Reference no: EM131709810

Question - Consider an infinite-horizon groundwater management problem where x_t is the stock of groundwater at time t, y_t is the quantity of groundwater extracted at time t, g(y_t) gives the amount of total recharge to the aquifer, B(y_t) is the benefit of extracting yt, and C(x_t, y_t) is the cost of extracting y_t from a stock of size x_t. Suppose that there are property rights to groundwater, but a large number of users. Groundwater used in agriculture is unregulated. Suppose further that:

• g(y)= A + θy
• B(y) = α√y
• C(x, y) = (γ - δx)y

(a) Determine the steady-state levels of x and y under myopic behavior (x^c and y^c). (This is not the social plannerâs problem.) Hint: you don't have to set up a Lagrangian if you already know what the right equilibrium conditions are.

(b) Now suppose that the government subsidizes electricity for farmers, which is the primary cost component of pumping groundwater. Thus, instead of producers paying costs C(x, y) to pump groundwater, they only pay a fraction Ï of those costs where 0 < Φ < 1. Calculate the resulting steady-state levels of x and y under myopic behavior. What is the effect of the electricity subsidy on extractions y^c and stock levels x^c? How do your answers compare to your answers in part (a) above? Be sure to show your work and provide an intuitive explanation for any differences you find.