Question

⦁   Suppose the government is considering increased spending on maintaining a national park. You have been hired to evaluate the benefits of this proposal as part of a benefit-cost analysis. Use the travel cost approach to accomplish this goal, based on a $20 admission fee to the park and the following before and after recreational demand functions where Qd is the number of visitors in thousands and P is the admission fee:  
A: Before new-spending policy: P = 72 - 0.04Qd
B: After new-spending policy: P = 90 - 0.04Qd
Part C: Draw a diagram showing the before and after-spending demand functions and compute the estimated benefit of the increased spending on maintaining the park. Please explain Part C and draw a graph.

Answer for first two parts are

Here P = admission fee to the park = $20
Qd = number of visitors ( in 1000)
Also demand function before new spending policy, P = 72-0.04Qd or, 20 = 72-0.04Qd or Qd= 52/0.04=1300. Total cost benefits of the government before new spending policy = P*Qd = 20*1300= $26,000(In 1000). Also demand function after new spending policy is P = 90-0.04Qd or 20=90-0.04Qd or Qd= 70/0.04= 1750, therefore total cost benefit of the government after new spending policy = P*Qd = 20*1750= $35000 ( In 1000), therefore benefit of increased spending = $35000-$26000= $9000 (in 1000) = $90,00,000

Answer 1

From the solved part, we can easily draw a graph of the cost-benefit analysis.

Line D shows the initial spending demand function, whereas the line D' shows the after new policy demand function. The equilibrium is at point E and E' respectively.

The shaded part of the graph shows the benefits of the new policy at the same rate as the admission fee.

The benefit of increased spending = $35000 - $26000 = $9000 (in thousands).