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Problem Set #1 PS1 – Page 1 of 5
YOUR NAME: (MAIN WRITER) : _____________________________
NAME(S) OF OTHER STUDENTS IN THE WORK GROUP: (MAXIMUM 2) :
A. (38) Review of Demand/Supply and analysis of allocative efficiency and the analysis of market failure with externalities – this exercise will illustrate that taxes reduce aggregate welfare when there are NO market failures but may improve welfare when there are market failures
Assume that the market for gasoline (a private good…) is described by the following (inverse) demand and supply functions where price is in dollars and quantity in gallons: D: P = 10 - .01 (Qd) S: P = 1+ .02 (Q (^) s)
- (6) On the graph below, draw the supply and demand curves showing the equilibrium price and quantity. Write the correct numerical values here: Pe = _______ Qe = ______
- (2) Assume that the market is perfectly competitive and there are no market failures. What are the marginal social cost and marginal social benefits of producing Qe gallons of gas?
MSC= $_______ MSB= $________
- (5) Calculate the value of total benefits, total costs, and the net benefits when production = Qe (assume for simplicity that there are no fixed costs)
Total Benefits=$__________ Total Costs= $__________ Net Benefits= $_______
- (3) Given the assumptions of question 2, is this allocation of resources (producing Qe) Pareto efficient? Explain briefly.
Suppose now that the government decides to impose a tax of $3 on the sale of each gallon of gas. This in effect increases the marginal cost that suppliers face by $3 for each unit produced. So the supply curve becomes P = 4 + .02 (Q (^) s).
- (4) On the graph above, draw the new supply curve and show the new equilibrium market price and the quantity traded after the imposition of the tax. Write the correct numerical values here:
Pt =____ Qt = _____
- (8) Calculate the following when production is Qt
$P
Q
Problem Set #1 PS1 – Page 2 of 5
Benefits to society = ________ Costs to Society = _________ Net benefits to society = _________
Tax Revenue= ____________
[we assume here that the tax revenue is fully redistributed with no transaction costs]
- (2) Using your answers to questions 3 and 6, what is the dead weight loss caused by the $3 tax? (do not use the graph)? $ _____
- (3) What is the significance of the “dead weight loss” in plain English?
Now, none of us believe that there is no market failure in this market since gasoline is a fossil fuel and burning gas produces carbone dioxide (CO2), which is not so good for our health and has been shown to bethe principal cause of global warming. Neither producers nor consumers have to pay directly for the cost of pollution.
Suppose in addition that new technology allows to clean the air from the damage caused by gasoline consumption and it costs $3 to clean up the amount of damage caused by 1 gallon of gasoline consumed. (since it can be cleaned for $3 per unit, the damage can be avoided at a cost of $3 per unit).
- (2) How would that change your answers to questions 4 (i.e, is Qe the Pareto efficient level of production)? Explain
- (3) How would that change your answers to questions 7 (effect of the tax on the dead weight loss)? Explain.
Problem Set #1 PS1 – Page 4 of 5
C. (44) PUBLIC GOODS
There are important trade-offs involved in granting "Wild and Scenic River Status" to portions of a river. The critical issue is how much of this public good, a free-flowing river, should be protected from further development. As an analyst in the Office of Policy Analysis of the U.S. Department of the Interior (why not?), you are called upon to make a recommendation, based upon the following information. Each year, one thousand people benefit from the River's various services, exclusively for recreational purposes. A contingent valuation survey (we’ll learn about those) carried out by your office has estimated that each beneficiary has the same demand function for river preservation, q = 40 - (0.4)(P) [the inverse demand for each individual is therefore P=100-2.5q] where P is the price that individuals are willing to pay (per year) for the qth mile of river preserved.
Assume (for simplicity, not completeness!) that there are no other benefits to preserving the river… You estimate that the marginal (opportunity) cost of preservation is $20,000 per mile per year.
Question 1 through 4 should be solved WITHOUT the help of a graph (you can then use the graph to check your answers)
- (6) Why can we consider the free flowing river a public good? Make sure you address both aspects of a public good and illustrate how they apply/or not apply/or partially apply in this case.
- (4) What is the market demand for this public good? Recall there are 1000 identical idividuals. Express in algebraic form.
- (4) How many miles of the river would be preserved in an efficient allocation? Show your work. In particular, indicate the condition that you are using to find the efficient allocation)
- (6) You have already given the results of your analysis to the department of interior and they went ahead with the policy. Suppose that you later get an e-mail that a mistake was made in the calculation of demand elasticity. Instead of 0.4, it is 1! This translates into a demand function Q=40 – P [Inverse individual demand is now P=40- q ]. How many miles should you have recommended for the Wild and Scenic River Status? [You need to redo the work! Note that in “real life” the calculations would be much more messy!
Problem Set #1 PS1 – Page 5 of 5
- (8) On a NEAT graph on a separate full page , draw the 2 demand curves, the marginal cost curve, the quantity you chose in question 3 (Q), the quantity you found in question 4 (Q*).
- (8) Calculate the cost of your colleague’s mistake if your previous recommendation was already implemented. [to do this you need to compare the net social benefits of the 2 different allocations using the “correct” demand curve (which is the one calculated in (4)]. Show your work , i.e. I need to see a break down of benefits and cost for each allocation before you compare them tho calculate the dead weight loss.
- (2) shade the area corresponding to the dead weight loss you calculated in 6.
- (6) Do you think it would be possible to have the efficient amount of river preserved without the intervention of the government? In particular, address whether the beneficiaries of the project could get together and collectively pay the cost of preservation. What problems would they encounter?
