Anthony Soprano is head of Satriale Pork Producers, Inc., a family-run pork producer with a hog-processing facility in Musconetcong, New Jersey. Each hog processed yields both pork and a render by-product in a fixed 1:1 ratio. Although the by-product is unfit for human consumption, some can be sold to a local pet food company for further processing. Relevant annual demand and cost relations are as follows:
PP= $110 - $0.00005QP,
(Demand for pork)
MRP= ∂TRP/∂QP = $110 - $0.0001QP,
(Marginal revenue from pork)
PB= $10 - $0.0001QB,
(Demand for render by-product)
MRB= ∂TRB/∂QB = $10 - $0.0002QB,
(Marginal revenue from render by-product)
TC= $10,000,000 + $60Q,
MC= ∂TC/∂Q = $60.
Here, P is price in dollars, Q is the number of hogs processed (with an average weight of 100 pounds), and QP and QB are pork and render by-product per hog, respectively; both total and marginal costs are in dollars. Total costs include a risk-adjusted normal return of 15% on a $50 million investment in plant and equipment.
Currently, the city allows the company to dump excess by-product into its sewage treatment facility at no charge, viewing the service as an attractive means of keeping a valued employer in the area. However, the sewage treatment facility is quickly approaching peak capacity and must be expanded at an expected operating cost of $3 million per year. This is an impossible burden on an already strained city budget.
A. Calculate the profit-maximizing price/output combination and optimal total profit level for Satriale.
B. How much by-product will the company dump into the Musconetcong sewage treatment facility at the profit-maximizing activity level?
C. Calculate output and total profits if the city imposes a $35 per unit charge on the amount of by-product Satriale dumps.
D. Calculate output and total profits if the city imposes a fixed $3-million-per-year tax on Satriale to pay for the sewage treatment facility expansion.
E. Will either tax alternative permit Satriale to survive in the long run? In your opinion, what should the city of Musconetcong do about its sewage treatment problem?