Question

1. Manitoba is considering preserving a very scenic river. The community has 100 people each of whom has a demand given by q=10-0.1p where q is the number of miles preserved and p is the price per mile she/he is willing to pay for q miles of preserved river. The marginal cost of preserving the river is $500 per mile.
   1. Draw a full-labelled diagram to depict the problem described above.
   2. How many miles would be preserved in an efficient allocation? Explain your reasoning.
   3. Calculate the net benefit of this preservation project? Show this in you diagram.

Answer 1

a, b).

Consider the given problem here are 100 people each of whom having demand curve, “Q=10-0.1*P”, => “P=100-10*Q”. Now, the aggregate demand curve is given by the vertical summation of the individual demand curve (because, here the good is jointly consume able, => people will not disclose their true willingness to pay for the good).

=> P = 100*(100-10*Q) = 10,000 - 1,000*Q, => P = 10,000 - 1,000*Q. Now, the “MC=$500” per miles. So, at the equilibrium “MC=P”, => 10,000 - 1,000*Q = 500, => 9,500 = 1,000*Q, => Q = 9.5 miles. So, the efficient allocation is given by “Q=9.5 miles”.

Consider the following fig.

10,000 A1 MC= 500 АЗ A2 9.5 10

So, here “A1A2” be the aggregate demand curve and “MC” be the marginal cost curve, => “E” be the equilibrium point the intersection between “demand” and “supply” functions. So, here number of miles preserve is “9.5”.

c).

Now, in the above fig the net benefit is given by the area “A1EA3”.

=> A1EA3 = 0.5*9.5*(10,000-500) = $45,125.