The q (1 + e_p) < 0, and hence, ΔE (expenditure) has the opposite sign as Δp (price), if ...................

Option 1: e_p > -1 -> This means demand is inelastic. Here (1 + e_p) > 0, so ΔE and Δp have the same sign.

Option 2: e_p < -1 -> This means demand is elastic. Here (1 + e_p) < 0, so ΔE and Δp have opposite signs.

Option 3: e_p = -1 -> This means unit elastic demand. Here (1 + e_p) = 0, so ΔE = 0 regardless of price change.

Option 4: e_p = 0 -> This means perfectly inelastic demand. Here (1 + e_p) = 1 > 0, so ΔE and Δp have the same sign.

Hence, Option 2: e_p < -1 -> When elasticity is less than -1 (elastic demand), we have (1 + e_p) < 0. Since expenditure change ΔE = q(1 + e_p)Δp and q is always positive, a negative (1 + e_p) ensures that ΔE and Δp have opposite signs. This means when price increases, total expenditure decreases (and vice versa), which is characteristic of elastic demand where percentage change in quantity exceeds percentage change in price. -> correct