Question

The corn market is perfectly competitive, and the market supply and demand curves are given by the following equation: Qd =50,000,000 – 2,000,000 p Qs = 10,000,000 +5,500,000 p Where Qd and Qs are quantity demanded and quantity supplied measured in bushels, and P= price per bushel.

1) Determine consumer surplus at the equilibrium price and quantity.

Answer 1

ANSWER:

QD = 50,000,000 - 2,000,000 p

QS = 10,000,000 + 5,500,000 p

In order to find the equilibrium price and quantity we will equate QD = QS.

50,000,000 - 2,000,000 p = 10,000,000 + 5,500,000 p

50,000,000 - 10,000,000 = 5,500,000 p + 2,000,000 p

40,000,000 = 7,500,000 p

p = 40,000,000 / 7,500,000

p = 5.33

so the equilibrium price is $5.33

now to find the equilibrium quantity we will equate price of $5.33 in either of the equations.

qd = 50,000,000 - 2,000,000 * 5.33

qd = 50,000,000 - 10,666,666.67

qd = 39,333,333.33

so the equilibrium quantity is 39,333,333.33

To find the consumer surplus we will find the choke price (the price at which quantity demanded is zero).

Qd = 50,000,000 - 2,000,000 p

0 = 50,000,000 - 2,000,000 p

2,000,000 p = 50,000,000

p = 50,000,000 / 2,000,000

p = 25

so the choke price is $25

Consumer surplus = 1/2 * (choke price - equilibrium price) * equilibrium quantity

Cs = 1/2 * (25 - 5.33) * 39,333,333.33

Cs = 1/2 * 19.67 * 39,333,333.33

Cs = 1/2 * 773,686,666.601

Cs = 386,843,333.301

so the consumer surplus is 386,843,333.301