Question

Paco's Painting Service does interior and exterior house painting. They have a production function that uses three factors: brushes (?B), paint (?P), and labor (?L). In the short run, Paco's has already committed to orders of brushes and paint, but can adjust the number of hours of labor they use from week to week. Therefore, their short-run production function depends only on labor and is given by ?(?)= √L/2. which implies that Paco's marginal product of labor is ???=1/4√L.   

Suppose that Paco charges $4600 for a paint job and that the current wage he must pay his workers is $30 per hour.

How many worker hours should Paco use to maximize his profit? _________

How many painting jobs will Paco complete using this number of worker hours? ____19.17______

In addition to hiring workers, Paco spends $150 on brushes (50 brushes at $3 each) and $3000 on paint (100 gallons at $30 per gallon). What is Paco's profit using these values for his three factors (labor, brushes, and paint)? __________

Part 2

Now suppose that Paco is able to negotiate a lower price for paint and can buy the 100 gallons he needs for $27 instead of $30. Due to this cost savings, Paco's profit-maximizing choice of labor will stay the same and he will use ___________ worker hours.

He will complete ______19.17_____ projects (houses painted) and earn a profit of ___________

Answer 1