Microeconomics Quiz W7: Technology, Production and Costs

Question 1

Describe & explain whether the following function exhibits constant returns to scale: 𝑓(𝑥1, 𝑥2) = 𝑥1^𝑎 𝑥2^𝑏

Answer 1

It’s uncertain to say:
- Multiply all inputs by t:
f(tx1, tx2) = (tx1)^alpha(tx2)^beta=t^(a+b) x1^alphax2^beta = t^a+b f(x1,x2)
- In other words, increasing all inputs by a factor of t increases output by a factor of t^a+b.
- We only have constant returns to scale when a+b = 1 so t^a+b = t and f(tx1,tx2) = tf(x1,x2)
- We have increasing (decreasing) returns for scale when a+b>(<)1