Given that quantity demanded per period of time is a function of price and that the relation is expressed as: Q = 60 - 1/3 P, where Q is quantity demanded a...

Answer Details

The demand relation is \( Q = 60 - \tfrac{1}{3}P \). Substitute each price to find the quantity demanded.

(a)(i) When \( P = 30 \): \( Q = 60 - \tfrac{1}{3}(30) = 60 - 10 = 50 \) units.

(a)(ii) When \( P = 210 \): \( Q = 60 - \tfrac{1}{3}(210) = 60 - 70 = -10 \) units.

(a)(iii) When \( P = 0 \): \( Q = 60 - \tfrac{1}{3}(0) = 60 \) units.

(b) Comment on (a)(ii): A quantity of \( -10 \) is economically meaningless because quantity demanded cannot be negative. It shows that at a price of N210 the price is so high that no quantity is demanded; the demand curve has effectively reached zero before this price. In practice quantity demanded stops at zero, so we take demand as \( 0 \), not \( -10 \).

(c) Now \( P = 180 - 3Q \).

(i) When \( Q = 0 \): \( P = 180 - 3(0) = N180 \).

(ii) When \( Q = 60 \): \( P = 180 - 3(60) = 180 - 180 = N0 \).

(iii) When \( Q = 59 \): \( P = 180 - 3(59) = 180 - 177 = N3 \).

Notice that (c) is simply the first relation rearranged to make \( P \) the subject, so the price and quantity pairs are consistent: high quantity goes with low price and vice versa, confirming the law of demand.