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Quiz 12 Exchange3 - x 2(3 x 1 The good x 2 is the...

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Shomu Banerjee ECON 201 EXCHANGE WITH MORE THAN 2 PERSONS An economy consists of two types of consumers, males and females . There are 4 males and 8 females . There are two consumption goods, x 1 and x 2 , that can be traded. There is no production. Each male is initially endowed with 4 units of x 1 and 0 units of x 2 ; each female is endowed with 0 units of x 1 and 12 units of x 2 . Each male has identical utility functions given by u ( x 1 , x 2 ) = x 1 x 2 and his marginal rate of substitution equals - x 2 / x 1 . Each female has identical utility functions given by u ( x 1 , x 2 ) = x 1 ( x 2 ) 3 and her marginal rate of substitution equals -
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Unformatted text preview: x 2 /(3 x 1 ). The good x 2 is the numéraire good ( p 2 = $1); for simplicity write p 1 as just p . Then males’ demand for good x 1 is x 1 = m M /2 p and for good x 2 is x 2 = m M /2, where m M refers to the income of males. Similarly, for females, the demand for good x 1 is x 1 = m F /4 p and for good x 2 is x 2 = 3 m F /4, where m F is the income of females. (a) Find the Walras price of x 1 and the Walras allocation for this economy. (b) Check that the Walras allocation you found is Pareto efficient....
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