Instructions: Please answer the following questions related to current (Period 1) and future (Period 2) demands for groundwater within the context of our two-period model.
Suppose that Period 1 demand for groundwater is given by the linear equation QUOTE PToday=$10-0.4*Q Today. Furthermore, suppose climate change causes Period 2: demand for groundwater to be different linear equations, QUOTE PFuture=$12-0.3*Q future. The current reserves of groundwater to be allocated across both periods is Q=Q1+Q2=16, and future demand is discounted at a rate of so that the present value of future demand is given by 11.08*P2 and the present value of future net benefits is 11.08*NB2. The marginal cost of extraction is constant and equal in both periods: MC1=MC2=$3.
a) Determine the optimal quantity of groundwater to extract in Periods 1 and 2 when users in both periods are considered in one problem. Is more extracted today or in the future, and why? What does the marginal user cost?
b) Determine the number of units extracted in Periods 1 and 2 if current Period 1 user lack secure property rights over the aquifer. That is, solve the problem as if Period 1 users considered only their consumption in their problem.
c) Explain in words/in graphs/in equations (as you prefer) why the quantities extracted in b) represent a loss of overall welfare/net benefits when compared to the extraction in a).
d) What would the discount rate need to be to optimally solve the two-period model with equal quantities extracted in both periods? That is, what r sets present value of demand or net benefits equal in both periods while maintaining equilibrium extraction quantities at Q1*=Q2*=8?
Instructions: Please answer the following questions related to current (Period 1) and future (Period 2) demands for groundwater within the context of our two-period model.
Suppose that Period 1 demand for groundwater is given by the linear equation QUOTE PToday=$10-0.4*Q Today. Furthermore, suppose climate change causes Period 2: demand for groundwater to be different linear equations, QUOTE PFuture=$12-0.3*Q future. The current reserves of groundwater to be allocated across both periods is Q=Q1+Q2=16, and future demand is discounted at a rate of so that the present value of future demand is given by 11.08*P2 and the present value of future net benefits is 11.08*NB2. The marginal cost of extraction is constant and equal in both periods: MC1=MC2=$3.
a) Determine the optimal quantity of groundwater to extract in Periods 1 and 2 when users in both periods are considered in one problem. Is more extracted today or in the future, and why? What does the marginal user cost?
b) Determine the number of units extracted in Periods 1 and 2 if current Period 1 user lack secure property rights over the aquifer. That is, solve the problem as if Period 1 users considered only their consumption in their problem.
c) Explain in words/in graphs/in equations (as you prefer) why the quantities extracted in b) represent a loss of overall welfare/net benefits when compared to the extraction in a).
d) What would the discount rate need to be to optimally solve the two-period model with equal quantities extracted in both periods? That is, what r sets present value of demand or net benefits equal in both periods while maintaining equilibrium extraction quantities at Q1*=Q2*=8?
