Government policies affect who gets the scarce water in the western United States and how that water is used. In 2004, farmers in California’s Central Valley paid as little as $10 per acre-foot, while in urban San Jose, California, a water agency shelled out $80 an acre-foot. Price differentials between agricultural and other uses can persist only if the groups cannot trade. Critics argue that eliminating the agricultural subsidy would encourage farmers to conserve water. The California Department of Water Resources estimates that doubling water prices would reduce agricultural water use by roughly 30% (Jim Carlton, “Is Water Too Cheap?” Wall Street Journal, March 17, 2004, B1). Further, farmers would use water more efficiently. (An alternative approach is to allow farmers to sell their cheap water in a competitive market—an approach some areas are using.)

a. Based on the data in the description of this problem, what is the price elasticity of demand for water?

b. What is the relationship between the price elasticity of demand for water and the effect of a price increase on water conservation?

The government wants to drive the price of soybeans above the equilibrium price p₁, to p_2. It offers growers a payment of x to reduce their output from Q₁ (the equilibrium level) to Q_2, which is the quantity demanded by consumers at p₂. Show in a figure how large x must be for growers to reduce output to this level. What are the effects of this program on consumers, farmers, and total welfare? Compare this approach to (a) offering a price support of p_{2 ,} (b) offering a price support and a quota set at Q₁, (c) offering a price support and a quota set at Q_2.