The table below shows the various incomes and demand for different commodities. a) Calculate the income elasticity between i) A and B ii) C and D iii) E and F. b) What kind of goods is between i) A and B ii) C and D?

$Y_1 = 10,000$, $Q_1 = 60$  
$Y_2 = 18,000$, $Q_2 = 48$

$$
\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2} = \frac{48 - 60}{(48 + 60)/2} = \frac{-12}{108/2} = \frac{-12}{54} = -\frac{2}{9}
$$

$$
\frac{Y_2 - Y_1}{(Y_2 + Y_1)/2} = \frac{18,000 - 10,000}{(18,000 + 10,000)/2} = \frac{8,000}{28,000/2} = \frac{8,000}{14,000} = \frac{8}{14} = \frac{4}{7}
$$

$$
YED_{AB} = \frac{-2/9}{4/7} = -\frac{2}{9} \times \frac{7}{4} = -\frac{14}{36} = -\frac{7}{18}
$$
$$
YED_{AB} \approx -0.3889
$$
The income elasticity between A and B is $\boxed{-\frac{7}{18}}$.

$Y_1 = 20,000$, $Q_1 = 80$  
$Y_2 = 22,000$, $Q_2 = 100$

$$
\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2} = \frac{100 - 80}{(100 + 80)/2} = \frac{20}{180/2} = \frac{20}{90} = \frac{2}{9}
$$

$$
\frac{Y_2 - Y_1}{(Y_2 + Y_1)/2} = \frac{22,000 - 20,000}{(22,000 + 20,000)/2} = \frac{2,000}{42,000/2} = \frac{2,000}{21,000} = \frac{2}{21}
$$

$$
YED_{CD} = \frac{2/9}{2/21} = \frac{2}{9} \times \frac{21}{2} = \frac{21}{9} = \frac{7}{3}
$$
$$
YED_{CD} \approx 2.3333
$$
The income elasticity between C and D is $\boxed{\frac{7}{3}}$.

$Y_1 = 22,500$, $Q_1 = 120$  
$Y_2 = 25,500$, $Q_2 = 126$

$$
\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2} = \frac{126 - 120}{(126 + 120)/2} = \frac{6}{246/2} = \frac{6}{123}
$$

$$
\frac{Y_2 - Y_1}{(Y_2 + Y_1)/2} = \frac{25,500 - 22,500}{(25,500 + 22,500)/2} = \frac{3,000}{48,000/2} = \frac{3,000}{24,000} = \frac{1}{8}
$$

$$
YED_{EF} = \frac{6/123}{1/8} = \frac{6}{123} \times 8 = \frac{48}{123} = \frac{16}{41}
$$
$$
YED_{EF} \approx 0.3902
$$
The income elasticity between E and F is $\boxed{\frac{16}{41}}$.