Goods with Public and Private Characteristics 

Goal: Focus on the differences between private and public goods, in
particular on the vertical summation of individual demands (MWTP) for
public goods and the horizontal summation of individual demands for
private goods.

Background Information for the Problem Set: Wilderness camping and
hiking is an excludable good from the point of view of the supplier of
wilderness (usually a national park).

Suppose that Martha and George like hiking and camping and have the
income to enjoy the wilderness first hand.  Let Pw = the price a
client is willing to pay along a demand curve for hiking and camping
in the wilderness.  Qw is the wilderness area (measured in square
miles) hiked over and camped in by an individual.  Ignore the prices
of other, complementary goods associated with a camping and hiking
trip.  Suppose that Martha and George are not acquainted, that each is
quite independent, and that neither wants to see other hikers and
campers during their wilderness experience, i.e., they don?t want to
consume the wilderness collectively.  Because a personal demand curve
represents Martha?s (George?s) marginal benefit (MB) curve, it also is
Martha?s (George?s) marginal willingness to pay (MWTP) curve.  The
individuals have different preferences and, hence, different demand
curves:

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

Suppose the wilderness supplier spends $40 per square mile on park
maintenance, park rangers, and acquisition costs.  That is, MC = $40. 
Costs include the cost of capital (land in this case).  Suppose that
fixed costs (overhead) are $70.

3a. There are three interesting solutions to explore.  We start with
the price, quantity solutions and advance to benefits, costs, and net
benefits in later questions.  To begin, what are the equilibrium price
Pw and the equilibrium quantity Qw if the supplier 1) maximizes
profits (MR=MC), 2) breaks even (average cost pricing, Pw = ATC), and
3) maximizes net social benefits (Pw = MC)?

3b. How can we tell whether it is a socially efficient use of
resources for this wilderness park to exist?  What is the socially
efficient scale (size)?

4a. At each of the prices above, how many square miles of wilderness
will Martha want to hike and camp on?  How much is Martha?s total
benefit from wilderness at each price?  How much is her total
expenditure on wilderness at each?  How much consumer surplus does
Martha enjoy at each price?

4b. Repeat 4a for George. 

5a. How much is total consumer benefit, i.e., the area under the
combined demand curves from 0 to the quantity associated with each of
the three solution prices

5b. How much is total consumer expenditure at each solution? 

5c. How much is total consumer surplus at each solution? 

5d. How much revenue does the wilderness supplier collect at each solution? 

5e. How much total variable cost (TVC) does the supplier incur at each
solution? How much total cost (TC)?

5f. What are the supplier?s profits at each solution? 

5g. How much net benefit does the community gain from the wilderness
hiking and camping at each solution?