Consider an economy with two consumers A and B, one firm and two goods, 1 and2. The initial endowments of A and B are wAw = (1/2, 1/2). The utilityfunctions are:u^(r, ) = In r + In zandThe firm produces good 2 using good 1 as input, the production function is y2 Vh.The consumer B owns the firm (denote r the firm's profit). Good 2 is the numerairegood (i.e., p2= 1).(a)Determine the demand for good 1 of the Consumers and the firm.(b)Show that there is a unique equilibrium price p.(c)Prove or disprove that the final allocation is Pareto Optimal.BIUG

Pareto efficiency as developed by Vilfredo Pareto is an optimality condition that depicts a…

Consider an economy with two consumers A and B, one firm and two goods, 1 and w = (1/2,1/2). The utility 2. The initial endowments of A and B are w functions are: T (a) (b) (c) Fati APSALINES u^(₁,2)= ln x + In ₂ 2952 MANCE and √T. The firm produces good 2 using good 1 as input, the production function is y/₂ = The consumer B owns the firm (denote 7 the firm's profit). Good 2 is the numeraire good (i.e.. p2= 1). Determine the demand for good 1 of the consumers and the firm. Show that there is a unique equilibrium price p₁. Prove or disprove that the final allocation is Pareto Optimal.

Consider an economy with two consumers A and B, one firm and two goods, 1 and w = (1/2,1/2). The utility 2. The initial endowments of A and B are w functions are: T (a) (b) (c) Fati APSALINES u^(₁,2)= ln x + In ₂ 2952 MANCE and √T. The firm produces good 2 using good 1 as input, the production function is y/₂ = The consumer B owns the firm (denote 7 the firm's profit). Good 2 is the numeraire good (i.e.. p2= 1). Determine the demand for good 1 of the consumers and the firm. Show that there is a unique equilibrium price p₁. Prove or disprove that the final allocation is Pareto Optimal.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider an economy with two consumers A and B, one firm and two goods, 1 and
2. The initial endowments of A and B are wA
w = (1/2, 1/2). The utility
functions are:
u^(r, ) = In r + In z
and
The firm produces good 2 using good 1 as input, the production function is y2 Vh.
The consumer B owns the firm (denote r the firm's profit). Good 2 is the numeraire
good (i.e., p2
= 1).
(a)
Determine the demand for good 1 of the Consumers and the firm.
(b)
Show that there is a unique equilibrium price p.
(c)
Prove or disprove that the final allocation is Pareto Optimal.
BIUG

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Pankti consumes two goods, x and y. Her utility function is given byU(x, y) = ln(xy).(a) Are Pankti’s preferences homothetic? Explain.
a) 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 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. What are the conditions for Pareto efficiency in an exchange economy? Are these consumption levels economically efficient? Can these consumption allocations be observed in a perfectly competitive equilibrium in an exchange economy without production? Explain. b) There are two firms in the economy. Each firm employs positive amounts of capital and labour. The technology satisfies diminishing marginal rate of technical substitution of labour for capital. Currently, A’s marginal rate of technical substitution of labour for capital is 4 while B’s marginal rate of technical…
Give answer with explanation and Give Correct and incorrect answer explanation
2(a) Suppose x is a Pareto efficient allocation in which each agent holds a positive amount of each good. Also suppose that preferences are convex, continuous and monotonic. Then show that x' is a Walrasian equilibrium for the initial endowments that are redistributed such that w, = x' for i =1,.n.
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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.
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