With existing price ratios, shore cottages and non-shore cottages with access 

 to water were held to present levels. Shore cottages which were optimal for 

 resource use were those with smaller lot sizes and shortest shorelines. Private 

 non-shore tenting increased to maximum levels of resource use, while tenting 

 facihties with access to water were held at present levels. Public park facilities 

 for tenting use increased beyond present levels. 



Boating, in terms of 40-horsepower equivalent, was available to shore cottage 

 owners, non-shore cottage owners, tenting with access to water, public park 

 users, and private launching sites. Based on a recommendation by a Michigan 

 study, 10 acres of water surface were required by each boat while in use.' Boats 

 launched at private launching sites entered the basin at minimum levels. In total, 

 programmed boat use exceeded minimum usage by about one and one-half 

 times. 



4.3 Results: Implied Prices for Lake Surface, Shoreline, and Recreation Area 



The lake surface (through water-level management), shoreline, and the rec- 

 reation area are each fixed. In the Unear programming algorithm, fixed resources, 

 which are fully utihzed, receive a shadow price. This shadow or implied price 

 evaluates one unit of the activity, an acre of lake surface for example, at the 

 level of utilization obtained in the analysis. The shadow prices for the month of 

 August were obtained and extended to a three-month season by simple multi- 

 phcation. A capitahzed value was obtained by discounting the seasonal value 

 into perpetuity at three percentage rates of return. The shadow prices discussed 

 in this section where obtained by optimizing net benefits. 



In the northern area, the shadow or implied price for lake surface was $1.40 

 per acre for August. The corresponding value for the central and southern areas 

 was $2.45 (see Table 4.1). Because implied prices are primarily derived from 

 foregone opportunities, these estimates would not be expected to include scenic 

 splendor nor certain amenities. Expanding these data from a one-month base to 

 three-month season and then discounting at 5, 7, and 10 percent, estimated 

 surface-water value ranged from $42 per acre to $147 per acre. Where 7 percent 

 was used as the customary interest rate for individuals, values at this discount 

 rate tended to more closely approximate current values and to be consistent 

 with the assumption of the model. These values were $60 for the northern area 

 and $105 for the rest of the basin. 



For shoreline length measured in linear feet, market prices for comparison 

 are available. Actual asking prices for choice lots on lakes providing the range of 

 water activities are $100 per foot and greater. The imphcit programmed price of 

 $252 per foot, as indicated at the 5 percent discount level, does appear to have 

 been reached for intensively developed properties. Of course the price of shore- 

 line would vary with accessibility and quaHty of beach involved in the shoreline. 

 It is interesting to note that the model did reflect approximate market prices 

 and indicates a tendency toward even higher prices for shoreline. 



The item called "conservation reserve" was land set aside from development 

 by the model in a ratio of 20:1— one unit or recreation area was set aside in 

 conservation reserve for each 20 units used by the private sector. This land 

 would remain undeveloped. The unit is one foot of shoreline by 1,000 feet 



' Michigan Department of Conservation. Michigan Outdoor Recreation Plan. Lansing, 

 Michigan: Michigan Department of Conservation, 1967. 



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