Cost-Benefit Analysis
I. Measuring Benefits From Projects That Reduce Private Good Costs Of Production (No distortions.)The inverse demand function for a good is given by: P = 30 -Q/3. Assume that the initial supply curveis given by P = 9 + Q/6. Now due to a government project the supply curve shifts because at each Q the projectreduces costs by $6/unit. Find the old and new price and quantity equilibrium. Next calculate numerical valuesfor gains to consumers, producers, and society. Include a graph of the problem.
II. The town of No Bear lies in a desolate part of Alaska, so desolate that even bears fear to roam. The onlymajor town nearby is Wasilla, but there lies an enormous gorge between the two towns. Currently this gorgecan be crossed only by flying on Shooting Wolf Airlines. This private firm consists of a small Piper Cub planethat can take one passenger at a time.
Shooting Wolf charges $50/trip, and there are 40,000 trips being taken peryear. The costs are $35/trip; that is, average costs equal marginal costs equal $35/crossing.We also know that several years before, the government regulated the firm to charge $35 per trip. Atthat price, there had been 55,000 trips. The government no longer regulates this firm.The government is considering the building of a bridge across this gorge under a project called TheBridge to No Bear.
If the bridge were built, a toll of $22/trip would be charged to cover exactly the marginalcost of a car being driven across the bridge (high maintenance costs due to rumbling cars causing rocks to slide).The bridge and plane trips are seen as equally desirable by customers if the same price were to be charged.
a. Assuming a linear demand curve calculate the dollar benefits created by the bridge for old trip takers.(Provide a diagram of your estimated demand curve.) In addition, calculate the dollar benefits to new triptakers.
b. Assuming a linear demand curve calculate the net benefits to society from building the bridge, where theannualized fixed costs for building the bridge (charged to taxpayers) equals $1,500,000. Remember: show allwork!
Extra Credit:
c. Now assume a constant-elasticity demand curve describes the demand for bridge crossings. (Calculate theelasticity to three decimal places.) Estimate the number of crossings taking place at$22/crossing in this case.No benefit and cost calculation needed.