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Competitive prices, tax and lump sum cash transfer in case of externalities

An economy is made up of two people. The utility functions are $$u_1(x_{11},x_{12}) = x_{11}x_{12}$$ $$u_2(x_{21},x_{22}) = 2x_{21} + 2x_{22} −x_{11}$$ The initial endowments are $ω_1 = (1,0)$ and $...
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