Question

Refer to Example 2.5 (page 59) on the market for wheat. In 1998, the total demand for U.S. wheat was Q = 3244 - 283P and the domestic supply was QS = 1944 + 207P. At the end of 1998, both Brazil and Indonesia opened their wheat markets to U.Sfarmers. Suppose that these new markets add 200 million bushels to U.S. wheat demand. What will be the free-market price of wheat and what quantity will be produced and sold by U.S. farmers?

Short answer

The free market price will be $3.06, and the output produced and sold will be 2,578.02 units.

Step-by-step solution

Explanation 

If Brazil and Indonesia open their market up and add 200 million bushels to the U.S wheat market, the demand would change. The new demand would be:

Q = (3244 - 283P) + 200

Q = 3444 - 283P

The supply is, QS = 1944 + 207P

The free-market prices and quantity of wheat would be where the new demand of wheat equals supply.

Q = QS

3444 - 283P = 1944 + 207P

490P = 1500

P = 3.06

Substituting the price in the demand or supply equation will give the quantity:

Q = 3444 - 283P

Q = 3444 - 283(3.06)

Q = 3444 - 865.98

Q = 2578.02

Therefore, the free-market price and quantity would be:
$3.06 per bushel and 2,578.02 million bushels, respectively.