Consider an economy with 2 goods and 2 agents. The first agent has the utility function, u (x₁, x₂) = ln x₁ + 2 ln x2, and the other one has u (y₁, Y2) = 2 ln y₁ + ln y2. The aggregate endowments of the 2 goods are given by (50, 100). Suppose there is a social planner who cares about agents equally.
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(a)Set up the plannerís problem.
(b)Calculate the first-best outcome (i.e., the social plannerís solution)
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- You are considering going to a football game. However, the roads are cover in ice due to bad weather. Your ticket was a gift. You derive a value of z from attending the game, and a cost of D for driving on the icy roads. Your utility function is given by: ug(Z) + ui(D) = In(Z - 3) - In(2 - D). In your ultimate wisdom, you calculate that the cost of driving on the icy roads is 1 unit (So, D=1). What is the minimum value you must obtain from attending the game, so that you decide to go? Solution sent me fast ..A and B consume only two goods, cider (C) and dumplings (D). A has an initial endowment of 10 bottles of C and 30 of D. Bob has an initial endowment of 50 bottles of cider and 50 dumplings. Alice’s utility function is uA(CA,DA) = 9ln(CA) + 10ln(DA), where CA and DA represent consumption of C and D, respectively. B’s utility function is uB(CB,DB) = CBXDB, where CB and DB denote B's consumption of C and D. a) Find the competitive equilibrium, i.e. the price ratio, of this exchange economy and the resulting equilibrium allocation. b) Find the expression of the contract curve for this economy and use your answer to check that the equilibrium allocation you found in (b) is indeed Pareto optimal.Suppose the utility possibility frontier for two individuals is given by U_a+2U_b=200 Please plot the utility frontier on a graph.
- uestion1:Donna and Jim are two consumers purchasing strawberries and chocolates. Jim’s utility function is U (x, y) = xy and Donna’s utility function is U (x, y) = x2y where x denotes strawberries and y denoteschocolates. Jim’s marginal utility functions are MUX=y and MUy=x while Donna’s are MUX=2xy and MUy=x2. Jim’s income is $100, and Donna’s income is $150. What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4? What is the optimal bundle for Jim, and for Donna, when the price of strawberries rises to $3?Question2:Consider a one-period ecoMatthew Hamming is stranded on an island. He has decided that he will spend exactly 10 hours a day gathering food. He can either spend this time gathering coconuts or catching fish. He can catch 2 fish per hour and he can gather 3 coconuts per hour. Matthew's utility function is U(FC) = 3F0.60.3 a. How many fish should Matthew catch and how many coconuts should he gather so that his consumption maximizes his utility? Illustrate the equilibrium with a graph b. One day a native inhabitant of another island arrives on the island. The visitor offers Matthew trade of 3 fish for 1 coconut. The trade fee costs 1 fish (that must be paid prior to the exchange). Will Matthew decide to trade? What will Matthew produce and consume? Justify your answer and provide a graph.3. Christina loves pizza and hates burger. Her utility function is U(p – b) = p – 6", where is the number of pizzas she consumes and b is the number of burgers she consumes. John likes both pizza and burger. His utility function is U(p, b) = p + 2\b Christina has an initial endowment of no pizzas and 8 burgers. John has an initial endowment of 16 pizzas and 8 burgers. a. Graph the initial endowment and label it E b. If Christina hates burgers and John likes them, how many burgers can Christina and John be consuming at a Pareto optimal allocation? What is John's marginal utility for pizzas and burgers? Mark the locus of Pareto optimal allocations of pizzas and burgers between Christina and John on the grapsh above.
- Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries). There are two types of agents, h and g, and they have the same preferences over consumption, represented by the utility function: u(x1, 22) = In r1 + In #2. However, there are twice as many type-h agents as type-g agents. The only factors of production are their labour. When a type-h agent chooses to spend a fraction a of his day producing meat and the rest producing berries then his output is (yf, y ) = (2a, 2(1 – a)). A type-g agent is more productive. When she chooses to spend a fraction B of her day producing meat and the rest producing berries then her output is (v7, y2) = (38, 12(1 – B)). Which of the following statements is correct? a. Given equilibrium price p, each agent of type h demands one unit of good 1 (meat) and p units of good 2 (berries). Each agent of type g demands 6/p units of good 1 (meat) and 6 units of good 2 (berries). O b. Given equilibrium price p, each agent of…Ginny likes to eat Bertie Bott's Every Flavour Beans (b), and Chocolate Frogs (f). Her preferences over these lollies are Cobb-Douglas, and can be presented by the utility function u(b, ƒ) = }} (b − 2)(f+3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frog f) costs 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectly divisible goods. (a) Find Ginny's optimal bundle. (b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the time she is there, she is left only with 75 Knuts. What is her optimal bundle now? (c) Now, consider the general case, where Ginny's income is m, the price of Every Flavour Beans is pb, and the price of Chocolate Frogs is given by pf. In other words, treat Chocolate Frogs as the numeraire. Find Ginny's demand for each good in terms of m, pl and Pf. (d) Find the good on which Ginny will always spend more than half of her income. (e) Find the own-price, cross-price, and income elasticities of…Julio loves gardening. His favourite plants are tulips and hydrangeas. His utility function is ' u(t,h)= t +100h -h^2 where t is the number of tulipsin his garden and h is the number of hydrangeas in his garden. suppose he has a 500 square feet for his garden. each tulip takes up 1 square foot of space and each hydrangeas takes up 4 square feet. he gets both plants for free.If he wanted to maximize his utility, how many tulips should he plant, what about hydrangeas? b) if his yard was only 144 square feet, how many tulips would he plant? How many hydrangeas? C) In order to plant both tulips and hydrangeas, how big does his garden need to be. carfeully explain.
- Consider an economy with 2 goods and 2 agents. The Örst agent has the utilityfunction, u (x1; x2) = ln x1 + 2 ln x2, and the other one has u (y1; y2) = 2 ln y1 + ln y2.The aggregate endowments of the 2 goods are given by (50; 100). Suppose there is asocial planner who cares about agents equally.(a) Set up the plannerís problem b) Calculate the first-best outcome (i.e., the social plannerís solution).For the rest of this question consider a two goods economy where Kim and Jung can trade Ferraris (good x) and VR headsets (good y) with each other. Kim and Jung both enjoy driving Ferraris and having more VR headsets (so more friends can play the same game). They start at the same (high) level of income. Kim has an initial endowment of (x0k, y0k) = (10,30) and Jung has an initial endowment of (x0j, y0j) = (30,10) d) Assume that a social planner could redistribute initial wealth (the amounts of ? and ? that Kim and Jung have). Can they reallocate resources so that Kim and Jung reach the allocation (Xk, Yk) = (20,20) and (Xj, Yj) = (20,20) as a general equilibrium (i.e. post-trade) allocation? Can the social planner redistribute resources to make the allocation where Jung owns all the resources in the economy a general equilibrium allocation?Jack Sparrow and his wife consume wine (W) and books (B). Jack Sparrow's utility function is Ujack(W, B) = W. His wife's utility function is Uwife(W, B) = B. Jack's endowment is 17 bottles of wine and 5 books and Jack's wife's endowment is 20 bottles of wine and 14 books. In the Edgeworth box, Jack's consumption is measured from the lower left corner, and his wife's from the upper right corner of the box; the wine is on the horizontal axis and books are on the vertical axis. Therefore, in an Edgeworth box for Jack and his wife, there is only one Pareto Optimal allocation that is located in the top left corner of the box. True or False? Please submit 1 if True and O if False.