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Worked Examples · Example 6

Q.A firm uses 10 workers and 5 machines to produce 100 units of output. It then doubles both inputs to 20 workers and 10 machines and finds output rises to 250 units. Next it doubles them again to 40 workers and 20 machines, and output rises to 500 units. State the type of returns to scale at each step, with reasons.

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Given: three input-output combinations, with all inputs doubled between successive steps.

Step 1 — First doubling (10 workers/5 machines → 20 workers/10 machines): inputs are multiplied by 2; output goes from 100 to 250, a multiple of 250/100=2.5250/100 = 2.5. Since output rose by 150% while inputs rose by 100%, output rose more than proportionately. This is Increasing Returns to Scale, typically caused by economies of scale — greater specialisation and division of labour and fuller use of indivisible, more efficient machinery as the operation grows.

Step 2 — Second doubling (20 workers/10 machines → 40 workers/20 machines): inputs are again multiplied by 2; output goes from 250 to 500, a multiple of 500/250=2500/250 = 2. Output rose exactly in proportion to inputs. This is Constant Returns to Scale, occurring when the initial economies of scale have been broadly exhausted but serious managerial diseconomies have not yet set in. …

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