Question

The Upper Sangamon River Conservancy recently commissioned a study to estimate the demand for preservation of a stretch of the Sangamon River. The authors of the study estimated a demand curve for preservation given by the equation P(Q) = 4000 - 75Q, where P is the price and Q is the quantity of river miles preserved. The cost of preservation (obtaining easements or otherwise acquiring property rights to riparian segments) is given by the supply curve S = 500 + 25Q.

What is the marginal willingness to pay for the 20th mile of river preserved?

What is the total willingness to pay to preserve 20 miles of the Sangamon River?

What is the marginal cost of preserving the 20th mile of river?

What is the total cost of preserving 20 miles of the Sangamon River?

What is the largest number of river miles that can be preserved without violating economic principles given the Demand and Supply curves? Explain/Justify your answer using numbers.

Answer 1

Solution:

(a) marginal willingness to pay 20th mile of river preserved =  willing cost for 20th mile - willing cost for 19th mile

= [4000 - 75 (20)] - [4000 - 75 (19)] = -75

(b) Total willingness to pay 20th mile of river preserved= 4000 - 75(20) = 2500

(c) marginal cost of preserving the 20th mile of river = [500 + 25(20)] - [500 + 25(19)] = 25

(d) Total cost of preserving the 20th mile of river = [500 + 25(20)] = 1000

(e) largest number of river miles that can be preserved without violating economic principles is where Demand and supply are equal:

Demand = Supply

4000 - 75Q = 500 + 25Q

-100 Q = -3500

Q = 3500/100 = 35

Therefore; 35 river miles that can be preserved

that makes total cost and total revenue for 1375.