Suppose the demand function for corn is Qd 15 2 Pcorn and th

Suppose the demand function for corn is Qd= 15 –2 Pcorn and the supply function is Qs = 5 Pcorn–6. Suppose the government needs to buy 3.5 billion bushels of corn for a third-world famine relief program. What effect will the purchase have on the equilibrium price of corn? How will it change the amount of corn that consumers buy? (Hint: The Government’s action will shift the demand curve to the right by 3.5. That is, at every price point the new demand is QdNEW= Qd+ 3.5. The first step is to find out the formula for the shifted demand curve.)

Solution

With the current demand and supply curve, equilibrium price is attained when Quantity demanded = Quantity supplied

15- 2Pcorn= 5Pcorn- 6

P corn= 21/7 = 3 and Q corn = 5*3 - 6 = 9

Now with the given demand by Government, the demand curve shifts by 3.5

Qd new= 15 - 2 P corn+3.5 = 18.5 - 2 P corn

Equating the demand and supply to arrive at equilibrium price,

18.5 - 2 P corn = 5Pcorn- 6

P corn = 24.5/7 = 3.5 and Qcorn = 5*3.5 - 6 = 11.5

The equilibrium price increases and is now 3.5, and equilibrium quantity increases to 11.5