Statement 1: The sum of income of A and B is more than that of C and D taken together. Correct: This statement indicates that $A + B > C + D$, but it doesn't give direct information about individual incomes.

Statement 2: The sum of income of A and C is the same as that of B and D taken together. Correct: This means $A + C = B + D$, but again, it does not provide a direct comparison between the incomes of A, B, C, and D individually.

Statement 3: A earns half as much as the sum of the income of B and D. Correct: This can be written as $A = \frac{1}{2}(B + D)$, implying that A’s income is less than the combined income of B and D.

Conclusion on Highest Income: From Statement 3, we know A's income is relatively smaller compared to B and D combined. The inequality in Statement 1 suggests that A and B together earn more than C and D, which could imply B's income is higher than others when combined with A’s income. By inference, B has the highest income as it is not restricted by the other conditions provided in the statements.

Therefore, the answer is B. B.