A farm uses labour $L$ (hours) and capital $K$ (units) to produce output according to the Cobb‑Douglas function $Q = 10 L^{0.5} K^{0.5}$. The market price of the crop is $\text{₦}20$ per unit. The wage rate is $\text{₦}5$ per labour hour and the rental rate of capital is $\text{₦}8$ per unit.

(a) To achieve a target output of $Q = 200$ units, find the cost‑minimising quantities of labour and capital.

(b) Compute the total cost of producing 200 units and the profit at the given output price.

(c) If a per‑unit output tax of $\text{₦}4$ is introduced, recalculate the profit.

(d) What is the percentage change in profit caused by the tax? Give the percentage to one decimal place.

Question

A farm uses labour $L$ (hours) and capital $K$ (units) to produce output according to the Cobb‑Douglas function $Q = 10 L^{0.5} K^{0.5}$. The market price of the crop is $\text{₦}20$ per unit. The wage rate is $\text{₦}5$ per labour hour and the rental rate of capital is $\text{₦}8$ per unit.

(a) To achieve a target output of $Q = 200$ units, find the cost‑minimising quantities of labour and capital.

(b) Compute the total cost of producing 200 units and the profit at the given output price.

(c) If a per‑unit output tax of $\text{₦}4$ is introduced, recalculate the profit.

(d) What is the percentage change in profit caused by the tax? Give the percentage to one decimal place.

Accepted Answer

Labour ≈ 25.30 units, Capital ≈ 15.81 units; Total cost ≈ ₦253; Profit without tax ≈ ₦3,747; Profit with tax ≈ ₦2,947; Profit falls by 21.4%

Neco Model Questions Vol1 2018 Economics Question 7

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