Consider the production function $q = f(x_1, x_2)$ where the firm produces q amout of output $x_1$ amount of factor 1 and $x_2$ amount of factor 2. The firm decides to increase the employment level of both the factors $t (t>1)$. Identify the equation for decreasing returns to scale from the following:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $f (tx_1, tx_2) < t.f (x_1, x_2)$
In the production function q = f(x₁, x₂), if the firm increases all inputs by a factor t (where t > 1), then:
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If f(tx₁, tx₂) = t·f(x₁, x₂) → Constant Returns to Scale
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If f(tx₁, tx₂) > t·f(x₁, x₂) → Increasing Returns to Scale
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If f(tx₁, tx₂) < t·f(x₁, x₂) → Decreasing Returns to Scale
So, under decreasing returns to scale, output increases less than proportionately to the increase in inputs.