Question

The three isoquants in the graph below refer to production levels of 100 (red), 200 (green), and 255 (blue). As long as the quantity of capital (K) and labor (L) used in the production process lies on the line a, whenever is tripled K is also tripled. q=100 q=200 q=255 LL 3 Does this production function exhibit increasing, decreasing, or constant returns to scale? increasing decreasing constant not enough information 3 If I told you the production function that generated the isoquants is Q-21.5Lºks, is your answer to question 18 dependent on whether Q is a small number or a large number? increasing returns to scale if Q> 255 decreasing returns to scale only if Q> 255 increasing returns to soale only if 100 <Q< 200 O doesn't matter

If I told you the production function that generated the isoquants is Q = 21.5L0.35 K0.5, is your answer to question 18 dependent on whether Q is a small number or a large number?

Answer 1

This sort of a production is going to exhibit decreasing returns to scale and is not dependent on whether Q is a small number or a large number. Thus in short Q doesn't matter.

Explanation : Production function : Q = 21.5*(L^0.35)*(K^0.5)

Now if both L and K are multiplied by the same factor t, then new Q will be : Q(new) = 21.5*((tL)^0.35)*((tK)^0.5)

= t^(0.35+0.5)*21.5*(L^0.35)*(K^0.5)

= (t^0.85)*Q

Thus here we see that when L and K are increased by t factor, Q changes by t^0.85 (which is less than 1), thus showing decreasing returns to scale. No matter what value Q takes the answer will remain the same.