In this case, the rational individual consumer is ideally indifferent between the consumption preferences x and y as implied by the rational preference relation x~y. Now, based on the principle of transitivity, as the preference relation between the consumption choices, x and y is given as x~y implying the consumer is indifferent between the consumption choices x and y, the utility function representing this preference relation must be u(x)=u(y) where u(x) and u(y) denote the utility or satisfaction obtained by the rational consumer from choosing consumption choices x and y respectively. Therefore, the transitivity principle essentially implies that the utility or satisfaction obtained by the consumers from choosing either consumption preference would be equal or identical given or provided that he or she is indifferent about both the choices.

Now, according to the principle of completeness under rational preference relation, given that u(x)=u(y) implying that any rational consumer would obtain the same level or units of utility or satisfaction from choosing both consumption choices x and y and u represents the rational preferences, it consequently implies that x~y or the indifference between the consumption choices x and y by the consumer. In other words, the completeness principle implies that considering that the consumer obtains the same level of utility of satisfaction from choosing either consumption choices, he or she would be therefore, indifference about either choices. Hence, the preference relation would be complete, in this case.

10. Find the marginal-product functions for the CES production function y = AW+ wax,'+ With A >0, r > -1,0