Q.Write a short note on: Complementaries

Concept — cross-price elasticity

Cross-price elasticity of demand measures how the demand for one good responds to a change in the price of another:

Reading the sign

• Positive $E_c$ ⇒ substitutes (options A, C).
• Negative $E_c$ ⇒ complements (option D).
• Zero $E_c$ ⇒ the goods are unrelated / independent — a change in $P_y$ produces no change in $Q_x$.

Since $E_c = 0$ here, the correct description is 'totally unrelated'. …

Concept

Cross elasticity of demand measures how the demand for one good responds to a change in another good's price. A high positive cross elasticity signals close substitutes. Since a monopolist by definition produces a good with no close substitutes, changes in other products' prices leave its demand almost unchanged:

Thus the value is zero or very small — indeed, a very low cross elasticity is one test of monopoly.

Why the others are wrong

• (A), (B) and (C) all imply meaningful substitutability, which contradicts the definition of monopoly. …

Step 1 — Formula

Step 2 — Change in quantity of sugar

Step 3 — Change in price of coffee

Step 4 — Cross elasticity

The negative value shows sugar and coffee are complements (people sweeten coffee with sugar), so cheaper coffee raises sugar demand.

Why the other options are wrong …

Step 1 — Write the formula

Step 2 — Substitute the data

Price of A rises by 20%; demand for B rises by 30%.

Step 3 — Interpret the sign

A positive cross elasticity means the two goods move together — when A's price rises, buyers switch to B — confirming they are substitutes, which matches the question. Magnitude 1.5 (>1) shows a fairly strong substitution response. …

Step 1 — Definition

Cross elasticity of demand measures how the quantity demanded of good X responds to a change in the price of good Y:

Step 2 — Sign for complements

Complementary goods (e.g. car and petrol) are consumed jointly. If $P_Y$ rises, buyers use less of Y and therefore less of X too, so $Q_X$ falls. A price rise causing a quantity fall means numerator and denominator have opposite signs → $E_{XY} < 0$ (negative).

Step 3 — Reject the others

• (A) Infinite / (B) Positive and large — describe substitutes (positive cross elasticity). …

Step 1 — Percentage change in the quantity of tea

Step 2 — Percentage change in the price of coffee

Step 3 — Apply the cross-elasticity formula

The positive value means the two goods are substitutes — a costlier coffee pushes buyers toward tea.

Step 4 — Why the other options are wrong

• (B) $-1.5$ / (D) $-1$ — a negative sign would mean complements; here demand for tea rises with coffee's price, so the sign is positive. …