Analyze the case of an inferior good when its price decreases. Use economic reasons to explain why the income and substitution effects work in opposite directions and predict the overall outcome for consumer demand.

The total effect is the change in consumption from the initial optimal point to the final optimal point.

$$\text{Total Effect (TE)} = R_2 - R_1$$ $$\text{TE} = 30 \text{ kg} - 20 \text{ kg}$$ $$\text{TE} = \boxed{\text{10 kg}}$$

The substitution effect is the change in consumption due to the change in relative prices, holding utility constant (from initial to compensated demand stage).

$$\text{Substitution Effect (SE)} = R_{SE} - R_1$$ $$\text{SE} = 25 \text{ kg} - 20 \text{ kg}$$ $$\text{SE} = \boxed{\text{5 kg}}$$

The income effect is the change in consumption due to the change in purchasing power, holding relative prices constant (from compensated demand stage to final optimal point).

$$\text{Income Effect (IE)} = R_2 - R_{SE}$$ $$\text{IE} = 30 \text{ kg} - 25 \text{ kg}$$ $$\text{IE} = \boxed{\text{5 kg}}$$

The total effect is the sum of the substitution effect and the income effect.

$$\text{Total Effect} = \text{Substitution Effect} + \text{Income Effect}$$ $$10 \text{ kg} = 5 \text{ kg} + 5 \text{ kg}$$ $$10 \text{ kg} = 10 \text{ kg}$$

The calculations are verified.