In a pure exchange economy with two goods and two consumers, if the consumers have identical Cobb-Douglas utility functions, then in any competitive allocation, they consume all goods in the same proportion only if they have identical endowments. True or False?

If allocation is a competitive equilibrium at price vector and if everybody likes his bundle in allocation better than his bundle in allocation , then the total value of allocation at price vector exceeds the total value of allocation at price vector p. True or False?