apples she eats each week, while B is the number of bananas she eats each week. Ceja has $20 to spend on fruit each week. The price of an apple is $1, while the price of a banana is $0.25. Find out the combination of Apples and Bananas that maximize Ceja’s satisfaction. If price of Banana is increased by $.25, what will be the new combination of A and B that would maximize her utility? Show graphically and drive the demand curve for Bananas
- Consider an economy composed of 16 consumers. Of these, 5 consumers each own one right shoe and 11 consumers each own one left shoe. Shoes are indivisible. Everyone has the same utility function, which is Min(2R, L}, where R and L are, respectively, the quantities of right and left shoes con sumed. A) (10%) Is the status quo (where each individual has his own shoe) Pareto efficient? If so, briefly explain why. If not, provide a Pareto improvement b) (10%) Characterize all Pareto efficient allocationsConsider a couple whose behaviour follows the unitary household model. Their preferences can be represented by the utility function: U(CM; CH) = min (CM, CH), where CM, denotes market goods and CH denotes home production. Each spouse can work up to 50 hours per week, and those 50 hours can be divided between market work and home production. Joe and Anna are each paid £20 per hour for market work. Joe produces £20 of home production per hour, while Anna produces £30 per hour of home production. (a)How many hours are each of the spouses allocating to home production and market work? and Suppose that Anna is offered a pay raise, so that her hourly market wage increases to £25, and nothing else changes. Will that change the identity of the spouse who works more hours on the market? Explain your answer.Two students go out to lunch and decide to split the bill evenly between them. Each student has a quasi-linear utility function given by ui(fi , xi) = φi(fi) + xi , where φi(·) is strictly concave, fi is the amount of food consumed by student i, and xi is a composite numeraire good. Each student has a fixed budget of mi . EVALUATE THIS CLAIM: Both students eat too much!