Question

Which function represents a production function with constant returns to scale? (Select each correct answer.)

q=sqrt(k+l)

q=sqrt(k) +sqrt(l)

q=sqrt(k*l)

q=5k + l

q=5k +5l

q=min{k,l)

Answer 1

To check constant returns to scale, we will increase the scale by a constant proportion m (i.e. multiply both factors of production by m), and then see the impact on output q.

Let's say q' is the new output.

So if q' > mq --> increasing returns

If q' = mq --> constant returns

If q' < mq --> decreasing returns

1. q = √(k+l)

q' = √(mk+ml) = m√(k+l) = mq --> constant returns

2. q = √(k) + √(l)

q' = √(mk) + √(ml) = √m (√k + √l) = √m(q) < mq --> decreasing returns

3. q = √(kl)

q' = √((mk)(ml)) = m√(kl) = mq --> constant returns

4. q = 5k + l

q' = 5(mk) + ml = m (5k + l) = mq --> constant returns

5. q = 5k + 5l

q' = 5mk + 5ml = m(5k + 5l) = mq --> constant returns

6. q = min{k,l)

q' = min{mk, ml) = m min{k,l} = mq --> constant returns