Need solution within 12 hours
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.
3. Average Cost Pricing: Since going broke is not a good way to serve
a good cause, suppose the nonprofit board requires the operation to
break even. What is the solution pair (Pw, Qw) at the Pw = ATC ?
Dw/Qw solution? What is NSB at that solution? DWL? (Work this like
you worked earlier solutions at Pw = ATC ? Dw/Qw.)
4. What price Pm will the park charge Martha? What price Pg will it
charge George? How much Qw will each use? What are the individual
price elasticities for Martha and George? Do the prices follow the
inverse elasticity rule? Will both pay more than MC? Why? (Hint: A
lot to do with the inverse elasticity rule.) What share of fixed costs
will the donors cover, will Martha pay, and George pay? Is cross
subsidization occurring? What is your evidence? For the Ramsey
solution NSB will be less than with first best pricing, but will NSB
under Ramsey pricing exceed NSB under average cost pricing? How much?
Why? (Hint: The reason has to do with price elasticity.) Find DWL. IS
DWL under Ramsey pricing less than with P = ATC ? Dw/Qw? |
