Question

Suppose soft drink production at bottling plant is described by the production function: ? =??^.? where...

Suppose soft drink production at bottling plant is described by the production function:

? =??^.?

where y is the number of cases of soft drinks produced and x is the number of hours of labor hired. We also assume the wage for labor is r, price for soft drink is p and fixed costs is $1,000.

k. Find the optimal input of x that maximizes the profit. (Hint: this is the input-side

optimization, you should derive optimal x as a function of r and p)

l. Based on your answer in question (k), if labor cost $20/hour and the price of soft drinks is $10/case, that is r = 20 and p = 10, how many hours of labor should be employed? How many cases of soft drinks are produced?

m. Find the optimal output of y that maximizes the profit. (Hint: this is the output-side optimization, you should derive optimal y as a function of r and p)

n. Based on your answer in question (m), if labor cost $20/hour and the price of soft drinks is $10/case, that is r = 20 and p = 10, how many cases of soft drinks are produced? How many hours of labor should be employed? [Hint: if you have answered questions (k) and (m) correctly, answers in questions (i) and (n) should be the same]

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