Question

The market demand function for corn is Qd = 15 − 2p and the market supply function is Qs = 5p − 6, both quantities are measured in billions of bushels per year. What are the aggregate surplus, consumer surplus, and producer surplus at the competitive equilibrium?

Answer 1

Answer

the equilibrium is at Qd=Qs

15-2P=5P-6

7P=21

P=$3

Q=15-2*3=9 billion

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converting the demand curve to inverse demand curve

Q=15-2P

2P=15-Q

P=7.5-0.5Q

Consumer reservation price is $7.5

converting the supply curve to inverse supply curve

Q=5P-6

5P=Q+6

P=0.2Q+1.2

producer reservation price is $1.2

the aggregate surplus is the area between demand and supply and left of the quantity

aggregate surplus or the total surplus =0.5*(consumer reservation price -producer reservation price)*Q

=0.5*(7.5-0.2)*9

=32.85 billion

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CS is the area above price and below the demand curve

CS=0.5*(consumer reservation price -P)*Q

=0.5*(7.5-3)*9

=20.25 billion

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PS is the area above the supply curve and below the price

PS=0.5*(P- producer reservation price)*Q

=0.5*(3-0.2)*9

=12.6 billion