John Johnson and Kevin Murphy own and operate a van conversion operation for the major auto companies. Johnson and Murphy 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 Johnson and Murphy products:
Q=1,000-0.1 P
where Q is the number of van conversions (output) and P is price.
A. Calculate Johnson and Murphy’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 Johnson and Murphy’s output to 300 conversions during the coming year.
C. Calculate and interpret ?, the Lagrangian multiplier.
D. Calculate the value of Johnson and Murphy of having the parts shortage eliminated.
