Question

Joe’s coffee house operates under the production function Q =2√? + ?^2/3, where L is the...

Joe’s coffee house operates under the production function Q =2√? + ?^2/3, where L is the number of worker hours and K is the number of coffee machine hours.

a. Clearly show what type of returns to scale is exhibited.

b. Does labor exhibit diminishing marginal returns when capital is fixed? Explain.

Homework Answers

Answer #1

Q = F(k, L) = 2√? + ?^2/3
Let L = K = 2

then Q = 2√2 + 2^2/3

Q = 2.83 + 1.6

Q = 4.3

Now, we double the input L = K = 4

Q = 2√4 + 4^2/3

Q = 4 + 2.53

Q = 6.53

We saw that as we double the inputs L and K, The output is less than doubled. So, the production function exhibits Diminising Returs to Scale DRS

b)

MPL = dQ/dL = (2 / 2√?) = 1/√?

d(MPL)/dL = - (1/2√?*L)

Hence, the second-order derivative of MPL is negative which tells us that there are diminishing marginal returns to labor.

**if you liked the answer, then please upvote. Would be motivating for me. Thanks.

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