（Due to Jan Brueckner）Consumer’s utility function is given by U(c, q, a)=c1/2q1/2a1/2
Where q is land, c is all non-land goods and a is amenity.
Consumer provides labor(L) and the wage rate is y per unit of L.
The production function of non-land goods is given by
F(q,L,a)=L的1/2次方 x q的1/2次方 x a的θ次方
Assume that both land and non-land good markets are competitive.
(1)Derive the equation that relates p and y that provide equal utility for consumers, given the amenity. Graph the relationship between p and y. Does it slope upward or downward? Explain.
(2)Derive the equation that relates p and y that provide equal profit for the producers of non-land good, given the amenity. Graph the relationship between p and y. Does it slope upward or downward? Explain.
(3)Suppose is θ positive. How does p change when a increases? How does y change as a increases?
(4)Suppose is θ negative. How does p change when a increases? How does y change as a increase?
(5)Summarize your conclusions about how amenities affect wage and land rent.