Question

A business whose only inputs are labour and capital expands its employment level in the long run from 12 to 18 workers and its capital from 4 to 6 machines. Write out dollars and cents, e.g. $1.00 or $0.10 for any monetary amounts entered as a solution below.

Assuming that the daily wage of $100 and the daily upkeep (including wear and tear) per machine of $20 remain constant in the long run, identify the relevant returns to scale and the change in long-run average cost if daily output were to expand in each of the following possible ways.

a. If daily output expands from 60 to 120 units then in this output range the business is experiencing (Click to select)constantdecreasingincreasing returns to scale while long-run average cost is (Click to select)fallingrisingstaying the same. At 60 units long-run average cost is $ and at 120 units it is $.

b. If daily output expands from 60 to 90 units then in this output range the business is experiencing (Click to select)constantdecreasingincreasing returns to scale while long-run average cost is (Click to select)fallingrisingstaying the same. At 60 units long-run average cost is $ and at 90 units it is $.

c. If daily output expands from 60 to 80 units then in this output range the business is experiencing (Click to select)constantdecreasingincreasing returns to scale while long-run average cost is (Click to select)fallingrisingstaying the same. At 60 units long-run average cost is $ and at 80 units it is $.

Answer 1

Solution:

Long run average cost = long run total cost/output level

So, initially long run average cost = (100*12 + 20*4)/q = 1280/q

While on expansion, it becomes = (100*18 + 20*6)/q = 1920/q

Returns to scale indicates how the output changes when inputs are changed by same factor. If the output increases by a factor greater than the common factor of inputs, it exhibits increasing returns to scale. If output changes by same factor as inputs, it exhibits constant returns to scale, and finally if output changes by a smaller factor, production exhibits decreasing returns to scale.

Here, as the workers increase from 12 to 18, factor increase = 18/12 = 1.5, and capital increases from 4 to 6, so factor increase in capital = 6/4 = 1.5 (so, both inputs change by same factor of 1.5). We have to compare this with factor by which the output changes).

a) Daily output expansion from 60 to 120 units, so factor increase in output = 120/60 = 2, which is greater than 1.5. So here, increasing returns to scale is exhibited.

Long run average cost at 60 units = 1280/60 = $21.33

Long run average cost at 120 units = 1920/120 = $16

So, long run average cost is falling.

b) Daily output expansion from 60 to 90 units, so factor increase in output = 90/60 = 1.5. So here, constant returns to scale is exhibited.

Long run average cost at 60 units = $21.33 (as calculated above)

Long run average cost at 90 units = 1920/90 = $21.33

So, long run average cost has stayed the same.

c) Daily output expansion from 60 to 80 units, so factor increase in output = 80/60 = 1.33, which is lower than 1.5. So here, decreasing returns to scale is exhibited.

Long run average cost at 60 units = $21.33 (as calculated in part (a))

Long run average cost at 80 units = 1920/80 = $24

So, long run average cost is rising.