Consider the following two-period model of dynamically efficient extraction of a non-renewable natural resource. The constant social marginal cost of extraction is 40 in each period and the total stock of the resource is Q = 300 units. Moreover, the social marginal benefit is MB(Qt) = 200 Qt, where Qt is the quantity of resource extracted in period t, for t = 0; 1. The discount factor is 0:8. What is the marginal user cost (or scarcity rent) of the resource in each period?

Consider the allocation of a fixed, renewable supply of surface water in a given year between two competing users: municipal and industrial users (M) and agricultural users (A). The demand for water by M-users is MB­M = 250 – QM and the marginal extraction cost is MXCM = 50. The demand for water by A-users is MB­M = 170 – 0.5*QM and the marginal extraction cost is MXCM = 20. S is the annual supply of surface water is the basin. Assuming that there is no water scarcity in the basing (i.e., S > S’), what is the efficient level of water use for M- and A-users?

Consider the following two-period model of dynamically efficient extraction of a non-renewable natural resource. The constant social marginal cost of extraction is 40 in each period and the total stock of the resource is Q = 300 units. Moreover, the social marginal benefit is MB(Qt) = 200 - Qt, where Qt is the quantity of resource extracted in period t, for t = 0; 1. The discount factor is 0.8. What is the efficient quantity of resources extracted in each period? Provide a graphical representation of the solution.

Suppose there is a nonrenewable resource with inverse demand function p= 30-0.8q and with marginal extraction costs (MEC)= 8. The resource stock, S is finite and = 35 units. Suppose the time horizon is 2 periods and the discount rate is r= 8%. What quantity should be extracted in each period? What is the optimal price of the resource in the 2 periods?

HighFlyer Airlines wants to build new airplanes with greatly increased cabin space. This will allow HighFlyer Airlines to give passengers more comfort and sell more tickets at a higher price. However, redesigning the cabin means rethinking many other elements of the airplane as well, like engine and luggage placement, and the most efficient shape of the plane for moving through the air, which requires investment spending. The table below shows the level of R&D spending necessary to achieve different rates of return (due to higher ticket revenue).   Private Rate of Return Level of R&D Spending 12% $100 10% $200 8% $300 6% $400 4% $500   If the opportunity cost of financial capital for HighFlyer Airlines is 6%, how much should the firm invest in R&D? Assume that the social rate of return for R&D is an additional 2% on top of the private return; that is, an R&D investment that had a 7% private return to HighFlyer Airlines would…

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Consider a firm with marginal costs of MC=70+2Q. The firm is considering investing in research and development to find a production process that will allow it to make its output using less raw material inputs. The new production process is expected to lower the firm's marginal costs to MC=(70-10)+2Q. The firm is currently producing 60 units per year and plans to keep its output level the same after it innovates. Calculate the annual incentive for the firm to make the research and development investment.

Compare two versions of the two-period depletable resource model that differ only in the treatment of marginal extraction cost. Assume that in the second version the constant marginal extraction cost is lower in the second period than the first (perhaps due to the anticipated arrival of a new, superior extraction technology). The constant marginal extraction cost is the same in both periods in the first version and is equal to the marginal extraction cost in the first period of the second version. In a dynamic efficient allocation, how would the extraction profile in the second version differ from the first? Would relatively more or less be allocated to the second period in the second version than in the first version? Would the marginal user cost be higher or lower in the second version? Why?C  

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