4. (b) There are three people and two goods in an economy. The utility functions and initialbundles are given below:U1 = X11X12U2 = 2x21 + X22U3 = X31X32 + X32W1 = (0,8)W2 = (2, 2)W3 = (8,0)%3DSuppose it is suggested that the three traders move to the allocation x given by:X1 = (1,2), x2 = (8,4), x3 = (1,4).%3D%3Diii) Show that x is not in the core.

Utility function can be defined as the measure for a group of goods and services preferred by…

(b) There are three people and two goods in an economy. The utility functions and initial bundles are given below: U₁ = X11X12 W₁ = (0,8) U₂ = 2x21 + x22 W₂=(2, 2) U3 = X31X32 + x32 W3 = (8,0) Suppose it is suggested that the three traders move to the allocation x given by: x₁ = (1,2), x₂ = (8,4), x3 = (1,4). iii) Show that x is not in the core.