Question

Production function, Q = 10L + 5K^0.9+10L^0.5K^0.4 is subject to:

		a) increasing returns to scale.
		b) decreasing returns to scale.
		c) constant returns to scale.
		d) economies of scope.
		e) diseconomies of scope.

Answer 1

b) decreasing returns to scale.

Q = 10L + 5K^0.9 + 10L^0.5K^0.4
Let L = tL and K = tK where t > 1
So, Q' = 10(tL) + 5(tK)^0.9 + 10(tL)^0.5(tK)^0.4
So, Q' = 10(tL) + 5t^0.9K^0.9 + 10t^0.5L^0.5t^0.4K^0.4
So, Q' = t(10L) + t^0.9(5K^0.9) + t^0.5+0.4(10L^0.5K^0.4)
So, Q' = t(10L) + t^0.9(5K^0.9) + t^0.9(10L^0.5K^0.4)
So, Q' = t(10L) + t^0.9(5K^0.9 + 10L^0.5K^0.4)

Now, comparing it with original Q, we can see that t^0.9(5K^0.9 + 10L^0.5K^0.4) < 5K^0.9 + 10L^0.5K^0.4
So, there are decreasing returns to scale.