Question 18
NECO_MODEL_QUESTIONS_VOL1
•
2021
•
GEOGRAPHY
•
objective
A tile factory has the production function \(Q = 20 L^{0.5} K^{0.5}\), where \(Q\) is the number of tiles produced per week, \(L\) is labour hours per week and \(K\) is the number of capital units (machines). Labour costs ₦150 per hour and each capital unit costs ₦2000 per week (depreciated). Tiles sell for ₦500 each. \n\n(a) Determine the combination of \(L\) and \(K\) that yields at least \(2000\) tiles per week at minimum total cost, and compute that minimum weekly cost. \n\n(b) If the wage rises to ₦250 per hour while the capital cost remains unchanged, should the firm increase its use of labour or capital to maintain minimum cost? Justify.
Answer Options
A.
Minimum cost achieved at \\(L \\approx 400\\) h, \\(K \\approx 25\\) units, cost ≈ ₦112,000. After wage increase, cost‑minimising point shifts to \\(L \\approx 300\\) h, \\(K \\approx 30\\) units, so the firm should use relatively more labour (increase labour, reduce capital).
Correct Answer
B.
Minimum cost achieved at \(L \approx 365\) h, \(K \approx 27\) units, cost ≈ ₦109,500. After wage increase, cost‑minimising point shifts to \(L \approx 283\) h, \(K \approx 35\) units, so the firm should use relatively more capital (increase capital, reduce labour).
C.
Minimum cost achieved at \\(L \\approx 350\\) h, \\(K \\approx 30\\) units, cost ≈ ₦108,000. After wage increase, cost‑minimising point shifts to \\(L \\approx 260\\) h, \\(K \\approx 38\\) units, so the firm should keep the same mix of inputs.
D.
Minimum cost achieved at \\(L \\approx 380\\) h, \\(K \\approx 22\\) units, cost ≈ ₦110,500. After wage increase, cost‑minimising point shifts to \\(L \\approx 320\\) h, \\(K \\approx 28\\) units, so the firm should use relatively more capital (increase capital, reduce labour).
Correct Answer
B
Correct Option:
Minimum cost achieved at \(L \approx 365\) h, \(K \approx 27\) units, cost ≈ ₦109,500. After wage increase, cost‑minimising point shifts to \(L \approx 283\) h, \(K \approx 35\) units, so the firm should use relatively more capital (increase capital, reduce labour).
About This Question
This is
Neco Model Questions Vol1
2021
Geography
Question 18.
It is one of the
objective
questions from the
2021
Neco Model Questions Vol1
Geography
examination.
Difficulty level:
Hard
.