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Ramsey Pricing for Nonprofit Firms 

Goal: To understand price discrimination, cross subsidization, and
Ramsey?s pricing rule as they apply to Non Profit organizations. 
There are many applications of Ramsey?s rule.  In public finance,
Ramsey?s rule implies that it is efficient to levy higher taxes on
goods that are less price elastic because the taxing a price inelastic
good produces little DWL.  In our case we want to discover the prices
that will lead to the most efficient resource allocation of the
wilderness park between Martha and George given their separate
demands, given costs, and given the break-even constraint.  Ramsey?s
rule implies that it is efficient to charge the high (low) price to
the customer who is less (more) sensitive to price.

Problem Structure: Suppose there exist two distinct classes of
customers for the nonprofit wilderness park (represented by Martha and
George).  George is a bird watcher and the park has unusual bird
species plus great hiking.  The park sells as a bird watching,
camping, and hiking vacations by reservations in advance.  All major
credit cards are accepted.  Martha just likes to hike, but is not
attracted by the unusual birds.  She is more price sensitive than
George.  The niche markets are effectively segmented (arbitrage is
difficult or impossible).

Private Benefits: Martha?s demand curve for Wilderness is Pw = 80 ? 10*Qw. 
George?s demand curve for Wilderness is Pw = 100 ? 20*Qw. 

Private Costs:  Suppose the wilderness supplier spends $25 per square
mile on park maintenance, park rangers, and acquisition costs.  That
is MC = $25.  Costs include in the cost of capital (land in this
case).  Suppose that fixed costs (overhead) are $175.

External Benefits:  Mary?s external benefit demand curve for
wilderness is Dw = 17, Qw less than or equal to 13.  Greg?s external
benefit demand curve for wilderness is Dw = 25, Qw less than or equal
to 13.

1a. Existence: Is it efficient for the wilderness park to exist?  That
is, is TB>TC?  Does the horizontally summed demand curve for Martha
and George lie everywhere above or below the ATC curve?  Can the
wilderness park survive ? exist -- as a for profit park?

1b. Suppose Mary and Greg donate $42 in aggregate.  Plot the ATC curve
net of average donations (ATC ? Dw/Qw). Does the horizontally summed
demand curve for Martha and George lie everywhere below the ATC ?
Dw/Qw? Can the wilderness survive as a nonprofit that charges user
fees and collects donations?

2. First Best Pricing: The rule that maximizes NSB is marginal cost
pricing: P = MC.  This is sometimes called the ?first best pricing?
rule.  What is the solution pair (Pw,Qw) using first best pricing? 
What is NSB at that solution? What is deadweight loss (DWL) at the
first best solution? How much money does the nonprofit lose even after
donation revenue? (When P = MC < ATC, marginal cost pricing results in
loses.) Can the nonprofit survive with first best, marginal cost
pricing? (Work like this you worked earlier solutions at Pw = MC)