Question

Does the production function of table 7-1 below show constant, increasing, or decreasing return to scale if the firm increases the quantity of labor and capital used from (a) 2L and 2K to 4L and 4K?

(b) 2L and 4K to 3L and 6K?

TABLE 7-1 Production Function with Two Inputs 36 40 40 36 30 14 40 42 40 36 30 14 39 40 36 Output (0) 10 12 12 10 24 28 28 23 18 31 36 36 Capital (k) 6 28 12 28 12 し→ Labor (L)

Answer 1

a)

When capital and labor were 2K, 2L respectively,

output produced = 18

When capital and labor were 4K, 4L respectively,

output produced = 40

Hence when factors of production (K and L) doubled, output increases by more than double

=> thus production function shows increasing returns to scale.

b)

When capital and labor were 4K, 2L respectively,

output produced = 28

When capital and labor were 6K, 3L respectively,

output produced = 31

Hence when factors of production (K and L) increases 1.5 times, output decreases by less than 1.5 times (31/28 = 1.11 times to be precise)

=> thus production function shows decreasing returns to scale.