WesterholdName:______
Econ 432
HW #3: Efficient Provision of Private and Public Goods due Monday, June 21st. Undergraduates should answer questions 1-3 only. Graduate students should complete the entire assignment.
- Assume we have the following information for two consumers, Bill and Jessica, for office supplies. Show the private market results in an efficient allocation of resources for private goods.
Bill: P=100-5QdJessica: P=75-2.5Qd
- Determine each person’s demand equation (Qd=) and graph each person’s demand curve separately showing the values for the x and y intercepts for Bill and Jessica. Also create the market demand equation and graph the market demand curve showing the x and y intercept values.
- Assume the market supply curve is given as Qs= -20 + 2P. Show this on your market graph above and indicate the value of the minimum selling price.
- Determine the equilibrium price (Pe) and quantity (Qe) and show this on your graph in part A.
- At the market price, determine the amount of office supplies that Bill will purchase (show on graph) and Jessica will purchase (show on graph). Does this match your equilibrium quantity?
- Determine the efficient level of provision of the public good given the following information for Bill and Jessica
Bill: P=20 -0.4QdJessica: P=15-0.5QdQs= -10 + 3P
- Draw individual graphs for Bill, Jessica, and the entire market indicating each person’s willingness to pay (WTP) for quantity Q=15 units and the total market willingness to pay at this quantity. Round all numbers to two decimal places (dollars and cents!)
- Impose the supply curve on the market demand graph, showing the minimum selling price, and determine the efficient level of the public good and the corresponding total contribution necessary.
- Double-check your work by determining Bill’s WTP and Jessica’s WTP for the efficient quantity and make sure their collective WTP covers the necessary total contribution required (remember, your numbers could be off slightly due to rounding).
- By making the public good available at this efficient level, Q*, determine the net benefit accruing to the consumers (consumer surplus) in aggregate (for the entire market and not each person individually).
- Suppose there are two fishermen, Zach and Jacob, who fish along the coast. They would each benefit if lighthouses were built along the coast where they fish. The marginal cost of building each additional lighthouse is $100. The marginal benefit to Zach of each additional lighthouse is 90-Q and the marginal benefit to Jacob is 40-Q where Q is the number of lighthouses.
- Explain why we might not expect to find the efficient number of lighthouses along the coast in the absence of government intervention.
- What is the efficient number of lighthouses? Show your work.
- What would be the net benefits to Zach and Jacob if the efficient number were provided? Show graphically and estimate net benefits in dollars. Show your work.
Graduate Students Only
- Suppose ten people each have the demand Q=20 -4P for streetlights, and 5 people have the demand Q=18-2P for streetlights. The cost of building each streetlight is 3. If it is impossible to purchase a fractional number of streetlights, how many streetlights are socially optimal? Show your work.
Graduate Students Only!
- The town of Springfield has two residents: Homer and Bart. The town currently funds its fire department solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (X) and total firefighters (M) of the form:
U=4log(x) + 2log(M)
The total provision of firefighters hired, M, is the sum of the number hired by each of the two persons: M=Mb+Mh. Homer and Bart both have incomes of $100 and the price of both the private good and a firefighter is $1 per unit.
- How many firefighters are hired if the government does not intervene (private provision of the public good)? How many are paid for by Homer? By Bart?
- What is the socially optimal number of firefighters? If your answer differs from (a), why?
- How does the efficient provision level change if Homer’s income increases to $200 and Bart’s income decreases to $50? Show your work.
- Starting with the initial utility functions and income levels ($100 each) determine the efficient level of provision if the price of a firefighter is now $2 instead of $1.