Question 20
GCE_MODEL_QUESTIONS_VOL1
•
2018
•
ECONOMICS
•
objective
The market demand for a product is \(P = 120 - 0.5Q\). The firm's total cost function is \(TC = 20Q + 0.02Q^{2} + 100\).
(a) Find the profit‑maximising output level, the corresponding price and the profit.
(b) Compute the price elasticity of demand at the profit‑maximising output and comment on its magnitude in relation to the profit‑maximising rule.
Answer Options
Correct Answer
A.
Profit‑maximising output ≈ 96.2 units, price ≈ £71.92, profit ≈ £4,707.70. The price elasticity at this output is about -1.5 (elastic), satisfying the rule that profit maximisation requires elastic demand.
B.
Profit‑maximising output ≈ 110.5 units, price ≈ £65.30, profit ≈ £5,200.00. The price elasticity at this output is about -2.2 (elastic), satisfying the rule that profit maximisation requires elastic demand.
C.
Profit‑maximising output ≈ 85.0 units, price ≈ £78.00, profit ≈ £3,500.00. The price elasticity at this output is about -0.8 (inelastic), which does not satisfy the rule that profit maximisation requires elastic demand.
D.
Profit‑maximising output ≈ 92.0 units, price ≈ £70.10, profit ≈ £4,200.00. The price elasticity at this output is about -1.0 (unit elastic), which marginally meets the rule for profit maximisation.
Correct Answer
A
Correct Option:
Profit‑maximising output ≈ 96.2 units, price ≈ £71.92, profit ≈ £4,707.70. The price elasticity at this output is about -1.5 (elastic), satisfying the rule that profit maximisation requires elastic demand.
About This Question
This is
Gce Model Questions Vol1
2018
Economics
Question 20.
It is one of the
objective
questions from the
2018
Gce Model Questions Vol1
Economics
examination.
Difficulty level:
Medium
.