Consider an exchange economy with two types of agents, A and B, and two goods, r and Y. Preferences are given byuA(XA, YA) = xA+ 6 In(yA) and up(xB, YB) = In(*BYB). Suppose the government wants to reach the goal of 2B = 5 with thecompetitive equilibrium by setting a redistribution r such that wa =the government's goal. Round your answer to 2 decimal points.(10, r) and wg = (0, 20 – r). Let Py =1. Find r reachesAnswer:The correct answer is: 1.82Tom and Jerry live together, and they plan to do the chores on the weekends. They have 4 tasks to finish, and each of them needsto pick 2 tasks to finish. The table below demonstrates the their utilities of doing a task. The higher the utility is, the more preferredthe task is.[Laundry] [Moaning]l[Car Washing] [Floor Cleaning]Tom-5-10-10Jerry-6-3-12-3The current allocation is that Tom does moaning and car washing while Jerry does laundry and floor cleaning. What is theminimum value that X can be to make the current allocation Pareto optimal?Answer:The correct answer is: -5

UA = xA + 6 ln (yA ) UB = ln (xB yB ) Goal of xB =5 Endowments: wA = (10 , r) wB = (0 , 20-r) py…

Consider an exchange economy with two types of agents, A and B, and two goods, a and y. Preferences are given by uA(TA, YA) = XA +6 ln(yA) and ug(xB, YB) = In(rBYB). Suppose the government wants to reach the goal of rB = 5 with the competitive equilibrium by setting a redistribution r such that wa = (10, r) and wy = (0, 20 – r). Let Py = 1. Findr reaches the government's goal. Round your answer to 2 decimal points. Answer:

Consider an exchange economy with two types of agents, A and B, and two goods, a and y. Preferences are given by uA(TA, YA) = XA +6 ln(yA) and ug(xB, YB) = In(rBYB). Suppose the government wants to reach the goal of rB = 5 with the competitive equilibrium by setting a redistribution r such that wa = (10, r) and wy = (0, 20 – r). Let Py = 1. Findr reaches the government's goal. Round your answer to 2 decimal points. Answer:

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider an exchange economy with two types of agents, A and B, and two goods, r and Y. Preferences are given by
uA(XA, YA) = xA+ 6 In(yA) and up(xB, YB) = In(*BYB). Suppose the government wants to reach the goal of 2B = 5 with the
competitive equilibrium by setting a redistribution r such that wa =
the government's goal. Round your answer to 2 decimal points.
(10, r) and wg = (0, 20 – r). Let Py =1. Find r reaches
Answer:
The correct answer is: 1.82
Tom and Jerry live together, and they plan to do the chores on the weekends. They have 4 tasks to finish, and each of them needs
to pick 2 tasks to finish. The table below demonstrates the their utilities of doing a task. The higher the utility is, the more preferred
the task is.
[Laundry] [Moaning]l[Car Washing] [Floor Cleaning]
Tom
-5
-10
-10
Jerry
-6
-3
-12
-3
The current allocation is that Tom does moaning and car washing while Jerry does laundry and floor cleaning. What is the
minimum value that X can be to make the current allocation Pareto optimal?
Answer:
The correct answer is: -5

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Consider an economy with 100 units of labor and capital that must be completely distributed to Firms X and Y. With this information, recommend an efficient allocation of the two inputs between the two firms. Discuss and show the necessary solution to support your recommendationX = KL2 – L3;Y = 10K1.5L0.5;Graphically illustrate and discuss how an economy can achieve production efficiency if at its current allocation on L and K, the MRTSLKY > MRTSLKZ (you may use your own values to represent the available L and K and the initial distribution)
Consider an exchange economy with two types of agents, A and B, and two goods, x and y. Preferences are given by UA (XA, YA) = = A + 6 ln(y₁) and UB(TB, YB) = ln(TBYB). Suppose the government wants to reach the goal of XB = 5 with the competitive equilibrium by setting a redistribution r such that w₁ = (10,r) and wB = (0,20 - r). 1. Find r reaches the government's goal. Round your answer to 2 decimal points. Let Py = Answer:
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Output √w 2. Consider a one-consumer one-firm economy in which u(x) = x₂ + √√q and f(2)=√z. (a) Derive the Pareto set of this economy. Solution. Pareto-efficient allocations are solutions to the problem ₂+√√q subject to √w- x₂ = xq, which is illustrated in Figure 3. Any solution to this problem in which , x > 0 must solve the first-order condition = f'(wx), or 2₁/x = max 0≤x≤w,xq 20 au(x*) Əxz _u(x*) Əxq By substituting = √w - x, we have that x = (¹/2)¹/³ and x = w − (1/2)³/³. Any solution to the Pareto problem with x = 0 would have to be such that ə Figure 5: No corner solution with x = 0 Əxz — *²)=0² u(x*)x=0 which, using that = √w in this case, reduces to w≤ (1/2) 8/³. In words, if the consumer's endowment of input is small, then the Pareto-efficient allocations have the firm use up all of the input to produce output, leaving the consumer with no consumption of input. This is illustrated in Figure 4. Any solution to the Pareto problem with x = 0 would have to be such that ≤ f(w-x)…
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.
Consider a two-good exchange economy with two types of consumers. Type A have the utility function And an endowment of 3 units of good 1 and k units of good 2. Type B has the utility function And an endowment of 6 units of good 1 and 21 - k units of good 2. a. Find the competitive equilibrium outcome and show that the equilibrium price p* = p1/p2 of good 1 in terms of good 2 is p* = 21+k/15. b. Find the income levels (MA; MB) of both types in equilibrium as a function of k. c. Suppose that the government can make a lump-sum transfer of good 2, but it is impossible to transfer good 1. Use your answer to part b to describe the set of income distributions attainable through such transfers. Draw this in a diagram. d. Suppose that the government can affect the initial distribution of resources by varying k. Find the optimal distribution of income if (i) the SWF is W = log(MA) + log(MB) and (ii) W = MA + MB.