A firm has a production function f(x, y) = 1.80(x^0.80 + y^0.80)³ whenever x 0 and y 0. When the amounts of both inputs are positive, this firm has A) increasing returns to scale if x + y 1 and decreasing returns to scale otherwise. B) decreasing returns to scale. C) constant returns to scale. D) increasing returns to scale. E) increasing returns to scale if output is less than 1 and decreasing returns to scale if output is greater than 1.

Question

A firm has a production function f(x, y) = 1.80(x^0.80 + y^0.80)³ whenever x > 0 and y > 0. When the amounts of both inputs are positive, this firm has A) increasing returns to scale if x + y > 1 and decreasing returns to scale otherwise. B) decreasing returns to scale. C) constant returns to scale. D) increasing returns to scale. E) increasing returns to scale if output is less than 1 and decreasing returns to scale if output is greater than 1.

Quizplus · Accepted Answer

The production function exhibits increasing returns to scale because when both inputs are scaled by a factor, the output increases by a greater factor due to the exponent 3 applied to the sum of the inputs raised to 0.80.

A Firm Has a Production Function F(x, Y) = 1