Problem 1: Public Goods Suppose that there are four households living on a lake near K'jipuktuk (Halifax) in Mi'kma'ki. The lake has been contaminated by a nasty pollutant which will make the water unsafe to drink or swim in, and kill all sh, insects, birds, beavers, muskrats, frogs, deer, wolves, bobcats, mink, and other wildlife which live in and around the lake. Suppose that a technology can be purchased to remove the pollutant with the following marginal cost function: MC(Q) = 5000 + 20Q Suppose that removing the pollutant will benet all households independent of the other household's benets such that the pollutant removal is non-rival. Also, suppose that it is legally impossible to exclude any household from use of the clean water, so the lake is non-excludable. The marginal willingness to pay (MWTP) functions to clean up the lake for each of the households are described as follows: MWTP1(Q)= 3000 6Q MWTPz (Q) = 4000 8Q MWTP3 (Q) = 5000 10Q MWTP4 (Q) = 9000 18Q Q is an , with Q = 0 indicating the unclean state and larger values indicating "cleaner" water. The units of MWTP and MC are "13/ pollutant per liter". a) Given the description, is the lake best categorized as a pure public good, impure public good, or private good? Briey explain in ONE sentence. b) With Q on the horizontal axis, on 4 separate graphs (one beneath the other such that Q-axis units are identical at a given horizontal position on the page), (see Fig. l), graph each respective household i's MWTPi curve for clean water. These MWTPs also correspond to the marginal private benet of each of the respective consumer (MBiC'ms').1 c) Find the aggregate MWTP equation (by adding up the individual MWTP equations (this graphically corresponds to vertical aggregation). This is also the marginal benet social.2 1 using the monetary non equity weighted measure. 2 again, using the monetary non-equity weighted measure. d) On each of the 4 graphs, plot the MC curve. This is both the social MC and private MC if a given household incurs the entire cleanup cost. e) On a 5th graph on Fig. 1, plot the social marginal benefit (MBExternal) and MCSocial curves and label the socially efficient (SE) level of ambient water quality and also the SE price. f) Calculate the SE level of water quality and the SE price. Calculate the total social surplus (TSSocial) at the SE allocation and label on your graph. Show your work. g) Suppose each household believes that the other households do not value clean water and are therefore not WTP for the cleanup. Find the privately efficient water quality level for each household and in aggregate. Find the total social surplus at this privately efficient output level and calculate the deadweight loss (loss of TSSocial at the privately efficient allocation compared to the socially efficient level). h) If the households instead believe that other households are WTP for the cleanup but don't know how much, how might this affect your answer? i) From household 5's perspective, what is its marginal external benefit (MBExternal) of providing water quality? On a 6th graph, plot household 5's MB Consumer, the MBExternal, the marginal social benefit (MBSocial), the MCPrivate. Label the socially and privately efficient quanties of water quality and its price. j) Discuss methods of collective action that could potentially be used to attain the SE level of water quality.Problem 2: CBA In the UK, for 2000 years, rivers have been straightened resulting in faster ow causing damages to the river ecosystems including more soil erosion and harm to sh eggs. Also, beavers were hunted to extinction to make hats. Over shing also occurred providing less food for beavers, otters and other animals. Pesticides killed insects reducing food for sh, frogs, and birds which affected animals that eat these other animals and also plants which are in symbiotic relationships with the animals in a manner. Also, fertilizers created algae blooms causing harm such as blocking light reducing by plants on the river bottom resulting in dead zones. Soil erosion also happened due to farming right up the edge of the river instead of maintaining the natural with to hold the soil in place and also to act as . slow the water ow and create habitat such as places for . Recently have been put into place under " " and this has included reintroducing beavers om Europe where they did not go extinct. Suppose that humans sh in the river but there are in that allow only with no sonar and only shing from canoes or row boats or from the shore (but not motor boats) is allowed and there are limits on when shing is allowed. For simplicity assume that the restoration project occurs in year 0 during which costs are incurred and all other benets and costs occur in year 1,2,3, and 4 and are identical in each year in "future value". Suppose the world then ends. help to Suppose that one of the benets of restoring the river is the . Suppose that the inverse demand (also the marginal willingness to pay, MWTP) for sh is: PD(Q)= 150 - Q and the initial marginal cost, also the inverse supply equation, was: MCOLD(Q) = PSOLD (Q) = l 10 + 2Q/3 Aer the , there are far more sh so it takes less time to catch them so the new marginal cost is: MCNEW(Q) = PSOLD (Q) = 10 + 2Q/3 Units of quantity are sh per year while units of price are $/sh. a) Find the competitive equilibrium market quantity and price of sh before and after the river rewilding project. b) Use the "letter" labels on the graph to identify the before and aer the river restoration project and the change. Repeat for the total producer surplus and total private surplus. Calculate the change in total private surplus (TSP'iV'm') (call this the future value and assume no ination). Suppose this change in total private surplus is experienced in years t = 1, 2, 3, and 4. Put this monetary future value on the appropriate spaces at the end of the questions. c) Assume that economists estimate that the rewilding project has other recreational value benets such as improving the quality of picnics, hikes, and canoeing and providing mental health benets due to . These occur in years t = 1,2,3 and 4 and are valued at $5000/year as shown on the timeline. Discuss one way you might attempt to monetize ONE of the above benets. d) Suppose that of the river species like the otters is estimated to be $6000/year. These are shown on the timeline. Discuss a way you might attempt to monetize this. e) Supposing (unrealistically) that the opportunity cost of the river rewilding project (like bringing the beavers from Europe and planting indigenous trees and other plants) all occur in year t = 0 and equal $30,000. Add this to the timeline. Sum down the columns in the chart to get the future values of the change in the total social surplus for each period. Then discount to convert these to present values and then use these to calculate the net present value mPV) of the total social surplus change due to the restoration project assuming that the social discount rate is 2% = 0.02 (a Stern type number). Fill in Figure 3 as you do this and be sure to show your work under this time line. f) Repeat e) but assume a social discount rate of 5.5% = 0.055 (a Nordhaus type number). Compare the results and discuss and the choice of social discount rate (SDR) affects the decision. g) Identify ONE net benet of the restoration project that has been ignored and suggest how you might attempt to monetize it. If there are ethical issues with this monetization and you would prefer not to count it in your cost benet analysis, please discuss