The production function of a firm is $Q = L^{0.5}K^{0.5}$, where $L$ is labour input and $K$ is capital input. The firm currently employs $K = 36$ units of capital and produces $Q = 100$ units of output.

(a) How much additional labour must be employed to raise output to $Q = 121$ units, assuming capital remains at 36 units?

(b) At the initial input combination, compute the marginal rate of technical substitution (MRTS) of labour for capital (expressed as a decimal, rounded to two decimal places).

Question

The production function of a firm is $Q = L^{0.5}K^{0.5}$, where $L$ is labour input and $K$ is capital input. The firm currently employs $K = 36$ units of capital and produces $Q = 100$ units of output.

(a) How much additional labour must be employed to raise output to $Q = 121$ units, assuming capital remains at 36 units?

(b) At the initial input combination, compute the marginal rate of technical substitution (MRTS) of labour for capital (expressed as a decimal, rounded to two decimal places).

Accepted Answer

Labour must increase by about 129 units; MRTS ≈ 0.13.

Gce Model Questions Vol1 2025 Economics Question 25

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