The long-run supply curve for a good is a horizontal line at a price $3 per unit of the good. The demand curve for the good is QD = 50-2P.
(a) What is the equilibrium output of the good?
(b) A $1 excise tax is imposed on the good. What will be the long-run effect on the equilibrium output of the good? Explain.
(c) Shortly after the tax is imposed, a unit of the good can be purchased for $3.60. Is this the long-run equilibrium price? Explain.
(a) To find the equilibrium output, we need to set the quantity demanded equal to the quantity supplied.
Quantity demanded (QD) = 50 - 2P
Quantity supplied (QS) = Equilibrium output
Setting QD = QS:
50 - 2P = QS
Since the long-run supply curve is a horizontal line at a price of $3 per unit, the quantity supplied will be constant at any price equal to or above $3. Therefore:
QS = Equilibrium output = 50 - 2P
(b) When a $1 excise tax is imposed on the good, the sellers are responsible for paying the tax to the government. This effectively increases the cost of production for the sellers, resulting in a leftward shift of the supply curve.
Since the long-run supply curve is a horizontal line at $3 per unit, the new supply curve will be a horizontal line at $3 + $1 = $4 per unit.
The new equilibrium output can be found by setting the quantity demanded equal to the new supply level:
50 - 2P = 4
Rearranging the equation:
2P = 50 - 4
2P = 46
P = 23
Substituting the value of P back into the demand equation to find the equilibrium output:
QD = 50 - 2P
QD = 50 - 2(23)
QD = 50 - 46
QD = 4
Therefore, the equilibrium output of the good after the tax is imposed is 4 units.
(c) Shortly after the tax is imposed, a unit of the good can be purchased for $3.60. This is not the long-run equilibrium price because the long-run equilibrium price is determined by the intersection of the new supply curve and the demand curve.
Since the new supply curve is a horizontal line at $4 per unit, the long-run equilibrium price will be determined by the point where the quantity demanded equals the quantity supplied:
50 - 2P = 4
Rearranging the equation:
2P = 50 - 4
2P = 46
P = 23
Therefore, the long-run equilibrium price is $23 per unit. Since $3.60 is lower than the equilibrium price, it is not the long-run equilibrium price.
(a) To find the equilibrium output, we need to find the point where the quantity demanded (QD) equals the quantity supplied (QS). By setting QD equal to QS, we can solve for the equilibrium price (P) and substitute it back into either QD or QS to find the equilibrium output.
Given:
QD = 50 - 2P
QS is a horizontal line at $3 per unit of the good
Setting QD equal to QS:
50 - 2P = QS = 3
Simplifying the equation:
-2P = -47
P = 23.5
Substituting P into the QS equation to find the equilibrium output:
QS = 3
QD = 50 - 2(23.5)
QD = 50 - 47
QD = 3
Therefore, the equilibrium output of the good is 3 units.
(b) When an excise tax of $1 is imposed on the good, it increases the cost of production. However, since the long-run supply curve is a horizontal line at $3 per unit, the tax will be entirely borne by the producers, meaning they will have to absorb the additional cost.
Since the supply curve remains unchanged, the equilibrium price will still be $23.5. However, now the producers will receive $22.5 per unit ($23.5 - $1 tax) instead of the full $23.5. As a result, the producer surplus will decrease, but the equilibrium output will remain the same because the supply curve is unaffected.
Therefore, the long-run effect on the equilibrium output of the good will be no change.
(c) If a unit of the good is being purchased for $3.60 shortly after the tax is imposed, it suggests that the price is higher than the long-run equilibrium price. In the long run, the equilibrium price will be determined by the intersection of the demand and supply curves.
However, in this scenario, the price of $3.60 is above the original equilibrium price of $23.5, indicating an excess supply in the market. This could occur immediately after the tax is imposed when sellers have not yet adjusted their prices fully.
Over time, sellers may adjust their prices downward to align with the equilibrium price, and buyers could negotiate or find different sellers to obtain the good at a lower price. This process will continue until the market reaches the long-run equilibrium price of $23.5, at which point there will be no excess supply or demand.
In conclusion, a price of $3.60 shortly after the tax is imposed is not the long-run equilibrium price, but rather a temporary adjustment phase as the market reaches the new equilibrium.