Question

The (market-level) choke price for admission to Lake Lurleen State Park is $25. The current admission fee is $5, which generates gross revenue of $50,000 for the state park service.To receive full credit show all work. a.Derive the underlying parameters of the market-level demand function for annual visits to Lake Lurleen State Park. b.Obtain an estimate of the elasticity of demand for visits at the current price-quantity combination. Interpret this estimate. c.Obtain an estimate of total willingness to pay for visits at the current admission price. d.Obtain the corresponding estimate of consumer surplus. 2.Consider again the information in question 1, but now assume that the supply of park services’ interacts with demand to determine the admission fee. The current admission fee of $5 per person is an equilibrium outcome. Moreover, supply is such that the quantity supplied at a price of $0 is 0. To receive full credit show all work. a.Derive the underlying parameters of the market-level supply function of park services for annual visits to Lake Lurleen State Park. b.Obtain an estimate of the elasticity of supply for visits at the current price-quantity combination. Interpret this estimate. c.Obtain an estimate of total cost for visits at the current admission price. d.Obtain the corresponding estimate of producer surplus. e.What is the net benefit in this case? 3.Consider again the information provided as well as derived by you in problems 1 and 2. Suppose that the Alabama Department of Conservation and Natural Resources has determined that the fee should instead be set at $10. a.Obtain an estimate of consumer surplus in this case. b.Obtain an estimate of producer surplus. c.Obtain the corresponding estimate of net benefit. How does it compare to the net benefit estimate obtained previously? d.Is there a deadweight loss? If so, what is the amount? e.Are consumersor producers better off than before? Are any worse off? 4.Consider again the information in problem 1. Assume now, however, that you are told that the elasticity of demand at the current admission fee (which still generates gross revenue of $50,000) is-0.5. a.Derive the underlying parameters of the market-level demand function for annual visits to Lake Lurleen State Park. (Note: The choke price will change). b.Obtain an estimate of total willingness to pay for visits at the current admission price. c.Obtain the corresponding estimate of consumer surplus. d.Again, what is the net benefit in this case? e.Compare your answers in parts b and c to those for parts c and d in question 1. What do you conclude about the role of elasticity of demand in WTP? In consumer surplus?

Answer 1

d) As we know that "PS" is the area under the "price" above the supply curve, => here "PS" is "OEP1" which is given by, => OEP1 = (1/2)*5*10,000 = $25,000.

e). Here total revenue is given by, "P1Eq1O". So, the "net benefit" in the case is the difference between "TR" and "TC".

So, Net Benefit = TR - TC = P1Eq1O - OEq1 = OP1E = PS. So, "PS" is the net benefit.