Quiz 21. Consumption externality Ans

Quiz 21. Consumption externality Ans - Atkins and Bodkins...

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Shomu Banerjee ECON 201 CONSUMPTION EXTERNALITY ANSWERS Suppose Atkins and Bodkins are the only two consumers in our economy, there are two goods x and y , and Atkins’ endowment is ω a = (10, 0) while Bodkins’ is ω b = (0, 10). Their utility functions are given by u A ( x a , y a , x b ) = x a y a + x b and u B ( x b , y b ) = x b y b . Bodkins’ preferences are Cobb-Douglas. Atkins’ preferences are Cobb-Douglas in his own consumption of x a and y a . But x b also enters A ’s utility function as a ‘good’; Atkins has no part in choosing x b but derives a positive utility from Bodkins’ consumption of it. The (private) marginal rates of substitution for
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Unformatted text preview: Atkins and Bodkins are -y a / x a and -y b / x b . Find the contract curve for this two-person Edgeworth box. From society’s point of view, A ’s utility function is actually u A = x a y a + (10 – x a ) = x a y a + 10 – x a , so A ’s social MRS a = –( y a – 1)/ x a . Set the social MRS a equal to MRS b = -y b / x b and substitute x b = 10 - x a and y b = 10 - y a to get the equation of the contract curve: y a = 1 + 0.9 x a . x a x b y a y b O b O a 5 5 10 10...
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