Question

The market demand function for corn is Qd = 5 15 - 2P and the market supply function is Qs= 5P- 6, both quantities measured in billions of bushels per year. Suppose the government wants to raise the price to $4 per bushel. What are the aggregate surplus, consumer surplus, and producer surplus at the competitive equilibrium?

Answer 1

The Producer surplus = 19.6.

consumer surplus = 12.25.

Aggregate supply = 31.85.

Step-by-step explanation:

Normally, the demand equilibrium function equals to supply equilibrium function will get us the price which is $3 that is Qd = Qs. Hence, if we equate both function together like;

15 - 2P = 5P - 6.

15 +6 = 5P + 2P.

21 = 7P.

P = $3.

Thus, Qd = 15 - 2P= 15 - 2(3) = 15 - 6 = 9 units.

Qs = 5P - 6 = 5(3) - 6 = 15 - 6 = 9.

Therefore, if the price is going to be Increased by $4, we will have that;

Qd = 15 - 2P= 15 - 2(4) = 15 - 8 = 7 units.

=> The Producer surplus = 1/2 × 14 (4 - 1.2) = 19.6.

=> consumer surplus = 1/2 × 7 (7.5 - 4) = 12.25.

Aggregate supply = Producer surplus + consumer surplus = 19.6 + 12.25 = 31.85.