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 of the good, we need to find the quantity at which the quantity demanded (QD) equals the quantity supplied (QS).
Given the demand curve: QD = 50 - 2P and the long-run supply curve: QS = QD = 50 - 2P.
Setting QD equal to QS: 50 - 2P = 50 - 2P.
Simplifying: 0 = 0.
Since the equation simplifies to 0 = 0, this means that any quantity produced will result in equilibrium. Therefore, we cannot determine a specific equilibrium output from this information alone.
(b) The imposition of a $1 excise tax will affect the supply side of the market. In this case, the tax is imposed on the producers/suppliers of the good. When a tax is imposed on a good, the supply curve shifts upward by the amount of the tax.
Since the long-run supply curve is a horizontal line at a price of $3 per unit, the imposition of a $1 excise tax will shift the supply curve vertically upwards to a price of $4 per unit ($3 + $1).
As a result, the new equilibrium output will be where the new supply curve intersects with the demand curve. The equilibrium quantity will decrease, as the higher price of $4 per unit will result in a decreased quantity demanded.
(c) Shortly after the tax is imposed, if a unit of the good can be purchased for $3.60, this price is not the long-run equilibrium price.
In the long run, the price of the good will adjust to reflect the changes in supply and demand caused by the tax. Initially, the price might be higher than the long-run equilibrium price due to the tax burden being passed onto consumers. However, in the long run, the burden of the tax will be shared between producers and consumers, leading to adjustments in the price.
To determine the long-run equilibrium price, we would need more information about the market and the specific dynamics of supply and demand.