Question

Production function, Q = 10K^0.2L^0.4M^o.4 + 100L^0.8K^0.2, is subject to:

Answers:	a) increasing returns to scale.
	b) decreasing returns to scale.
	c) constant returns to scale
	d) economies of scope.

If a firm currently employs imperfect substitute inputs a and b such that MPa/Pa < MPb/Pb, the firm can attain optimal input combination by:

Answers:	a) using less a and more b.
	b) using more a and less b.
	c) using only a.
	d) using only b.

Answer 1

1. c) constant returns to scale
(Q = 10K^0.2L^0.4M^o.4 + 100L^0.8K^0.2
Let K = tK, L = tL, and M = tM where t >1
So, Q' = 10(tK)^0.2(tL)^0.4(tM)^o.4 + 100(tL)^0.8(tK)^0.2 = t^0.2+0.4+0.410K^0.2L^0.4M^o.4 + t^0.8+0.2100L^0.8K^0.2 = t10K^0.2L^0.4M^o.4 + t100L^0.8K^0.2 = t(10K^0.2L^0.4M^o.4 + 100L^0.8K^0.2) = tQ
So, there are constant returns to scale as power of t is 1.)

2. a) using less a and more b.
(By using more b, MPb will decrease and by using less a, MPa will increase so MPa/Pa will increase and MPb/Pb will decrease until they become equal and optimal combination is reached.)