In: Economics
Suppose that the demand curve for wheat is
D
(
p
) = 120
−
10
p
, and the supply curve is
S
(
p
) = 10
p
. The government imposes a price floor of $8 per unit.
1. Draw a clearly marked graph to illustrate the demand, supply, competitive equilibrium
point (without government intervention), and the price floor.
2. Compute the equilibrium price and quantity after the price floor and interpret the results.
3. Explain who benefits and who loses from this measure and by how much. What can you
say about the welfare of the society as a whole?
1) Demand curve: Q = 120 - 10P
10P = 120 - Q
P = 12 - 0.1Q [This is inverse demand curve]
Supply curve: Q = 10P
At equilibrium,
Demand = Supply
120 - 10P = 10P
20P = 120
P = 120 / 20 = $6
Q = 120 - 10(6) = 60
2) When the government imposes a price floor of $8 per unit,
QD = 120 - 10P = 120 - 10(8) = 40
QS = 10P = 10(8) = 80
Since at the price floor of $8, quantity demanded is less than the quantity supplied, there is surplus of 40 units (i.e., 80 - 40). So, the quantity sold at the price of $8 would be 40 units.
3) Consumer surplus before imposition of price floor = 0.5[($12 - $6) * 60] = $180
Consumer surplus aftre imposition of price floor = 0.5[($12 - $8) * 40] = $80
So, consumers loses due to imposition of tariff.
Producer surplus before imposition of price floor = 0.5($6 * 60) = $180
Producer surplus aftre imposition of price floor = [($8 - $4) * 40] + 0.5($4 * 40) = $160 + $80 = $240
So, producers benefits due to imposition of tariff.
Welfare loss = 0.5[($8 - $4) * (60 - 40)] = $40