JAMB 2019 Economics · Question 9

Given two substitute goods (X and Y) with demand and supply function; Qd = 7p - 12 Qs = 4p + 9 Find the magnitude of excess demand when p = ₦18

Options

A.303
B.30
C.114
D.33

Answer: D. 33

Explanation written with AI and checked against the answer key

Analyze the question: We are given a demand function and a supply function, and we need the excess demand at a price of ₦18. Excess demand is the amount by which quantity demanded exceeds quantity supplied at a given price. Concept: Excess demand = Qd − Qs (when Qd > Qs) Solution: Step 1: Find Qd at p = 18 Qd = 7p − 12 = 7(18) − 12 = 126 − 12 = 114 Step 2: Find Qs at p = 18 Qs = 4p + 9 = 4(18) + 9 = 72 + 9 = 81 Step 3: Find the excess demand Excess demand = Qd − Qs = 114 − 81 = 33 Check: The equilibrium price is where 7p − 12 = 4p + 9, so 3p = 21 and p = 7. Since ₦18 is above the equilibrium price of ₦7, you might expect excess supply, but with these functions Qd (114) is greater than Qs (81) at p = 18, because the demand curve as given is steeper (slope 7) than the supply curve (slope 4). The question's functions are unusual (demand rises with price), but the question asks only for the magnitude of the gap, which is 33. Answer: The magnitude of excess demand is 33, which is option D. Tip: Always substitute the price into both functions separately, then subtract. Option C (114) is the trap: it is only the quantity demanded, not the excess.

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