Answer to Question #205157 in Financial Math for Madzanga Mutshinya

Question

5. Parexel Co. produces and sells cell phone batteries. Its production function is 𝒒 = 𝟑𝟐𝟏𝑲𝟎.𝟑𝑳𝟎.𝟑, while its cost function is 𝒄 = 𝟐𝟏𝟎𝑲 + 𝟗𝟎𝑳. Parexel can sell its batteries at 𝒑 = 𝟔𝟑.

a. Does this production function exhibit increasing, decreasing or constant returns to scale? Explain briefly.

Answer 1

Q=321K0.3L0.3

Let's take the inputs to be:

L=1

K=1

The production function will be:

Q=321(1)0.3(1)0.3

=28.89

Let's now double the inputs;

that is K=2

L=2

The new production function will be;

Q=321(2)0.3(2)0.3

=115.56

We have increasing returns to scale. This is because on doubling of inputs leads to more than doubling of output