Neco 2023 Economics Question 40

Practice objective / multiple choice question 40 from the 2023 Neco Economics examination.

Neco 2023 Economics Objective / Multiple Choice Hard Difficulty
Question 40 NECO • 2023 • ECONOMICS • objective

A farm produces output according to the Cobb‑Douglas function \( Q = L^{0.5}K^{0.5} \), where \( L \) is labour (cost \( w = \)\u20A620 per unit) and \( K \) is capital (cost \( r = \)\u20A650 per unit). The farmer wishes to produce exactly \( Q = 100 \) units at minimum cost. Determine the cost‑minimising quantities of labour and capital and compute the minimum total cost (express the exact answer and a rounded figure).

Answer Options

A. Labour \\( L = 50\\sqrt{5} \\approx 111.8 \\) units; Capital \\( K = 20\\sqrt{5} \\approx 44.7 \\) units; Minimum cost \\( C = 2000\\sqrt{5} \\approx \u20A64472 \\).
B. Labour \\( L = 50\\sqrt{10} \\approx 158.1 \\) units; Capital \\( K = 20\\sqrt{10} \\approx 63.2 \\) units; Minimum cost \\( C = 2100\\sqrt{10} \\approx \u20A66645 \\).
C. Labour \\( L = 40\\sqrt{10} \\approx 126.5 \\) units; Capital \\( K = 25\\sqrt{10} \\approx 79.1 \\) units; Minimum cost \\( C = 1800\\sqrt{10} \\approx \u20A65692 \\).
Correct Answer D. Labour \( L = 50\sqrt{10} \approx 158.1 \) units; Capital \( K = 20\sqrt{10} \approx 63.2 \) units; Minimum cost \( C = 2000\sqrt{10} \approx \u20A66325 \).
Correct Answer
D
Correct Option:
Labour \( L = 50\sqrt{10} \approx 158.1 \) units; Capital \( K = 20\sqrt{10} \approx 63.2 \) units; Minimum cost \( C = 2000\sqrt{10} \approx \u20A66325 \).

About This Question

This is Neco 2023 Economics Question 40. It is one of the objective questions from the 2023 Neco Economics examination.

Difficulty level: Hard .

View More Neco 2023 Economics Questions More Neco Practice Questions Back to Questions

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Chat with Support