Suppose the economy has 24 units of good F and 20 units of good C. If consumer J is endowed with 12 units of good F and the consumers are given a Pareto efficient allocation, how many units of good C will consumer **K** be provided?
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- Consider two people in the market for tilapia, Reagan and Cheryl. The marginal benefit curves for both individuals are shown in the accompanying graph. a. Suppose the market price of tilapia is $2.00 per pound. Move point A to Cheryl’s quantity purchased. Move point B to Reagan’s quantity purchased. b. How many pounds of tilapia do they collectively purchase? _________ pounds c. To achieve an efficient allocation, Cheryl should purchase _______(more tilapia than, the same amount of tilapia as, less tilapia than) she is currently purchasing, and Reagan should purchase ________ (more tilapia than, the same amount of tilapia as, less tilapia than) she is currently purchasing.Consider a two-person exchange economy in which person 1 owns 200 units of x and 100 units of y while person 2 owns 100 units of x and 200 units y. Suppose their preferences over the two goods can be represented as: U1 (x, y) = y + 50Inx U2 (x, y) = y + 150lnx 1. How much of x do they trade among each other? 2. Does the First Welfare Theorem (FWT) hold in this economy? 3. Can some individuals be made better off if we are at the Pareto efficient allocation?Consider a two-person exchange economy in which person 1 owns 200 units of x and 100 units of y while person 2 owns 100 units of x and 200 units y. Suppose their preferences over the two goods can be represented as: U1 (x, y) = y + 50Inx U2 (x, y) = y + 150lnx 1. How much of x do they trade among each other? 2. Does the First Welfare Theorem (FWT) hold in this economy?
- Jane has 11 liters of soft drinks and 10 sandwiches. Bob, on the other hand, has 9 liters of soft drinks and 10 sandwiches. With these endowments, Jane's marginal rate of substitution (MRS) of soft drinks for sandwiches is 6 and Bob's MRS is equal to 8. Draw an Edgeworth box diagram to show whether this allocation of resources is efficient. If it is explain why. If it is not, what changes will make both parties better off? Part 2 1.) Using the three-point curved line drawing tool, draw an indifference curve for Jane when consuming 11 liters of soft drinks and 10 sandwiches. Label this curve UJ. 2.) Using the three-point curved line drawing tool, draw an indifference curve for Bob when consuming 9 liters of soft drinks and 10 sandwiches. Label this curve UB.Two individuals, Fred and Helen, are in an economy with no production, and each have the utility function U = 10XY. Prices of both X and Y are set at $1. Initial endowments for Fred are 10 units of X and 6 units of Y. Helen has 8 units of X and 12 units of Y. Find the general equilibrium prices and allocation, then show that the G.E. allocation is Pareto efficient.First and second welfare theorems There are two goods A and B and two inputs K and L. The production functions are Ya=AKaαLa1-α Yb=BKbβLbβ The production functions display the standard properties including constatnt returns to scale A representative household has utility U(ca,cb) where ci is the consumption of good i. The total supply of each factor is fixed. K=Ka+Kb L=La+Lb a) A social planner allocates consumption of both goods and determines production and allocation of inputs. Derive the optimal allocation and demonstrate the marginal rate of substitution is equal to the marginal rate of transformation between the consumption goods. Draw a graph of the production possibility frontier. b) Now assume a maret system i. Households own the labor and capital which is rented to firms. The households face a budget constraint waLa+wbLb+raKa+≥PaCa+PbCb where wi is the real wage paid in industry i and ri is the rental rate in industry i. The total supply of each factor is fixed, as described…
- Please define and draw the utility possibilities curve. On your graph explain what is meant by pareto efficiency. Define social welfare functions. On your graph demonstrate that some efficient points need not be as good, given the social welfare function, as some inefficient points.Consider an Edgeworth box economy, where preferences and endowments are given by. ( attached below ) In the following, use the normalization p2 = 1.(a) Find all the Pareto optimal allocations (use x1 to parameterize thePO allocations). (b) Suppose the government wants individual 1 to have the bundle x1 = (5, 9). Show whether the government can induce this outcome an equilib- rium with transfers. Find the supporting prices and transfers if possible. (c) State the Second Fundamental Theorem of Welfare and explain how the result in part (b) relates to that theorem. (d) Suppose the government does not care what bundle individual 1 gets and only wants to ensure that the individual 1 receives utility level equal to 45. Show whether this can be achieved as an equilibrium with transfers. Find the supporting prices and transfers if possible.I need help with this homework problem. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = (X^1/2)*(Y^1/2) UB(X,Y) = X + Y The initial endowments are: A: X = 8; Y = 3 B: X = 4; Y = 5 What is the marginal rate of substitution for consumer A at the initial allocation? What is the marginal rate of substitution for consumer B at the initial allocation? Is the initial allocation Pareto Efficient?
- Consider an economy with 3 agents, Mohammed (M), David (D) and Susan (S). There are two goods available, good x, and good y. The marginal rates of substitution (where good x is on the horizontal axis and good y is on the vertical axis) are given by for Mohammed, for David and for Suzan. Mohammed and David are both consuming twice as much of the good x than good y, while Susan is consuming equal amounts of x and y. (image of functions and equations attached) A. What are the conditions for Pareto efficiency in an exchange economy? Are these consumption levels economically efficient? B. Can these consumption allocations be observed in a perfectly competitive equilibrium in an exchange economy without production? Explain.True/false, no need to explain. (a) There is no perfect way to aggregate individual preferences to a single "social" preferences (b) “Before enacting a policy, try to put ourself in the shoes of those who will be negatively impacted mostly.” This sentence is best to summarise the Benthamite welfare function (c) If a person's utility is simply a function of her own consumption, and the welfare function is derived from individuals utility function, then we will not have consumption externalities. (d) An allocation cannot be both equitable and Pareto efficient.4. Aaron and Burris have the following utility functions over two goods, x and y. Aaron’s utility function: UA(xA, yA) = min{xA/3, yA} Burris’s utility function: UB(xB, yB) = 9xB + 3yB Aaron’s endowment is eA = (2, 4). Burris’ endowment is eB = (10, 8). In an Edgeworth Box diagram, show which allocations are in the core. Solve for the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram. Let good y be the numeraire (i.e. set py = 1 and let px = p). Solve for the Walrasian competitive equilibrium allocation and price ratio.