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

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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