Problem 2:

Consider a landowner that uses water as a primary input into the production of food. Similar to the problem

above, suppose the land has a general production function of f(w) =awb/2(w^2), where w is the amount of

water applied to the land. Suppose food output receives a price of pf

in a perfectly competitive market.

2.A.

Suppose that water is allocated in a competitive market. Denote the price of water pw. Derive the landowner's demand for water.

2.B.

Suppose now that there are two types of uses for water: cheese and potatoes. Using the

parameter values in the Table below, find the market equilibrium water allocation and price if the amount

of water supplied to the market is w= 9.

Cheese Potatoes

a= 3 9

b= 1 1

p= 10 2

2.C.

Now suppose that cheese producer is allocated all the available water supply as a water

right. Suppose that the cheese producer can trade any amount of her water rights with the potato farmer,

but every unit of water exchanged incurs a cost of d= 12. What is the equilibrium water allocation?

2.D.

Now suppose that the potato farmer is allocated all the available water supply as a water

right. As before, suppose that the potato farmer can trade any amount of her water rights with the cheese

producer, but every unit of water exchanged incurs a cost of

d= 12. What is the equilibrium water allocation?

2.E.

What do Parts C and D tell us about the allocation of water rights in the presence of trans-

action costs?