Question

Suppose the production function for widgets is given by: q = kl – 0.8k² – 0.2l², where q represents the annual quantity of widgets produced, k represents annual capital input, and l represents annual labor input. Which of the following statements is correct?

	a.	The widget production function exhibits constant returns to scale.
	b.	The widget production function exhibits increasing returns to scale.
	c.	The widget production function exhibits decreasing returns to scale.
	d.	The widget production function is homogeneous of degree 1.

Answer 1

Solution:

The production function is: q(k, l) = kl - 0.8*k² - 0.2*l²

We can check for returns to scale as follows:

If all the inputs (here k and l) are changed by a common factor, how does the output change.

q' = q (tk, tl) = (tk)(tl) - 0.8*(tk)² - 0.2*(tl)²

q' = t²(kl - 0.8k² - 0.2l²)

q' = t²q

Clearly, changing all inputs by factor t changes output by a factor greater than t (that is t²), this production function exhibits increasing returns to scale.

Thus, correct option is (b).