Consider an economy with two consumers A and B, one firm and two goods, 1 and2. The initial endowments of A and B are w = wB = (1/2, 1/2). The utilityfunctions are:u^(rf, 12) = In z{' + In rand "(f.) = Vzf + V=?The firm produces good 2 using good 1 as input, the production function is y2 =The consumer B owns the firm (denote z 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.

In economics, a situation known as pareto efficiency occurs when no one can get richer without…

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 w₁ = wB = (1/2, 1/2). The utility functions are: u^(x, z) = In x + In and = The firm produces good 2 using good 1 as input, the production function is y₂ = √√√ The consumer B owns the firm (denote the firm's profit). Good 2 is the numeraire good (i.e., p=1). Determine the demand for good 1 of the consumers and the firm. (a) (b) Show that there is a unique equilibrium price p₁. (c) 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 2. The initial endowments of A and B are w₁ = wB = (1/2, 1/2). The utility functions are: u^(x, z) = In x + In and = The firm produces good 2 using good 1 as input, the production function is y₂ = √√√ The consumer B owns the firm (denote the firm's profit). Good 2 is the numeraire good (i.e., p=1). Determine the demand for good 1 of the consumers and the firm. (a) (b) Show that there is a unique equilibrium price p₁. (c) 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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