A recent report by IBIS (available on Bb) on the state of the Pet Industry in the United States was recently published (May 2015). It reveals a thriving industry with an average annual rate of growth of 3.7% to $17.5 billion in the five years to 2015. Spending on pet services increased from $48.4 billion in 2010 to $58.5 billion in 2014. Profits increased by $1.4 billion (2010-14) and wages by $2.4 billion. There are an estimated number of pet-based businesses of 13,556.
In Moorpark, Ca, there are two major providers of pet grooming and care services:
a) Alcazar Hounds (AH), operated by Dr. Claudia, DVM
b) Peruvian Pampered Paws (PPP), operated by Dr. Sandra, DVM
AH and PPP are price takers and provide a basic Groom and Check service for $40 per pet (dog). AH has fixed costs of $8,000 less than PPP and average variable cost of $33, which is 10% more than PPP. AH has a break-even output which is 15% less than PPP, and produces 25% less revenue than PPP. AH also makes $12,000 less profits than PPP.
a) Calculate the cost functions of both firms.
b) Calculate the outputs of both firms.
c) Calculate the profits of both firms.
d) How do AH and PPP compare?
Hints:
This is a two-firm problem. Set out the data in tabular form
Express the relationships summarized in the table by means of 4 equations in 4 unknowns, than reduce them to one equation in one unknown, e.g., BEOPPP, the breakeven output of PPP.
Write out the cost functions in terms of fixed and variable costs, e.g. : CPPP = FCppp + ?Qppp
Write out the profit functions in terms of 4 equations in 4 unknowns and reduce them to one.