6. In the central United States, farm ground is devoted to corn and beans as far as the eye can see. The supply of beans (in millions of bushels)

is given by Q b s

= 2P b – P c . The supply of corn is given by Q c s

= 2 P c – P b . Let the demand for beans be given by Q b d = 30 – P b , and the demand for corn be given by Q c d = 30 – P c .

a. Solve the general equilibrium price and quantity of both beans and corn. (Hint: If you have trouble with this step, follow the procedures outlined in Problem 3.)

b. Suppose there is a shock to bean demand, so that the quantity demanded at each price increases by 8 million bushels. The new demand for beans can be written as Q b d =

38 – P b . Solve for the new general equilibrium price and quantity of beans and corn.

c. What happens to the price of beans and the quantity sold as a result of the demand increase?

d. What happens to the price of corn and quantity sold as a result of the increase in the demand for beans? Explain.