Question

In: Economics

Suppose the production function for high-quality bourbon is given by Q = (K · L)1/2 where...

Suppose the production function for high-quality bourbon is given by Q = (K · L)^1/2 where Q is the output of bourbon per week and L is labor hours per week. Assume that in the short run, K is fixed at 144. Then, the short-run production function becomes:

Q = 12L^(1/2)

(A) If the rental rate of capital is $12 and wages are $9 per hour, obtain the short-run total costs function.

(B) If the SMC for this firm is SMC = 0.125q, what would the production level of the firm be at a price of $20 per bottle? (Hint: assume this firm is a price taker).

(C) At the output level you obtained above, how many labors per hour will be hired per week?

Expert Solution

(A) Given short run production function :

Rental rate of capital R=$12

Wages W=$9

Capital K is fixed at 144

Labor is represented by L

imply

Short run Total Cost=

Inserting , W=$9 , R=$12 and K=144 in imply :

So, Short run Total Cost is .

(B) Short run marginal cost given in question is , price P= $12

A price taker firm will produce such that this imply:

Production level of the firm at price $12 per bottle is 96 units.

(C) From part (A) of the question . At production level of 96 units -

At production level of 96 units, 64 labor hours per week will be hired.

Rahul Sunny answered 2 years ago

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