Managerial Economics 12th Edition by Mark Hirschey

Exercise 1

Lagrangian Multipliers. Amos Jones and Andrew Brown own and operate Amos Andy, Inc., a Minneapolis-based installer of conversion packages for vans manufactured by the major auto companies. Amos Andy has fixed capital and labor expenses of $1.2 million per year, and variable materials expenses average $2,000 per van conversion. Recent operating experience suggests the following annual demand relation for Amos Andy products:
Q = 1,000 - 0.1 P
where Q is the number of van conversions (output) and P is price.
A. Calculate Amos Andy's profit-maximizing output, price, and profit levels.
B. Using the Lagrangian multiplier method, calculate profit-maximizing output, price, and profit
levels in light of a parts shortage that limits Amos Andy's output to 300 conversions during
the coming year.
C. Calculate and interpret ?, the Lagrangian multiplier.
D. Calculate the value to Amos Andy of having the parts shortage eliminated.