A farmer and a banker live for two periods. The banker has an endowment of grain in each period e B = ( 1 , 1 ) , while the farmer has an endowment of grain only in the second period e F = ( 0 , 1 ) . The banker prefers to consume today rather than tomorrow: u B ? ( x 1 ? , x 2 ? ) = x 1 ? + 2 1 ? x 2 ? , while the farmer need to consume in both periods and has a utility function u F ? ( x 1 ? , x 2 ? ) = x 1 ? x 2 ? . - Argue that the banker will only loan strictly positive amounts to the farmer if he promises to pay at least twice back as he receives. - Use the fact that the equilibrium is Pareto efficient to derive the price vector. 1 Applied Microeconomics HW3 WS 2022 - Use this price vector to derive the WE allocation. A farmer and a banker live for two periods. The banker has an endowment of grain in each period e B = ( 1 , 1 ) , while the farmer has an endowment of grain only in the second period e F = ( 0 , 1 ) . The banker prefers to consume today rather than tomorrow: u B ? ( x 1 ? , x 2 ? ) = x 1 ? + 2 1 ? x 2 ? , while the farmer need to consume in both periods and has a utility function u F ? ( x 1 ? , x 2 ? ) = x 1 ? x 2 ? . - Argue that the banker will only loan strictly positive amounts to the farmer if he promises to pay at least twice back as he receives. - Use the fact that the equilibrium is Pareto efficient to derive the price vector. 1 Applied Microeconomics HW3 WS 2022 - Use this price vector to derive the WE allocation